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Modeling financial time-series with generative adversarial networks
Abstract
Financial time-series modeling is a challenging problem as it retains various complex statistical properties and the mechanism behind the process is unrevealed to a large extent. In this paper, a deep neural networks based approach, generative adversarial networks (GANs) for financial time-series modeling is presented. GANs learn the properties of data and generate realistic data in a data-driven manner. The GAN model produces a time-series that recovers the statistical properties of financial time-series such as the linear unpredictability, the heavy-tailed price return distribution, volatility clustering, leverage effects, the coarse-fine volatility correlation, and the gain/loss asymmetry.
... Traditionally, statistical models like the autoregressive (AR) or the generalized autoregressive conditional heteroscedasticity (GARCH) and their variants [29] have been developed and used for simulation of time-series data. Specifically, the simulation of asset price data is an exceptionally difficult endeavor due to the complexity of financial markets [3,30], which not only requires accurate, precise and timely modelling, but one that is also heavily dependent on the assumption of the underlying data distribution. With the advent of deep learning, generative methods offer to address such challenges via data-driven, i.e. model-free methods. ...
... where the value of the fitted is typically between 3 to 5 [30]. We found this value to be 4.69 for simulated data, and 3.79 for realized data. ...
... We used = 1 as the correlation was found to be highest for this value [10], given any time-lag . For time-lags ≤ 100 days, this autocorrelation for both the realized and simulated portfolio returns exhibits a power-law decay [30] which implies a long-range temporal dependence in the portfolio returns, as shown in Figure 8. Figure 7: Out-of-sample log-log plots of the density of positive normalized returns. The left (resp. ...
... Instead, asymmetric distributions and fat-tailed behavior are often observed in financial time series, e.g., stock returns. It is empirically established that the probability distribution of price returns has a power-law decay in the tails [15,16]. This means that extreme occurrences, such as market collapses or spikes, happen more frequently than a normal distribution would suggest. ...
... Another phenomenon that has been observed is called volatility clustering, which occurs when periods of high volatility are followed by others with similarly high volatility, and vice versa [17]. Volatility clustering can be quantitatively defined as the powerlaw decay of the auto-correlation function of absolute price returns [16]. 5. Autocorrelation and cross-correlation: Autocorrelation in financial time series may occur, referring to the correlation of a time series' current values with its historical values [18]. ...
... 6. Leverage effects: Leverage effects describe the negative relationship between asset value and volatility. It is observed that negative shocks tend to have a larger impact on volatility than positive shocks of the same magnitude [16]. In financial time series, the relationship between returns and volatility can be asymmetric, with downward movements leading to increased volatility. ...
Financial time series prediction, whether for classification or regression, has been a heated research topic over the last decade. While traditional machine learning algorithms have experienced mediocre results, deep learning has largely contributed to the elevation of the prediction performance. Currently, the most up-to-date review of advanced machine learning techniques for financial time series prediction is still lacking, making it challenging for finance domain experts and relevant practitioners to determine which model potentially performs better, what techniques and components are involved, and how the model can be designed and implemented. This review article provides an overview of techniques, components and frameworks for financial time series prediction, with an emphasis on state-of-the-art deep learning models in the literature from 2015 to 2023, including standalone models like convolutional neural networks (CNN) that are capable of extracting spatial dependencies within data, and long short-term memory (LSTM) that is designed for handling temporal dependencies; and hybrid models integrating CNN, LSTM, attention mechanism (AM) and other techniques. For illustration and comparison purposes, models proposed in recent studies are mapped to relevant elements of a generalized framework comprised of input, output, feature extraction, prediction, and related processes. Among the state-of-the-art models, hybrid models like CNN-LSTM and CNN-LSTM-AM in general have been reported superior in performance to stand-alone models like the CNN-only model. Some remaining challenges have been discussed, including non-friendliness for finance domain experts, delayed prediction, domain knowledge negligence, lack of standards, and inability of real-time and high-frequency predictions. The principal contributions of this paper are to provide a one-stop guide for both academia and industry to review, compare and summarize technologies and recent advances in this area, to facilitate smooth and informed implementation, and to highlight future research directions.
... SigCWGAN (Ni et al. 2020) combines continuous-time stochastic models with its signature metric. Stock-GAN (Takahashi, Chen, and Tanaka-Ishii 2019) is a generative model that generates the order stream instead of the market features. While FIN-GAN (Takahashi, Chen, and Tanaka-Ishii 2019) introduces GAN to generate price features, the use of vanilla GAN is rudimentary compared to the benchmark methods of time-series generative models. ...
... Stock-GAN (Takahashi, Chen, and Tanaka-Ishii 2019) is a generative model that generates the order stream instead of the market features. While FIN-GAN (Takahashi, Chen, and Tanaka-Ishii 2019) introduces GAN to generate price features, the use of vanilla GAN is rudimentary compared to the benchmark methods of time-series generative models. Contextual Generation. ...
Financial simulators play an important role in enhancing forecasting accuracy, managing risks, and fostering strategic financial decision-making. Despite the development of financial market simulation methodologies, existing frameworks often struggle with adapting to specialized simulation context. We pinpoint the challenges as i) current financial datasets do not contain context labels; ii) current techniques are not designed to generate financial data with context as control, which demands greater precision compared to other modalities; iii) the inherent difficulties in generating context-aligned, high-fidelity data given the non-stationary, noisy nature of financial data. To address these challenges, our contributions are: i) we proposed the Contextual Market Dataset with market dynamics, stock ticker, and history state as context, leveraging a market dynamics modeling method that combines linear regression and clustering to extract market dynamics; ii) we present Market-GAN, a novel architecture incorporating a Generative Adversarial Networks (GAN) for the controllable generation with context, an autoencoder for learning low-dimension features, and supervisors for knowledge transfer; iii) we introduce a two-stage training scheme to ensure that Market-GAN captures the intrinsic market distribution with multiple objectives. In the pertaining stage, with the use of the autoencoder and supervisors, we prepare the generator with a better initialization for the adversarial training stage. We propose a set of holistic evaluation metrics that consider alignment, fidelity, data usability on downstream tasks, and market facts. We evaluate Market-GAN with the Dow Jones Industrial Average data from 2000 to 2023 and showcase superior performance in comparison to 4 state-of-the-art time-series generative models.
... Generative Adversarial Neural Networks (GANs) (Goodfellow et al., 2014) have attracted a great deal of attention from the research community since their introduction in 2014 and much of their activities are focused on image generation (Reed et al., 2016). They are classes of unsupervised deep learning frameworks with the ability to learn an unknown probability distribution of a given data set and can map the learnt distribution to generate synthetic data sets that follow the same distribution (Takahashi et al., 2019). GANs involve the pitching of two deep neural networks against each other. ...
... This adversarial training continues until Nash equilibrium is achieved; where the discriminator cannot distinguish the generated samples from the true samples. At this point, the Generator is able to capture the data distributions (Takahashi et al., 2019). Denote the training dataset D = (x n ) N n=1 , the generative adversarial nets (GAN) aim to learn the Generator's distribution over the data x. ...
In this thesis, three novel machine learning techniques are introduced to address distinct
yet interrelated challenges involved in financial risk management tasks. These approaches
collectively offer a comprehensive strategy, beginning with the precise classification of credit
risks, advancing through the nuanced forecasting of financial asset volatility, and ending
with the strategic optimisation of financial asset portfolios.
Firstly, a Hybrid Dual-Resampling and Cost-Sensitive technique has been proposed to combat the prevalent issue of class imbalance in financial datasets, particularly in credit risk
assessment. The key process involves the creation of heuristically balanced datasets to effectively address the problem. It uses a resampling technique based on Gaussian mixture
modelling to generate a synthetic minority class from the minority class data and concurrently uses k-means clustering on the majority class. Feature selection is then performed
using the Extra Tree Ensemble technique. Subsequently, a cost-sensitive logistic regression
model is then applied to predict the probability of default using the heuristically balanced
datasets. The results underscore the effectiveness of our proposed technique, with superior
performance observed in comparison to other imbalanced preprocessing approaches. This
advancement in credit risk classification lays a solid foundation for understanding individual
financial behaviours, a crucial first step in the broader context of financial risk management.
Building on this foundation, the thesis then explores the forecasting of financial asset volatility, a critical aspect of understanding market dynamics. A novel model that combines a
Triple Discriminator Generative Adversarial Network with a continuous wavelet transform
is proposed. The proposed model has the ability to decompose volatility time series into
signal-like and noise-like frequency components, to allow the separate detection and monitoring of non-stationary volatility data. The network comprises of a wavelet transform
component consisting of continuous wavelet transforms and inverse wavelet transform components, an auto-encoder component made up of encoder and decoder networks, and a
Generative Adversarial Network consisting of triple Discriminator and Generator networks.
The proposed Generative Adversarial Network employs an ensemble of unsupervised loss derived from the Generative Adversarial Network component during training, supervised
loss and reconstruction loss as part of its framework. Data from nine financial assets are
employed to demonstrate the effectiveness of the proposed model. This approach not only
enhances our understanding of market fluctuations but also bridges the gap between individual credit risk assessment and macro-level market analysis.
Finally the thesis ends with a novel proposal of a novel technique or Portfolio optimisation. This involves the use of a model-free reinforcement learning strategy for portfolio
optimisation using historical Low, High, and Close prices of assets as input with weights of
assets as output. A deep Capsules Network is employed to simulate the investment strategy, which involves the reallocation of the different assets to maximise the expected return
on investment based on deep reinforcement learning. To provide more learning stability in
an online training process, a Markov Differential Sharpe Ratio reward function has been
proposed as the reinforcement learning objective function. Additionally, a Multi-Memory
Weight Reservoir has also been introduced to facilitate the learning process and optimisation of computed asset weights, helping to sequentially re-balance the portfolio throughout
a specified trading period. The use of the insights gained from volatility forecasting into
this strategy shows the interconnected nature of the financial markets. Comparative experiments with other models demonstrated that our proposed technique is capable of achieving
superior results based on risk-adjusted reward performance measures.
