Time series analysis: Forecasting and control. Rev. ed
... The load time series L t is regarded as the realisation of a nonstatic stochastic process. General form of ARIMA model [70] is (2) ...
... Substituting (7) in (3), general multiplicative linear model is [70] : ...
Numerous short-term load forecasting models are available in the literature. However, the improvement in forecast accuracy using the combination models has yet to be analyzed on a daily rolling basis for a very long test period. In this paper, the characteristics of a combination of the Seasonal Autoregressive Integrated Moving Average (SARIMA) – a linear model and Radial Basis Function networks (RBFN) – a non-linear model have been studied in two different modeling frameworks namely single series (SS) and variable segmented series (VSS). The hourly load data of the Ontario Electricity Market (OEM) and the Iberian Electricity Market (MIBEL) are used as the case system to produce the daily load forecast. The impact on prediction accuracy by the size of training data and the combining individual forecasts has been studied for 12 years of OEM and one year of MIBEL demands, respectively. In order to achieve the empirical objective, a large number of models(1,447,740 in number) are estimated to produce load forecasts on a daily rolling basis. The forecast performance has been compared with the other models proposed in the literature.Among the linear models, for all window sizes of training data, the forecast accuracy of the combination model is better than the model selected with the minimum Akaike information criterion (AIC) and Bayesian information criterion (BIC) in both frameworks. Moreover, the ensemble of RBFN and linear models produces the best forecast. The results pinpointed that the proposed model’s precision and stability are higher than the earlier forecasting models proposed for both markets. The novelty in the model is that only a single hourly time-series is used for forecasting and there is no need for other explanatory variables.
... Unfortunately, likelihoods are not available for most system dynamics models due to nonlinearity, process noise, and highdimensional parameter spaces. Absent likelihoods, some may opt for simplifying the model to enable explicit likelihood calculations (Box and Jenkins 1976), trading off model quality for tractability. Another approach is to use approximations of the likelihood function that may be inaccurate but flexible enough to quantify parameter uncertainty (Li, Rahmandad, and Sterman 2022). ...
Estimating parameters and their credible intervals for complex system dynamics models is challenging but critical to continuous model improvement and reliable communication with an increasing fraction of audiences. The purpose of this study is to integrate Amortized Bayesian Inference (ABI) methods with system dynamics. Utilizing Neural Posterior Estimation (NPE), we train neural networks using synthetic data (pairs of ground truth parameters and outcome time series) to estimate parameters of system dynamics models. We apply this method to two example models: a simple Random Walk model and a moderately complex SEIRb model. We show that the trained neural networks can output the posterior for parameters instantly given new unseen time series data. Our analysis highlights the potential of ABI to facilitate a principled, scalable, and likelihood‐free inference workflow that enhance the integration of models of complex systems with data. Accompanying code streamlines application to diverse system dynamics models.
... Модели экономики, как и в других областях знаний, делятся на модели стационарные и динамические, представленные соответственно алгебраическими и дифференциальными уравнениями, при выводе которых часто исходят из принципа аналогии с известными фундаментальными законами природы, например термодинамики [Цирлин, 2003], [Цирлин, 2008]. Если математический аппарат моделей первого, стационарного типа составляют, по существу, методы математического программирования, методы анализа временных рядов, линейной и нелинейной регрессии, сглаживания и прогноза [Цирлин, 2008], [Box, 2016], [Montgomery, 2008], [Stulajtor, 2002], [Yong, 2011], [Полунин, 2019], то в аппарате моделей динамического типа существенное место занимают методы теории динамических систем, включая методы теории колебаний и систем оптимального управления. Перечень встречающихся в литературе динамических моделей можно найти в [Сафронов, 2015], [Андрианов и др., 2015]. ...
Во многих теоретических и прикладных науках, практически во всех областях человеческой деятельности, в частности, экономической, существует потребность в постановке и решении задач анализа временных рядов и динамических процессов, как правило, с неопределенными параметрами. Целью настоящей работы является рассмотрение двух возникающих при этом задач. А именно, задачи сглаживания временного ряда или процесса, точнее, представления его гладкой, во всех точках временной оси, функцией. Другая задача состоит в анализе результатов моделирования системы предсказания, построенной на основе