In a nut-shell, this thesis not only addresses individual challenges in financial risk management but it also incorporates them into a comprehensive framework; from enhancing the
accuracy of credit risk classification, through the improvement and understanding of market
volatility, to optimisation of investment strategies. These methodologies collectively show
the potential of the use of machine learning to improve financial risk management.
... Additionally, the research in [18] offers a deep neural network-based method for financial time-series modeling that makes use of GANs. After learning the characteristics of financial data, the GAN model produces realistic timeseries data that restores the statistical features of financial time-series, including gain/loss asymmetry, leverage effects, heavy-tailed price return distribution, volatility clustering, and linear unpredictability. ...
The financial industry is increasingly interested in predictive analysis and forecasting using time series data. Understanding the relationship between recessions and oil markets is crucial for developing financial forecasts and strategic decisions. This study uses advanced deep learning models to examine the interaction between recession signals and crude oil prices. Data covering recession periods include key economic indicators such as Gross Domestic Product (GDP) fluctuations, unemployment rates, consumer spending trends, business investments, and housing market dynamics. Additionally, Federal Open Market Committee (FOMC) minutes are used to capture economic assessments and monetary policy decisions by the Federal Reserve during recessions, providing insights into policymakers’ expectations and responses. Data is augmented using Time-series Generative Adversarial Networks (TimeGAN) to capture intricate patterns in oil prices. By focusing on feature selection, this study aims to identify patterns from historical data and relationships between recession signals and oil price movements. Long Short-Term Memory networks (LSTMs), Gated Recurrent Units (GRUs), Transformer, and ensemble learning techniques are used to predict crude oil prices during recessions. This research provides insights into how recession signals and Federal Reserve policy decisions influence crude oil prices, offering a comprehensive view of the dynamics between economic downturns and the energy market.
... Moreover, GANs have been employed for domain adaptation tasks, effectively bridging the domain gap between different data distributions [29]. GANs have also been successfully employed in various medical [30] and financial applications [31,32]-extending beyond their traditional visual data domain. ...
In the rapidly evolving domain of large-scale retail data systems, envisioning and simulating future consumer transactions has become a crucial area of interest. It offers significant potential to fortify demand forecasting and fine-tune inventory management. This paper presents an innovative application of Generative Adversarial Networks (GANs) to generate synthetic retail transaction data, specifically focusing on a novel system architecture that combines consumer behavior modeling with stock-keeping unit (SKU) availability constraints to address real-world assortment optimization challenges. We diverge from conventional methodologies by integrating SKU data into our GAN architecture and using more sophisticated embedding methods (e.g., hyper-graphs). This design choice enables our system to generate not only simulated consumer purchase behaviors but also reflects the dynamic interplay between consumer behavior and SKU availability—an aspect often overlooked, among others, because of data scarcity in legacy retail simulation models. Our GAN model generates transactions under stock constraints, pioneering a resourceful experimental system with practical implications for real-world retail operation and strategy. Preliminary results demonstrate enhanced realism in simulated transactions measured by comparing generated items with real ones using methods employed earlier in related studies. This underscores the potential for more accurate predictive modeling.
... These frameworks aim to create datasets that are statistically similar to real data but without revealing any entity information, thus supporting financial analysis and research while maintaining privacy constraints [9]. Academic research has also explored different variations of GANs to improve performance in financial data synthesis, including architectural variants and loss function variants [11,12,13]. ...
The financial industry is increasingly seeking robust methods to address the challenges posed by data scarcity and low signal-to-noise ratios, which limit the application of deep learning techniques in stock market analysis. This paper presents two innovative generative model-based approaches to synthesize stock data, specifically tailored for different scenarios within the A-share market in China. The first method, a sector-based synthesis approach, enhances the signal-to-noise ratio of stock data by classifying the characteristics of stocks from various sectors in China's A-share market. This method employs an Approximate Non-Local Total Variation algorithm to smooth the generated data, a bandpass filtering method based on Fourier Transform to eliminate noise, and Denoising Diffusion Implicit Models to accelerate sampling speed. The second method, a recursive stock data synthesis approach based on pattern recognition, is designed to synthesize data for stocks with short listing periods and limited comparable companies. It leverages pattern recognition techniques and Markov models to learn and generate variable-length stock sequences, while introducing a sub-time-level data augmentation method to alleviate data scarcity issues.We validate the effectiveness of these methods through extensive experiments on various datasets, including those from the main board, STAR Market, Growth Enterprise Market Board, Beijing Stock Exchange, NASDAQ, NYSE, and AMEX. The results demonstrate that our synthesized data not only improve the performance of predictive models but also enhance the signal-to-noise ratio of individual stock signals in price trading strategies. Furthermore, the introduction of sub-time-level data significantly improves the quality of synthesized data.
... Notably, RNN variants such as long short-term memory (LSTM) networks and gated recurrent units (GRUs) have been specifically employed to forecast U.S. stock market volatility [61], while CNNs have been used to predict future prices in the Chinese and Indian stock markets [15,50]. GANs have been proposed for price prediction in indices like the FTSE MIB, CSI 300, and S&P 500 [72,73,86]. Hybrid models that combine neural networks with traditional machine learning techniques have also shown promise in enhancing prediction accuracy [45,56,83]. ...
In the era where social media significantly influences public sentiment, platforms such as Twitter have become vital in predicting stock market trends. This paper presents a cutting-edge predictive model that integrates historical stock market data, Twitter sentiment analysis, and an extensive array of tweet-related features. Utilizing advanced regression techniques and deep neural networks, our model forecasts the daily closing prices of the U.S. stock market indices with notable accuracy and demonstrates a strong link between market values, sentiment scores, and social media activities. Our analysis particularly emphasizes the importance of tweet diffusion and the influence of prominent Twitter users in refining prediction accuracy. Contrary to conventional wisdom, we discovered that incorporating a wide range of tweet-derived features significantly improves the model’s performance without leading to sparsity challenges. This study not only questions established paradigms but also underscores the potential of social media analytics in financial market forecasting, with substantial implications for investors, market analysts, and policy makers.
... Early work on FTS using DGMs include FIN-GAN ( [44]) and Quant GAN ( [51]). FIN-GAN examined if GANs using multi-layer and convolution architectures could satisfy stylized facts of FTS ( [11]) such as volatility clustering. ...
Financial time series (FTS) generation models are a core pillar to applications in finance. Risk management and portfolio optimization rely on realistic multivariate price generation models. Accordingly, there is a strong modelling literature dating back to Bachelier's Theory of Speculation in 1901. Generating FTS using deep generative models (DGMs) is still in its infancy. In this work, we systematically compare DGMs against state-of-the-art parametric alternatives for multivariate FTS generation. We initially compare both DGMs and parametric models over increasingly complex synthetic datasets. The models are evaluated through distance measures for varying distribution moments of both the full and rolling FTS. We then apply the best performing DGM models to empirical data, demonstrating the benefit of DGMs through a implied volatility trading task.
... f e-mail: anton.albino@fieb.org.br of domains [11][12][13]. In the finance domain, applications of GANs include financial data generation [12,14,15], stock market prediction [16,17], credit scoring [18] and fraud detection [19,20]. In the image processing domain, GANs are used notably for image superresolution (ISR) [21,22] that can also improve early medical diagnosis in clinical pathology [23] to name a few. ...
Data integrity and privacy are critical concerns in the financial sector. Traditional methods of data collection face challenges due to privacy regulations and time-consuming anonymization processes. In collaboration with Banco BV, we trained a hybrid quantum-classical generative adversarial network (HQGAN), where a quantum circuit serves as the generator and a classical neural network acts as the discriminator, to generate synthetic financial data efficiently and securely. We compared our proposed HQGAN model with a fully classical GAN by evaluating loss convergence and the MSE distance between the synthetic and real data. Although initially promising, our evaluation revealed that HQGAN failed to achieve the necessary accuracy to understand the intricate patterns in financial data. This outcome underscores the current limitations of quantum-inspired methods in handling the complexities of financial datasets.
Graphical abstract
... For instance, [3] in RGAN and [17] in QuantGAN, employed recurrent neural networks (RNN) and temporal convolutional networks (TCN) respectively, to encapsulate the temporal structure of time series data. Conversely, [15] experimented with multiple architectures, including multi-layer perceptrons (MLP), convolutional neural networks (CNN), and a hybrid of the two, MLP-CNN. ...
... Other research mostly follows the GAN approach. This approach is first adapted to financial data generation in [TCT19], and later its variants are explored in [Efi+20;Mee19] For an extensive overview on synthetic data generation, we refer the reader to [Lu+23] (for general data), [Igl+23] (for time series), [EO21] (GANs for financial time series), and [Ass+20b] (for general data in finance). ...
We build a time-causal variational autoencoder (TC-VAE) for robust generation of financial time series data. Our approach imposes a causality constraint on the encoder and decoder networks, ensuring a causal transport from the real market time series to the fake generated time series. Specifically, we prove that the TC-VAE loss provides an upper bound on the causal Wasserstein distance between market distributions and generated distributions. Consequently, the TC-VAE loss controls the discrepancy between optimal values of various dynamic stochastic optimization problems under real and generated distributions. To further enhance the model's ability to approximate the latent representation of the real market distribution, we integrate a RealNVP prior into the TC-VAE framework. Finally, extensive numerical experiments show that TC-VAE achieves promising results on both synthetic and real market data. This is done by comparing real and generated distributions according to various statistical distances, demonstrating the effectiveness of the generated data for downstream financial optimization tasks, as well as showcasing that the generated data reproduces stylized facts of real financial market data.
... For instance, [Esteban et al. 2017] in RGAN and [Wiese et al. 2020] in QuantGAN, employed recurrent neural networks (RNN) and temporal convolutional networks (TCN) respectively, to encapsulate the temporal structure of time series data. Conversely, [Takahashi et al. 2019] experimented with multiple architectures, including multi-layer perceptrons (MLP), convolutional neural networks (CNN), and a hybrid of the two, MLP-CNN. ...
In the financial sector, a sophisticated financial time series simulator is essential for evaluating financial products and investment strategies. Traditional back-testing methods have mainly relied on historical data-driven approaches or mathematical model-driven approaches, such as various stochastic processes. However, in the current era of AI, data-driven approaches, where models learn the intrinsic characteristics of data directly, have emerged as promising techniques. Generative Adversarial Networks (GANs) have surfaced as promising generative models, capturing data distributions through adversarial learning. Financial time series, characterized 'stylized facts' such as random walks, mean-reverting patterns, unexpected jumps, and time-varying volatility, present significant challenges for deep neural networks to learn their intrinsic characteristics. This study examines the ability of GANs to learn diverse and complex temporal patterns (i.e., stylized facts) of both univariate and multivariate financial time series. Our extensive experiments revealed that GANs can capture various stylized facts of financial time series, but their performance varies significantly depending on the choice of generator architecture. This suggests that naively applying GANs might not effectively capture the intricate characteristics inherent in financial time series, highlighting the importance of carefully considering and validating the modeling choices.
... The tangent and length of the multi-line segment regression were specified as the output of the NN. Finally, the results showed that this method has excellent effects on stock price prediction [7]. Kim and Chun used an array probabilistic network with a multi-valued output model, which outperformed case-based reasoning models, recurrent NN methods, and traditional backpropagation NNs in terms of prediction results [8]. ...
With the development of finance, more and more people are paying attention to stock price prediction, hoping to gain economic benefits from it. From the literature review, due to the complexity of stock trends, it is necessary to study the analysis of industry stocks. This paper studies the effectiveness of the autoregressive moving average model (ARIMA) for 5 stocks in the technology industry. Then, we will compare and parameterize the ARIMA model by using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). After the data processing, we find that the development prospects of four head technology companies have steadily increased due to years of economic accumulation and stable operation. However, as a technology company that has emerged in recent years, OpenAI is extremely susceptible to external factors such as academic fraud and AI replacing manual labor. Its stock trend has fluctuated greatly and its prospects are sluggish.
... With successful applications of generative artificial intelligence (genAI) models on time series data in finance [8], [9] and climate science [10], [11], researchers have turned to AIbased tools to predict trajectories over time in healthcare [12], [13]. Compared to traditional autoregressive methods such as the ARIMA model [14], AI-based models have the potential to better capture complex relationships between variables. ...
Trajectory forecasting in healthcare data has been an important area of research in precision care and clinical integration for computational methods. In recent years, generative AI models have demonstrated promising results in capturing short and long range dependencies in time series data. While these models have also been applied in healthcare, most of them only predict one value at a time, which is unrealistic in a clinical setting where multiple measures are taken at once. In this work, we extend the framework temporal fusion transformer (TFT), a multi-horizon time series prediction tool, and propose TFT-multi, an end-to-end framework that can predict multiple vital trajectories simultaneously. We apply TFT-multi to forecast 5 vital signs recorded in the intensive care unit: blood pressure, pulse, SpO2, temperature and respiratory rate. We hypothesize that by jointly predicting these measures, which are often correlated with one another, we can make more accurate predictions, especially in variables with large missingness. We validate our model on the public MIMIC dataset and an independent institutional dataset, and demonstrate that this approach outperforms state-of-the-art univariate prediction tools including the original TFT and Prophet, as well as vector regression modeling for multivariate prediction. Furthermore, we perform a study case analysis by applying our pipeline to forecast blood pressure changes in response to actual and hypothetical pressor administration.
... The LSTM generator captures the data distributions of stocks from the given market data, generating data with similar distributions. Takahashi et al. [89] developed the FIN-GAN model for financial time-series modeling, which learns the properties of data and generates realistic time-series data. ...
The integration of generative AI (GAI) into the financial sector has brought about significant advancements, offering new solutions for various financial tasks. This review paper provides a comprehensive examination of recent trends and developments at the intersection of GAI and finance. By utilizing an advanced topic modeling method, BERTopic, we systematically categorize and analyze existing research to uncover predominant themes and emerging areas of interest. Our findings reveal the transformative impact of finance-specific large language models (LLMs), the innovative use of generative adversarial networks (GANs) in synthetic financial data generation, and the pressing necessity of a new regulatory framework to govern the use of GAI in the finance sector. This paper aims to provide researchers and practitioners with a structured overview of the current landscape of GAI in finance, offering insights into both the opportunities and challenges presented by these advanced technologies.
... Agent-based Modelling, particularly multi-agent systems, was initially employed to simulate orderdriven markets (Chiarella et al., 2009;Amrouni et al., 2021). With the advancement of deep learning technologies, several works have emerged that adopt the world model paradigm to simulate Limit Order Book (LOB) markets (Takahashi et al., 2019;Li et al., 2020;Coletta et al., 2021;. They mostly leveraged GANs (Goodfellow et al., 2020) to model the distribution of the LOB time series. ...
Generative models aim to simulate realistic effects of various actions across different contexts, from text generation to visual effects. Despite efforts to build real-world simulators, leveraging generative models for virtual worlds, like financial markets, remains underexplored. In financial markets, generative models can simulate market effects of various behaviors, enabling interaction with market scenes and players, and training strategies without financial risk. This simulation relies on the finest structured data in financial market like orders thus building the finest realistic simulation. We propose Large Market Model (LMM), an order-level generative foundation model, for financial market simulation, akin to language modeling in the digital world. Our financial Market Simulation engine (MarS), powered by LMM, addresses the need for realistic, interactive and controllable order generation. Key objectives of this paper include evaluating LMM's scaling law in financial markets, assessing MarS's realism, balancing controlled generation with market impact, and demonstrating MarS's potential applications. We showcase MarS as a forecast tool, detection system, analysis platform, and agent training environment. Our contributions include pioneering a generative model for financial markets, designing MarS to meet domain-specific needs, and demonstrating MarS-based applications' industry potential.
... This paper delved into the significance of residual analysis in assessing model adequacy for volatility forecasting. An ideal model for volatility forecasting should yield residuals that behave similarly to a series generated from white noise [25]. White noise is characterized by random and uncorrelated data points with a constant mean and variance. ...
This paper conducted a comprehensive comparative analysis of various GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models to forecast financial market volatility, with a specific focus on the Nairobi Stock Exchange Market. The examined models include symmetric and asymmetric GARCH types, such as sGARCH, GJR-GARCH, AR (1) GJG-GARCH, among others. The primary objective is to identify the most suitable model for capturing the complex dynamics of financial market volatility. The study employs rigorous evaluation criteria, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Mean Error (ME), and Root Mean Absolute Error (RMAE), to assess the performance of each model. These criteria facilitate the selection of the optimal model for volatility forecasting. The analysis reveals that the GJR-GARCH (1,1) model emerges as the best-fit model, with AIC and BIC values of −5.5008 and −5.4902, respectively. This selection aligns with the consensus in the literature, highlighting the superiority of asymmetric GARCH models in capturing volatility dynamics. The comparison also involves symmetric GARCH models, such as sGARCH (1,1), and other asymmetric models like AR (1) GJG-GARCH. While these models were considered, the GJR-GARCH (1,1) model demonstrated superior forecasting capabilities. The study emphasizes the importance of accurate model selection and the incorporation of asymmetry in volatility modeling. The research provides essential insights into financial market volatility modeling and forecasting using both asymmetric and symmetric GARCH models. These findings have significant implications for government policymakers, financial institutions, and investors, offering improved tools for risk assessment and decision-making during periods of market turbulence.
... [2020], Takahashi et al. [2019] applications -extending beyond their traditional visual data domain. ...
In the rapidly evolving domain of large-scale retail data systems, envisioning and simulating future consumer transactions has become a crucial area of interest. It offers significant potential to fortify demand forecasting and fine-tune inventory management. This paper presents an innovative application of Generative Adversarial Networks (GANs) to generate synthetic retail transaction data, specifically focusing on a novel system architecture that combines consumer behavior modeling with stock-keeping unit (SKU) availability constraints to address real-world assortment optimization challenges. We diverge from conventional methodologies by integrating SKU data into our GAN architecture and using more sophisticated embedding methods (e.g., hyper-graphs). This design choice enables our system to generate not only simulated consumer purchase behaviors but also reflects the dynamic interplay between consumer behavior and SKU availability -- an aspect often overlooked, among others, because of data scarcity in legacy retail simulation models. Our GAN model generates transactions under stock constraints, pioneering a resourceful experimental system with practical implications for real-world retail operation and strategy. Preliminary results demonstrate enhanced realism in simulated transactions measured by comparing generated items with real ones using methods employed earlier in related studies. This underscores the potential for more accurate predictive modeling.
... The LSTM generator captures the data distributions of stocks from the given market data, generating data with similar distributions. Takahashi et al. [86] developed the FIN-GAN model for financial time-series modeling, which learns the properties of data and generates realistic time-series data. ...
The integration of generative AI (GAI) into the financial sector has brought about significant advancements, offering new solutions for various financial tasks. This review paper provides a comprehensive examination of recent trends and developments at the intersection of GAI and finance. By utilizing an advanced topic modeling method, BERTopic, we systematically categorize and analyze existing research to uncover predominant themes and emerging areas of interest. Our findings reveal the transformative impact of finance-specific large language models (LLMs), the innovative use of generative adversarial networks (GANs) in synthetic financial data generation, and the pressing necessity of a new regulatory framework to govern the use of GAI in the finance sector. This paper aims to provide researchers and practitioners with a structured overview of the current landscape of GAI in finance, offering insights into both the opportunities and challenges presented by these advanced technologies.
... In [25], they aim to generate time series focusing on reproducing the statistical properties of financial time series. It takes 6 statistical properties of this type of series: 1) linear unpredictability, 2) thick-tailed distribution, 3) volatility clustering, 4) leverage effect, 5) coarse-fine volatility correlation, and 6) profit/loss asymmetry. ...
The need for more and better information for decision making is fundamental in modern organizations, especially in the financial industry. One type of this information is time series, which allow prediction and estimation of different scenarios, but are difficult to obtain for small and medium sized enterprises (SMEs). This research presents the design and validation of a generative adversarial network (GAN) capable of generating synthetic data for daily sales of Chilean SME. The problem that needs to be resolved is the lack of this kind of data within a Chilean fintech company called Dank. This data can be useful in developing an automatic risk evaluation model and, therefore, in reducing business process time, since risk evaluation is currently being carried out by people. The solution allows maintaining the anonymity of the data and using GAN to obtain different synthetic time series, increasing the data by 10%. It uses images from a vector of random numbers that are in temporal coherence and equal distribution. This research allows SMEs to obtain a greater amount of data, with a simple solution, to make better decisions.
... Financial applications of generative adversarial networks (GANS) include the group of synthetic financial data, the identification of abnormalities, and the simulation of market scenarios. Financial models can be tested and trained with GAN-generated data that is realistic in all material respects (Takahashi et al. 2019;Wei et al. 2020). Especially in high-stakes financial decisionmaking, explainable AI attempts to develop interpretable and transparent models. ...
The integration of artificial intelligence (AI) solutions in financial institutions has yielded substantial improvements in diverse domains, including decision-making, risk assessment, fraud detection, and customer service, among others. The implementation of AI has the capacity to considerably augment financial analysis, prognostication, and overall efficacy. However, extant literature lacks sufficient investigation to explicate the other pertinent studies. The objective of this investigation is to examine the utilization of artificial intelligence techniques within the financial services industry. The study was conducted by means of a systematic literature review in accordance with the PRISMA diagram guidelines. This study employed a systematic literature review approach, utilizing various academic databases including Science Direct, IEEE, EBSCO, SCOPUS, and Web of Science. The search was conducted using selected keywords within the timeframe of 2019 to 2023. The study's primary findings offer a synopsis of the increasing attention towards the implementation of AI technologies in the financial sector. The systematic literature review showed that AI tools have received noteworthy attention for their capacity to revolutionize diverse facets of the industry, encompassing but not limited to decision-making, risk evaluation, fraud identification, customer service, investment guidance, and customized banking. In addition, the amalgamation of deep learning techniques and artificial intelligence has exhibited the capability to mitigate cognitive and affective errors, leading to enhanced financial gains for banking organizations and increased satisfaction among their customers. This study aims to provide guidance to stakeholders in the finance sector regarding the integration of artificial intelligence tools into their operations.
Keywords: Artificial Intelligence, tools, finance, machine learning, fintech
... Firstly proposed in Goodfellow et al. (2014), these networks are composed of a generator network generating fake data and a discriminator network trying to distinguish between real and fake data, which leads to a min-max game. One of the first papers proposing GANs to generate financial data is Takahashi et al. (2019), where the generator and discriminator are a multi-layer perceptron, convolutional networks or a combination of both. In Wiese et al. (2020) both the generator and discriminator model consists of temporal convolutional networks addressing long-range dependencies within the time series. ...
Randomised signature has been proposed as a flexible and easily implementable alternative to the well-established path signature. In this article, we employ randomised signature to introduce a generative model for financial time series data in the spirit of reservoir computing. Specifically, we propose a novel Wasserstein-type distance based on discrete-time randomised signatures. This metric on the space of probability measures captures the distance between (conditional) distributions. Its use is justified by our novel universal approximation results for randomised signatures on the space of continuous functions taking the underlying path as an input. We then use our metric as the loss function in a non-adversarial generator model for synthetic time series data based on a reservoir neural stochastic differential equation. We compare the results of our model to benchmarks from the existing literature.
... As the need for deep learning grows, so does the need for greater data, with different fields where privacy is of the utmost importance benefiting from data synthesised, such as healthcare data using models such as SynSyn 12 or, financial data. 13 Synthetic data is already being used to generate data with greater privacy using recent advances in image generation. To address privacy and ethical concerns of using face image datasets of real people, 14 used StyleGAN2-ADA to generate their own dataset of synthetic face images named SFace. ...
In the aviation industry, predictive maintenance is vital to minimise Unscheduled faults and maintain the operational availability of aircraft. However, the amount of open data available for research is limited due to the proprietary nature of aircraft data. In this work, six time‐series datasets are synthesised using the DoppelGANger model trained on real Airbus datasets from landing gear systems. The synthesised datasets contain no proprietary information, but maintain the shape and patterns present in the original, making them suitable for testing novel PdM models. They can be used by researchers outside of the industry to explore a more diverse selection of aircraft systems, and the proposed methodology can be replicated by industry data scientists to synthesise and release more data to the public. The results of this study demonstrate the feasibility and effectiveness of using the DoppelGANger model from the Gretel.ai library to generate new time series data that can be used to train predictive maintenance models for industry problems. These synthetic datasets were subject to fidelity testing using six metrics. The six datasets are available on the UWE Library service.
... For heavy-tailed distribution data generation, FIN-GAN (Takahashi et al., 2019) demonstrated the capacity of vanilla GAN with the Multilayer Perceptron (MLP) and MLP-CNN network architectures to reproduce the heavy-tail distributed and long-range dependent time-series. HTGAN (Zhang & Zhou, 2021) employed student t-distribution to improve the applicability of vanilla GANs for industrial heavy tail data generation. ...
Accurate stock price prediction is essential for investing in the financial market. Aiming at the problem’s accuracy, the prediction model is restricted due to the lack of sufficient data samples for the stock price of newly listed companies. This paper proposes a novel approach to improve the generalization of Bidirectional Long Short-Term Memory Network (BiLSTM) with Wasserstein Generative Adversarial Network (WGAN) on stock time-series data augmentation. WGAN is used to learn the distribution rules of the real data, and the two-sample KS test and the area between the log–log plots are adopted to evaluate the extent of heavy-tailed distribution of the generated samples similar to that of real-world data. BiLSTM is employed to extract and predict data’s forward and reverse time information. With the stock price data, the prediction results of different algorithm models without and after augmented data are compared. Experimental results show that the accuracy of BiLSTM enhanced by WGAN is significantly improved, and the proposed WGAN-BiLSTM model is suitable for stock price prediction in few-shot settings.
... Moreover, DGMs have contributed to the reinvigoration of agent-based modeling in economics by generating synthetic data for creating realistic artificial environments and maintaining simulation realism (Axtell & Farmer, 2021). For example, DGM-based travel behavior simulations have employed restricted Boltzmann machines (Wong & Farooq, 2020), while GAN-based financial correlation matrices and time-series sampling have been used for simulating financial systems (Marti, 2020;Takahashi et al., 2019). ...
We present a deep learning solution to address the challenges of simulating realistic synthetic first-price sealed-bid auction data. The complexities encountered in this type of auction data include high-cardinality discrete feature spaces and a multilevel structure arising from multiple bids associated with a single auction instance. Our methodology combines deep generative modeling (DGM) with an artificial learner that predicts the conditional bid distribution based on auction characteristics, contributing to advancements in simulation-based research. This approach lays the groundwork for creating realistic auction environments suitable for agent-based learning and modeling applications. Our contribution is twofold: we introduce a comprehensive methodology for simulating multilevel discrete auction data, and we underscore the potential of DGM as a powerful instrument for refining simulation techniques and fostering the development of economic models grounded in generative AI.
... In recent years, more and more scholars have embarked on analyzing financial data using machine learning models because these models are relatively easy to implement in empirical experiments and are adept at capturing unique statistical characteristics of financial series [30,31]. In the field of convertible bond pricing, Zhou et al. [32] made a comparison analysis of the B-S model, binary tree model, and artificial neural network model on convertible bond pricing, noting that the artificial neural network model yielded superior estimation results. ...
In this paper, we explore a novel model for pricing Chinese convertible bonds that seamlessly integrates machine learning techniques with traditional models. The least squares Monte Carlo (LSM) method is effective in handling multiple state variables and complex path dependencies through simple regression analysis. In our approach, we incorporate machine learning techniques, specifically support vector regression (SVR) and random forest (RF). By employing Bayesian optimization to fine-tune the random forest, we achieve improved predictive performance. This integration is designed to enhance the precision and predictive capabilities of convertible bond pricing. Through the use of simulated data and real data from the Chinese convertible bond market, the results demonstrate the superiority of our proposed model over the classic LSM, confirming its effectiveness. The development of a pricing model incorporating machine learning techniques proves particularly effective in addressing the complex pricing system of Chinese convertible bonds. Our study contributes to the body of knowledge on convertible bond pricing and further deepens the application of machine learning in the field in an integrated and supportive manner.
... However, GAN may struggle to capture complex relationships and patterns in the data when dealing with sparse time series data. Therefore, it has been determined that GAN is not an effective method for processing time series data, as evidenced by studies conducted by various researchers [24][25][26]. In order to enhance the efficiency with which time series data are generated, Time-series Generative Adversarial Networks (TimeGAN) were proposed in 2019 [27], and have since demonstrated exceptional results in the field of generating data in time series. ...
The new energy vehicle industry has an increasing demand for safety, stability, and efficiency in the operation of essential equipment, particularly in the intelligent means of fault diagnosis of motor equipment, which is rising annually. For the past several years, there has been an increasing demand for accuracy and precision in troubleshooting fault diagnosis of permanent magnet synchronous motors. This paper presents a variable-scale Inception (VS-Inception) permanent magnet motor malfunction diagnostic method on the basis of R parameters. Firstly, the Time Series Generative Adversarial Network is utilized to expand the dataset samples of the collected vibration signals, resulting in many virtual signals with motor fault characteristics. Then, the variable parameter variable scale structure of the VS-Inception model is employed to carry out the fault diagnosis of permanent magnet synchronous motors on the expanded dataset. Finally, comparison experiments of VS-Inception with the existing state-of-the-art methods and with the original method are conducted to confirm the superiority even further and stability of the VS-Inception method in the field of permanent magnet synchronous motor malfunction diagnostic.
... Reference [20] used a WGAN with penalized gradients to generate solar irradiance data and train a convolutional neural network based weather classification model with an augmented dataset consisting of the original and generated data to improve the classification accuracy of the model. In [21], a GAN based on financial time-series models was proposed to generate real data in a data-driven manner by learning the properties of the data. Although a large number of studies have shown that GANs are effective in terms of generating new samples, they have rarely considered the temporal correlations among variables when performing time-series data generation, which tends to reduce the diversity and accuracy of the generated samples. ...
This study proposes a hybrid network model based on data enhancement to address the problem of low accuracy in photovoltaic (PV) power prediction that arises due to insufficient data samples for new PV plants. First, a time-series generative adversarial network (TimeGAN) is used to learn the distribution law of the original PV data samples and the temporal correlations between their features, and these are then used to generate new samples to enhance the training set. Subsequently, a hybrid network model that fuses bi-directional long-short term memory (BiLSTM) network with attention mechanism (AM) in the framework of deep & cross network (DCN) is constructed to effectively extract deep information from the original features while enhancing the impact of important information on the prediction results. Finally, the hyperparameters in the hybrid network model are optimized using the whale optimization algorithm (WOA), which prevents the network model from falling into a local optimum and gives the best prediction results. The simulation results show that after data enhancement by TimeGAN, the hybrid prediction model proposed in this paper can effectively improve the accuracy of short-term PV power prediction and has wide applicability.
Time series forecasting (TSF) has long been a crucial task in both industry and daily life. Most classical statistical models may have certain limitations when applied to practical scenarios in fields such as energy, healthcare, traffic, meteorology, and economics, especially when high accuracy is required. With the continuous development of deep learning, numerous new models have emerged in the field of time series forecasting in recent years. However, existing surveys have not provided a unified summary of the wide range of model architectures in this field, nor have they given detailed summaries of works in feature extraction and datasets. To address this gap, in this review, we comprehensively study the previous works and summarize the general paradigms of Deep Time Series Forecasting (DTSF) in terms of model architectures. Besides, we take an innovative approach by focusing on the composition of time series and systematically explain important feature extraction methods. Additionally, we provide an overall compilation of datasets from various domains in existing works. Finally, we systematically emphasize the significant challenges faced and future research directions in this field.
Purpose
Earlier studies used conventional time-series models to forecast the impact of the Covid-19 pandemic on stock market performance. This study aims to provide a more flexible model that offers more robust estimation features, such as incorporating additional information (prior) about the model parameters, capturing the evolving behavior of the parameters over time and being able to include several covariates using a spike and slab prior, within the context of the Covid-19 shock and its effect on stock market performance.
Design/methodology/approach
Empirically, this paper compares autoregressive integrated moving average (ARIMA) models and the proposed Bayesian structural time-series (BSTS) models regarding their forecasting accuracy for airline and petroleum stocks in the five countries most affected by the Coronavirus, namely, Brazil, France, India, Russia and the USA. In addition, the authors estimate the difference between the pre- and post-intervention periods of the observed series of stock prices and a simulated time-series that would have occurred without the extreme event of Covid-19, using intervention analysis under the best-performing models.
Findings
The forecasting results, based on the trend, seasonality and regression components, demonstrate that BSTS models respond faster to the diverse needs of time-series analysis in unprecedented and crisis conditions compared to ARIMA models. Therefore, the authors use intervention analysis under BSTS models to examine the impact of Covid-19 intervention on stock market performance. The authors find that the Covid-19 shock had an adverse effect on the stock markets of the selected countries. The impact was more pronounced in the Brazilian market, where the average weekly prices of airline and petroleum stocks plummeted by 76% and 29%, respectively.
Originality/value
To the best of the authors’ knowledge, no prior study has carried out intervention analysis under BSTS models to forecast the impact of Covid-19 intervention on stock market returns. This study attempts to fill this methodological gap in the literature.
Enhancing the forecasting accuracy of energy spot prices is vital for decision-making in energy trading. This study evaluates various feature selection methods and regression models to predict energy prices in Colombia. We compare Principal Components Analysis, Pearson Correlation Coefficients, Mutual Information, and Least Absolute Shrinkage methods with Ran-dom Forest, Extra Gradient boost, and CatBoost models. Mutual Information is the most compelling feature selection method, improving prediction accuracy notably. It identifies features such as reserves, month, and Ocean Nino Index in the study. The Random Forest model with Mutual Information-based selection achieved an R2 value of 95%. The research emphasizes the enhanced model accuracy in spot energy price prediction using Mutual Information-based feature selection. Future research should focus on cross-validation techniques and the impact of temporal data for further improvements.
With the significant increase in the amount of solar energy sources, the variation in the production caused by the stochastic nature of these sources becomes a larger problem for the electrical grid. Having a large percentage of installed units, therefore, requires some type of both short- and long-term planning of energy production. Most planning and forecasting tools require a large amount of solar energy data for the location in question and oftentimes that data is difficult to obtain. In this paper, we propose a method for generating synthetic solar irradiance data and test its applicability on forecasting and long-term planning problems. Synthetic data are generated using various generative adversarial networks and masked autoencoder based models, which are all trained on a dataset of solar irradiance data measured on the territory of the city of Banja Luka in Bosnia and Herzegovina. The synthetic data are evaluated both on different types of short-term forecasting tools and a long-term solar plant simulation tool, and the obtained results are compared with the cases where real data is used. By comparing the results, we have concluded that by using generative models we are able to generate synthetic data which is not only realistic, but applicable for both of these uses.
Time series data are widely used and provide a wealth of information for countless applications. However, some applications are faced with a limited amount of data, or the data cannot be used due to confidentiality concerns. To overcome these obstacles, time series can be generated synthetically. For example, electrocardiograms can be synthesized to make them available for building models to predict conditions such as cardiac arrhythmia without leaking patient information. Although many different approaches to time series synthesis have been proposed, evaluating the quality of synthetic time series data poses unique challenges and remains an open problem, as there is a lack of a clear definition of what constitutes a “good” synthesis. To this end, we present a comprehensive literature survey to identify different aspects of synthesis quality and their relationships. Based on this, we propose a definition of synthesis quality and a systematic evaluation procedure for assessing it. With this work, we aim to provide a common language and criteria for evaluating synthetic time series data. Our goal is to promote more rigorous and reproducible research in time series synthesis by enabling researchers and practitioners to generate high-quality synthetic time series data.
Generative adversarial networks (GANs), a novel framework for training generative models in an adversarial setup, have attracted significant attention in recent years. The two opposing neural networks of the GANs framework, i.e., a generator and a discriminator, are trained simultaneously in a zero-sum game, where the generator generates images to fool the discriminator that is trained to discriminate between real and synthetic images. In this paper, we provide a comprehensive review about the recent developments in GANs. Firstly, we introduce various deep generative models, basic theory and training mechanism of GANs, and the latent space. We further discuss several representative variants of GANs. Although GANs have been successfully utilized in various applications, they are known to be highly unstable to train. Generally, there is a lack of understanding as to how GANs converge. We briefly discuss the sources of instability and convergence issues in GANs from the perspectives of statistics, game theory and control theory, and describe several techniques for their stable training. Evaluating GANs has been a challenging task, as there is no consensus yet reached on which measure is more suitable for model comparison. Therefore, we provide a brief discussion on quantitative and qualitative evaluation measures for GANs. Then, we conduct several experiments to compare representative GANs variants based on these evaluation metrics. Furthermore, the application areas of GANs are briefly discussed. Finally, we outline several important open issues and future research trends in GANs.
We look into Generative Adversarial Network (GAN), its prevalent variants and applications in a number of sectors. GANs combine two neural networks that compete against one another using zero-sum game theory, allowing them to create much crisper and discrete outputs. GANs can be used to perform image processing, video generation and prediction, among other computer vision applications. GANs can also be utilised for a variety of science-related activities, including protein engineering, astronomical data processing, remote sensing image dehazing, and crystal structure synthesis. Other notable fields where GANs have made gains include finance, marketing, fashion design, sports, and music. Therefore in this article we provide a comprehensive overview of the applications of GANs in a wide variety of disciplines. We first cover the theory supporting GAN, GAN variants, and the metrics to evaluate GANs. Then we present how GAN and its variants can be applied in twelve domains, ranging from STEM fields, such as astronomy and biology, to business fields, such as marketing and finance, and to arts, such as music. As a result, researchers from other fields may grasp how GANs work and apply them to their own study. To the best of our knowledge, this article provides the most comprehensive survey of GAN’s applications in different field.
Stock price prediction is an important issue in the financial world, as it contributes to the development of effective strategies for stock exchange transactions. In this paper, we propose a generic framework employing Long Short-Term Memory (LSTM) and convolutional neural network (CNN) for adversarial training to forecast high-frequency stock market. This model takes the publicly available index provided by trading software as input to avoid complex financial theory research and difficult technical analysis, which provides the convenience for the ordinary trader of nonfinancial specialty. Our study simulates the trading mode of the actual trader and uses the method of rolling partition training set and testing set to analyze the effect of the model update cycle on the prediction performance. Extensive experiments show that our proposed approach can effectively improve stock price direction prediction accuracy and reduce forecast error.
For object detection, the two-stage approach (e.g., Faster R-CNN) has been achieving the highest accuracy, whereas the one-stage approach (e.g., SSD) has the advantage of high efficiency. To inherit the merits of both while overcoming their disadvantages, in this paper, we propose a novel single-shot based detector, called RefineDet, that achieves better accuracy than two-stage methods and maintains comparable efficiency of one-stage methods. RefineDet consists of two inter-connected modules, namely, the anchor refinement module and the object detection module. Specifically, the former aims to (1) filter out negative anchors to reduce search space for the classifier, and (2) coarsely adjust the locations and sizes of anchors to provide better initialization for the subsequent regressor. The latter module takes the refined anchors as the input from the former to further improve the regression and predict multi-class label. Meanwhile, we design a transfer connection block to transfer the features in the anchor refinement module to predict locations, sizes and class labels of objects in the object detection module. The multi-task loss function enables us to train the whole network in an end-to-end way. Extensive experiments on PASCAL VOC 2007, PASCAL VOC 2012, and MS COCO demonstrate that RefineDet achieves state-of-the-art detection accuracy with high efficiency. Code is available at https://github.com/sfzhang15/RefineDet.
In this paper, we present MidiNet, a deep convolutional neural network (CNN) based generative adversarial network (GAN) that is intended to provide a general, highly adaptive network structure for symbolic-domain music generation. The network takes random noise as input and generates a melody sequence one mea- sure (bar) after another. Moreover, it has a novel reflective CNN sub-model that allows us to guide the generation process by providing not only 1D but also 2D conditions. In our implementation, we used the intended chord of the current bar as a 1D condition to provide a harmonic context, and the melody generated for the preceding bar previously as a 2D condition to provide sequential information. The output of the network is a 16 by 128 matrix each time, representing the presence of each of the 128 MIDI notes in the generated melody sequence of that bar, with the smallest temporal unit being the sixteenth note. MidiNet can generate music of arbitrary number of bars, by concatenating these 16 by 128 matrices. The melody sequence can then be played back with a synthesizer. We provide example clips showing the effectiveness of MidiNet in generating harmonic music.
We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.
As a new way of training generative models, Generative Adversarial Nets (GAN) that uses a discriminative model to guide the training of the generative model has enjoyed considerable success in generating real-valued data. However, it has limitations when the goal is for generating sequences of discrete tokens. A major reason lies in that the discrete outputs from the generative model make it difficult to pass the gradient update from the discriminative model to the generative model. Also, the discriminative model can only assess a complete sequence, while for a partially generated sequence, it is non-trivial to balance its current score and the future one once the entire sequence has been generated. In this paper, we propose a sequence generation framework, called SeqGAN, to solve the problems. Modeling the data generator as a stochastic policy in reinforcement learning (RL), SeqGAN bypasses the generator differentiation problem by directly performing gradient policy update. The RL reward signal comes from the GAN discriminator judged on a complete sequence, and is passed back to the intermediate state-action steps using Monte Carlo search. Extensive experiments on synthetic data and real-world tasks demonstrate significant improvements over strong baselines.
We present a variety of new architectural features and training procedures that we apply to the generative adversarial networks (GANs) framework. We focus on two applications of GANs: semi-supervised learning, and the generation of images that humans find visually realistic. Unlike most work on generative models, our primary goal is not to train a model that assigns high likelihood to test data, nor do we require the model to be able to learn well without using any labels. Using our new techniques, we achieve state-of-the-art results in semi-supervised classification on MNIST, CIFAR-10 and SVHN. The generated images are of high quality as confirmed by a visual Turing test: our model generates MNIST samples that humans cannot distinguish from real data, and CIFAR-10 samples that yield a human error rate of 21.3%. We also present ImageNet samples with unprecedented resolution and show that our methods enable the model to learn recognizable features of ImageNet classes.
Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics. Deep learning discovers intricate structure in large data sets by using the backpropagation algorithm to indicate how a machine should change its internal parameters that are used to compute the representation in each layer from the representation in the previous layer. Deep convolutional nets have brought about breakthroughs in processing images, video, speech and audio, whereas recurrent nets have shone light on sequential data such as text and speech.
Power laws are theoretically interesting probability distributions that are also frequently used to describe empirical data. In recent years, effective statistical methods for fitting power laws have been developed, but appropriate use of these techniques requires significant programming and statistical insight. In order to greatly decrease the barriers to using good statistical methods for fitting power law distributions, we developed the powerlaw Python package. This software package provides easy commands for basic fitting and statistical analysis of distributions. Notably, it also seeks to support a variety of user needs by being exhaustive in the options available to the user. The source code is publicly available and easily extensible.
For complex financial systems, the negative and positive return-volatility correlations, i.e., the so-called leverage and anti-leverage effects, are particularly important for the understanding of the price dynamics. However, the microscopic origination of the leverage and anti-leverage effects is still not understood, and how to produce these effects in agent-based modeling remains open. On the other hand, in constructing microscopic models, it is a promising conception to determine model parameters from empirical data rather than from statistical fitting of the results.
To study the microscopic origination of the return-volatility correlation in financial systems, we take into account the individual and collective behaviors of investors in real markets, and construct an agent-based model. The agents are linked with each other and trade in groups, and particularly, two novel microscopic mechanisms, i.e., investors' asymmetric trading and herding in bull and bear markets, are introduced. Further, we propose effective methods to determine the key parameters in our model from historical market data.
With the model parameters determined for six representative stock-market indices in the world, respectively, we obtain the corresponding leverage or anti-leverage effect from the simulation, and the effect is in agreement with the empirical one on amplitude and duration. At the same time, our model produces other features of the real markets, such as the fat-tail distribution of returns and the long-term correlation of volatilities.
We reveal that for the leverage and anti-leverage effects, both the investors' asymmetric trading and herding are essential generation mechanisms. Among the six markets, however, the investors' trading is approximately symmetric for the five markets which exhibit the leverage effect, thus contributing very little. These two microscopic mechanisms and the methods for the determination of the key parameters can be applied to other complex systems with similar asymmetries.
Time series of financial asset returns often exhibit the volatility clustering property: large changes in prices tend to cluster together, resulting in persistence of the amplitudes of price changes. After recalling various methods for quantifying and modeling this phenomenon, we discuss several economic mechanisms which have been proposed to explain the origin of this volatility clustering in terms of behavior of market participants and the news arrival process. A common feature of these models seems to be a switching between low and high activity regimes with heavy-tailed durations of regimes. Finally, we discuss a simple agent-based model which links such variations in market activity to threshold behavior of market participants and suggests a link between volatility clustering and investor inertia.
This article and the companion paper aim at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since the name was coined in 1995 by merging the words 'Economics' and 'Physics', this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distribution), microstructure of financial markets (order book modeling), econometrics of financial bubbles and crashes, etc. We discuss the interactions between Physics, Mathematics, Economics and Finance that led to the emergence of Econophysics. We then present empirical studies revealing the statistical properties of financial time series. We begin the presentation with the widely acknowledged 'stylized facts', which describe the returns of financial assets—fat tails, volatility clustering, autocorrelation, etc.—and recall that some of these properties are directly linked to the way 'time' is taken into account. We continue with the statistical properties observed on order books in financial markets. For the sake of illustrating this review, (nearly) all the stated facts are reproduced using our own high-frequency financial database. Finally, contributions to the study of correlations of assets such as random matrix theory and graph theory are presented. The companion paper will review models in Econophysics from the point of view of agent-based modeling.
Advantages and limitations of the existing volatility models for forecasting foreign-exchange and stock market volatility from multiscale and high-dimensional data have been identified. Support vector machines (SVM) have been proposed as a complimentary volatility model that is capable of effectively extracting information from multiscale and high-dimensional market data. SVM-based models can handle both long memory and multiscale effects of inhomogeneous markets without restrictive assumptions and approximations required by other models. Preliminary results with foreign-exchange data suggest that SVM can effectively work with high-dimensional inputs to account for volatility long-memory and multiscale effects. Advantages of the SVM-based models are expected to be of the utmost importance in the emerging field of high-frequency finance and in multivariate models for portfolio risk management.
We investigate quantitatively the so-called "leverage effect," which corresponds to a negative correlation between past returns and future volatility. For individual stocks this correlation is moderate and decays over 50 days, while for stock indices it is much stronger but decays faster. For individual stocks the magnitude of this correlation has a universal value that can be rationalized in terms of a new "retarded" model which interpolates between a purely additive and a purely multiplicative stochastic process. For stock indices a specific amplification phenomenon seems to be necessary to account for the observed amplitude of the effect.
We study the statistical properties of volatility, measured by locally averaging over a time window T, the absolute value of price changes over a short time interval deltat. We analyze the S&P 500 stock index for the 13-year period Jan. 1984 to Dec. 1996. We find that the cumulative distribution of the volatility is consistent with a power-law asymptotic behavior, characterized by an exponent mu approximately 3, similar to what is found for the distribution of price changes. The volatility distribution retains the same functional form for a range of values of T. Further, we study the volatility correlations by using the power spectrum analysis. Both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents. Also, both methods show the presence of a crossover at approximately 1.5 days. In addition, we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 U.S. companies over the two-year period Jan. 1994 to Dec. 1995.
This paper reports statistical analyses performed on simulated data from a stochastic multi-agent model of speculative behaviour in a financial market. The price dynamics resulting from this artificial market process exhibits the same type of scaling laws as do empirical data from stock markets and foreign exchange markets: (i) one observes scaling in the probability distribution of relative price changes with a Pareto exponent around 2.6, (ii) volatility shows significant long-range correlation with a self-similarity parameter H around 0.85. This happens although we assume that news about the intrinsic or fundamental value of the asset follows a white noise process and, hence, incorporation of news about fundamental factors is insufficient to explain either of the characteristics (i) or (ii). As a consequence, in our model, the main stylised facts of financial data originate from the working of the market itself and one need not resort to scaling in unobservable extraneous signals as an explanation of the source of scaling in financial prices. The emergence of power laws can be explained by the existence of a critical state which is repeatedly approached in the course of the system's development.
A binary game is introduced and analysed. N players have to choose one of the
two sides independently and those on the minority side win. Players uses a
finite set of ad hoc strategies to make their decision, based on the past
record. The analysing power is limited and can adapt when necessary.
Interesting cooperation and competition pattern of the society seem to arise
and to be responsive to the payoff function.
Recently telecom fraud has become a serious problem especially in developing countries such as China. At present, it can be very difficult to coordinate different agencies to prevent fraud completely. In this paper we study how to detect large transfers that are sent from victims deceived by fraudsters at the receiving bank. We propose a new generative adversarial network (GAN) based model to calculate for each large transfer a probability that it is fraudulent, such that the bank can take appropriate measures to prevent potential fraudsters to take the money if the probability exceeds a threshold. The inference model uses a deep denoising autoencoder to effectively learn the complex probabilistic relationship among the input features, and employs adversarial training that establishes a minimax game between a discriminator and a generator to accurately discriminate between positive samples and negative samples in the data distribution. We show that the model outperforms a set of well-known classification methods in experiments, and its applications in two commercial banks have reduced losses of about 10 million RMB in twelve weeks and significantly improved their business reputation.
We propose NetGAN - the first implicit generative model for graphs able to mimic real-world networks. We pose the problem of graph generation as learning the distribution of biased random walks over the input graph. The proposed model is based on a stochastic neural network that generates discrete output samples and is trained using the Wasserstein GAN objective. NetGAN is able to produce graphs that exhibit the well-known network patterns without explicitly specifying them in the model definition. At the same time, our model exhibits strong generalization properties, as highlighted by its competitive link prediction performance, despite not being trained specifically for this task. Being the first approach to combine both of these desirable properties, NetGAN opens exciting further avenues for research.
While Generative Adversarial Networks (GANs) have seen wide success at the problem of synthesizing realistic images, they have seen little application to the problem of unsupervised audio generation. Unlike for images, a barrier to success is that the best discriminative representations for audio tend to be non-invertible, and thus cannot be used to synthesize listenable outputs. In this paper, we introduce WaveGAN, a first attempt at applying GANs to raw audio synthesis in an unsupervised setting. Our experiments on speech demonstrate that WaveGAN can produce intelligible words from a small vocabulary of human speech, as well as synthesize audio from other domains such as bird vocalizations, drums, and piano. Qualitatively, we find that human judges prefer the generated examples from WaveGAN over those from a method which naively apply GANs on image-like audio feature representations.
E-commerce companies such as Amazon, Alibaba and Flipkart process billions of orders every year. However, these orders represent only a small fraction of all plausible orders. Exploring the space of all plausible orders could help us better understand the relationships between the various entities in an e-commerce ecosystem, namely the customers and the products they purchase. In this paper, we propose a Generative Adversarial Network (GAN) for orders made in e-commerce websites. Once trained, the generator in the GAN could generate any number of plausible orders. Our contributions include: (a) creating a dense and low-dimensional representation of e-commerce orders, (b) train an ecommerceGAN (ecGAN) with real orders to show the feasibility of the proposed paradigm, and (c) train an ecommerce-conditional-GAN (ec^2GAN) to generate the plausible orders involving a particular product. We propose several qualitative methods to evaluate ecGAN and demonstrate its effectiveness. The ec^2GAN is used for various kinds of characterization of possible orders involving a product that has just been introduced into the e-commerce system. The proposed approach ec^2GAN performs significantly better than the baseline in most of the scenarios.
In the last years, the number of frauds in credit card-based online payments has grown dramatically, pushing banks and e-commerce organizations to implement automatic fraud detection systems, performing data mining on huge transaction logs. Machine learning seems to be one of the most promising solutions for spotting illicit transactions, by distinguishing fraudulent and non-fraudulent instances through the use of supervised binary classification systems properly trained from pre-screened sample datasets. However, in such a specific application domain, datasets available for training are strongly imbalanced, with the class of interest considerably less represented than the other. This significantly reduces the effectiveness of binary classifiers, undesirably biasing the results toward the prevailing class, while we are interested in the minority class. Oversampling the minority class has been adopted to alleviate this problem, but this method still has some drawbacks. Generative Adversarial Networks are general, flexible, and powerful generative deep learning models that have achieved success in producing convincingly real-looking images. We trained a GAN to output mimicked minority class examples, which were then merged with training data into an augmented training set so that the effectiveness of a classifier can be improved. Experiments show that a classifier trained on the augmented set outperforms the same classifier trained on the original data, especially as far the sensitivity is concerned, resulting in an effective fraud detection mechanism.
We propose generative neural network methods to generate DNA sequences and tune them to have desired properties. We present three approaches: creating synthetic DNA sequences using a generative adversarial network; a DNA-based variant of the activation maximization ("deep dream") design method; and a joint procedure which combines these two approaches together. We show that these tools capture important structures of the data and, when applied to designing probes for protein binding microarrays, allow us to generate new sequences whose properties are estimated to be superior to those found in the training data. We believe that these results open the door for applying deep generative models to advance genomics research.
In this paper, we show that the recent integration of statistical models with deep recurrent neural networks provides a new way of formulating volatility (the degree of variation of time series) models that have been widely used in time series analysis and prediction in finance. The model comprises a pair of complementary stochastic recurrent neural networks: the generative network models the joint distribution of the stochastic volatility process; the inference network approximates the conditional distribution of the latent variables given the observables. Our focus here is on the formulation of temporal dynamics of volatility over time under a stochastic recurrent neural network framework. Experiments on real-world stock price datasets demonstrate that the proposed model generates a better volatility estimation and prediction that outperforms stronge baseline methods, including the deterministic models, such as GARCH and its variants, and the stochastic MCMC-based models, and the Gaussian-process-based, on the average negative log-likelihood measure.
We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1/2 everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.0 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.
With the random matrix theory, we decompose the multi-dimensional time series of complex financial systems into a set of orthogonal eigenmode functions, which are classified into the market mode, sector mode, and random mode. In particular, the localized motion generated by the business sectors, plays an important role in financial systems. Both the business sectors and their impact on the stock market are identified from the localized motion. We clarify that the localized motion induces different characteristics of the time correlations for the stock-market index and individual stocks. With a variation of a two-factor model, we reproduce the return-volatility correlations of the eigenmodes.
Modeling the distribution of natural images is a landmark problem in unsupervised learning. This task requires an image model that is at once expressive, tractable and scalable. We present a deep neural network that sequentially predicts the pixels in an image along the two spatial dimensions. Our method models the discrete probability of the raw pixel values and encodes the complete set of dependencies in the image. Architectural novelties include fast two-dimensional recurrent layers and an effective use of residual connections in deep recurrent networks. We achieve log-likelihood scores on natural images that are considerably better than the previous state of the art. Our main results also provide benchmarks on the diverse ImageNet dataset. Samples generated from the model appear crisp, varied and globally coherent.
Deeper neural networks are more difficult to train. We present a residual
learning framework to ease the training of networks that are substantially
deeper than those used previously. We explicitly reformulate the layers as
learning residual functions with reference to the layer inputs, instead of
learning unreferenced functions. We provide comprehensive empirical evidence
showing that these residual networks are easier to optimize, and can gain
accuracy from considerably increased depth. On the ImageNet dataset we evaluate
residual nets with a depth of up to 152 layers---8x deeper than VGG nets but
still having lower complexity. An ensemble of these residual nets achieves
3.57% error on the ImageNet test set. This result won the 1st place on the
ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100
and 1000 layers.
The depth of representations is of central importance for many visual
recognition tasks. Solely due to our extremely deep representations, we obtain
a 28% relative improvement on the COCO object detection dataset. Deep residual
nets are foundations of our submissions to ILSVRC & COCO 2015 competitions,
where we also won the 1st places on the tasks of ImageNet detection, ImageNet
localization, COCO detection, and COCO segmentation.
In recent years, supervised learning with convolutional networks (CNNs) has
seen huge adoption in computer vision applications. Comparatively, unsupervised
learning with CNNs has received less attention. In this work we hope to help
bridge the gap between the success of CNNs for supervised learning and
unsupervised learning. We introduce a class of CNNs called deep convolutional
generative adversarial networks (DCGANs), that have certain architectural
constraints, and demonstrate that they are a strong candidate for unsupervised
learning. Training on various image datasets, we show convincing evidence that
our deep convolutional adversarial pair learns a hierarchy of representations
from object parts to scenes in both the generator and discriminator.
Additionally, we use the learned features for novel tasks - demonstrating their
applicability as general image representations.
The standard unsupervised recurrent neural network language model (RNNLM)
generates sentences one word at a time and does not work from an explicit
global distributed sentence representation. In this work, we present an
RNN-based variational autoencoder language model that incorporates distributed
latent representations of entire sentences. This factorization allows it to
explicitly model holistic properties of sentences such as style, topic, and
high-level syntactic features. Samples from the prior over these sentence
representations remarkably produce diverse and well-formed sentences through
simple deterministic decoding. By examining paths through this latent space, we
are able to generate coherent novel sentences that interpolate between known
sentences. We present techniques for solving the difficult learning problem
presented by this model, demonstrate strong performance in the imputation of
missing tokens, and explore many interesting properties of the latent sentence
space.
In this paper, we explore the inclusion of random variables into the dynamic
latent state of a recurrent neural network (RNN) by combining elements of the
variational autoencoder. We argue that through the use of high-level latent
random variables, our variational RNN (VRNN) is able to learn to model the kind
of variability observed in highly-structured sequential data (such as speech).
We empirically evaluate the proposed model against related sequential models on
five sequence datasets, four of speech and one of handwriting. Our results show
the importance of the role random variables can play in the RNN dynamic latent
state.
Training Deep Neural Networks is complicated by the fact that the
distribution of each layer's inputs changes during training, as the parameters
of the previous layers change. This slows down the training by requiring lower
learning rates and careful parameter initialization, and makes it notoriously
hard to train models with saturating nonlinearities. We refer to this
phenomenon as internal covariate shift, and address the problem by normalizing
layer inputs. Our method draws its strength from making normalization a part of
the model architecture and performing the normalization for each training
mini-batch}. Batch Normalization allows us to use much higher learning rates
and be less careful about initialization. It also acts as a regularizer, in
some cases eliminating the need for Dropout. Applied to a state-of-the-art
image classification model, Batch Normalization achieves the same accuracy with
14 times fewer training steps, and beats the original model by a significant
margin. Using an ensemble of batch-normalized networks, we improve upon the
best published result on ImageNet classification: reaching 4.9% top-5
validation error (and 4.8% test error), exceeding the accuracy of human raters.
We introduce Adam, an algorithm for first-order gradient-based optimization
of stochastic objective functions. The method is straightforward to implement
and is based an adaptive estimates of lower-order moments of the gradients. The
method is computationally efficient, has little memory requirements and is well
suited for problems that are large in terms of data and/or parameters. The
method is also ap- propriate for non-stationary objectives and problems with
very noisy and/or sparse gradients. The method exhibits invariance to diagonal
rescaling of the gradients by adapting to the geometry of the objective
function. The hyper-parameters have intuitive interpretations and typically
require little tuning. Some connections to related algorithms, on which Adam
was inspired, are discussed. We also analyze the theoretical convergence
properties of the algorithm and provide a regret bound on the convergence rate
that is comparable to the best known results under the online convex
optimization framework. We demonstrate that Adam works well in practice when
experimentally compared to other stochastic optimization methods.
Can we efficiently learn the parameters of directed probabilistic models, in
the presence of continuous latent variables with intractable posterior
distributions, and in case of large datasets? We introduce a novel learning and
approximate inference method that works efficiently, under some mild
conditions, even in the on-line and intractable case. The method involves
optimization of a stochastic objective function that can be straightforwardly
optimized w.r.t. all parameters, using standard gradient-based optimization
methods.
The method does not require the typically expensive sampling loops per
datapoint required for Monte Carlo EM, and all parameter updates correspond to
optimization of the variational lower bound of the marginal likelihood, unlike
the wake-sleep algorithm. These theoretical advantages are reflected in
experimental results.
The aim of this paper is to present some of the stylized features of financial data which have received a lot of attention both from practitioners and those with more theoretical backgrounds. Some of the models resulting from these efforts are reviewed and discussed. To facilitate the discussion two data sets are used: one of these contains all US trades in IMB stocks in 1995 at NYSE. /// Le but de cet exposé et d'essayer de comprendre pourquoi les données financières sont interessantes du point de vue de la statistique. J'essaierai en particulier de décrire ce que l'on cherche à modéliser et je présenterai certains des modèles les plus populaires ainsi que des modèles nouveaux. Pour faciliter la discussion, on analysera plusieurs ensembles de données. C'est pourquoi le nombre de graphiques sera important et le nombre de formules modéré. En particulier, on discuter en détail les données contenant tous les échanges américains sur les stocks IBM en 1995 au NYSE.
The diversity of agents in a heterogeneous market makes volatilities of different time resolutions behave differently. A lagged correlation study reveals that statistical volatility defined over a coarse time grid significantly predicts volatility defined over a fine grid. This empirical fact is not explained by conventional theories and models. We propose a new model class that takes into account squared price changes from time intervals of different size. This model is shown to reproduce the same empirical properties that have been found for FX intra-day data: long memory, fat-tailed distribution, and predictability of finely defined volatility by coarsely defined volatility.
Artificial neural networks are universal and highly flexible function approximators first used in the fields of cognitive science and engineering. In recent years, neural network applications in finance for such tasks as pattern recognition, classification, and time series forecasting have dramatically increased. However, the large number of parameters that must be selected to develop a neural network forecasting model have meant that the design process still involves much trial and error. The objective of this paper is to provide a practical introductory guide in the design of a neural network for forecasting economic time series data. An eight-step procedure to design a neural network forecasting model is explained including a discussion of tradeoffs in parameter selection, some common pitfalls, and points of disagreement among practitioners.
Research on this project was supported by a grant from the National Science Foundation. I am indebted to Arthur Laffer, Robert Aliber, Ray Ball, Michael Jensen, James Lorie, Merton Miller, Charles Nelson, Richard Roll, William Taylor, and Ross Watts for their helpful comments.
Previous research has shown that for stock indices, the most likely time until a return of a particular size has been observed is longer for gains than for losses. We establish that this so-called gain/loss asymmetry is present also for individual stocks and show that the phenomenon is closely linked to the well-known leverage effect -- in the EGARCH model and a modified retarded volatility model, the same parameter that governs the magnitude of the leverage effect also governs the gain/loss asymmetry.
We discuss a simple model based on the minority game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit. Stylized facts arise only close to a line of critical points with nontrivial properties, marking the transition to an unpredictable market. We show that the emergence of critical fluctuations close to the phase transition is governed by the interplay between the signal to noise ratio and the system size. These results provide a clear and consistent picture of financial markets, where stylized facts and verge of unpredictability are intimately related aspects of the same critical systems.
We investigate the return-volatility correlation both local and nonlocal in time with daily and minutely data of the German DAX and Chinese indices, and observe a leverage effect for the German DAX, while an antileverage effect for the Chinese indices. In the negative time direction, i.e., for the volatility-return correlation, an antileverage effect nonlocal in time is detected for both the German DAX and Chinese indices, although the duplicate local in time does not exist. A retarded volatility model may describe the asymmetric properties of the financial indices in the positive time direction.
Properties of three well-known and frequently applied first-order models for modelling and forecasting volatility in financial series such as stock and exchange rate returns are considered. These are the standard Generalized Autoregressive Conditional Heteroskedasticity (GARCH), the Exponential GARCH and the Autoregressive Stochastic Volatility model. The focus is on finding out how well these models are able to reproduce characteristic features of such series, also called stylized facts. These include high kurtosis and a rather low-starting and slowly decaying autocorrelation function of the squared or absolute-valued observations. Another stylized fact is that the autocorrelations of absolute-valued returns raised to a positive power are maximized when this power equals unity. A number of results for moments of the three models are given as well as the autocorrelation function of squared observations or, when available, the autocorrelation function of the absolute-valued observations raised to a positive power. These results make it possible to consider kurtosis-autocorrelation combinations that can be reproduced with these models and compare them with ones that have been estimated from financial time series. The ability of the models to reproduce the stylized fact that the autocorrelations of powers of absolute-valued observations are maximized when the power equals one is discussed as well. Finally, it is pointed out that none of these basic models can generate realizations with a skewed marginal distribution. Not unexpectedly, a conclusion that emerges from these considerations, largely based on results on the moment structure of these models, is that none of the models dominates the others when it comes to reproducing stylized facts in typical financial time series.
Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance. A regression model is then introduced with disturbances following an ARCH process. Maximum likelihood estimators are described and a simple scoring iteration formulated. Ordinary least squares maintains its optimality properties in this set-up, but maximum likelihood is more efficient. The relative efficiency is calculated and can be infinite. To test whether the disturbances follow an ARCH process, the Lagrange multiplier procedure is employed. The test is based simply on the autocorrelation of the squared OLS residuals. This model is used to estimate the means and variances of inflation in the U.K. The ARCH effect is found to be significant and the estimated variances increase substantially during the chaotic seventies.
A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.
Three networks are compared for low false alarm stock trend
predictions. Short-term trends, particularly attractive for neural
network analysis, can be used profitably in scenarios such as option
trading, but only with significant risk. Therefore, we focus on limiting
false alarms, which improves the risk/reward ratio by preventing losses.
To predict stock trends, we exploit time delay, recurrent, and
probabilistic neural networks (TDNN, RNN, and PNN, respectively),
utilizing conjugate gradient and multistream extended Kalman filter
training for TDNN and RNN. We also discuss different predictability
analysis techniques and perform an analysis of predictability based on a
history of daily closing price. Our results indicate that all the
networks are feasible, the primary preference being one of convenience
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunat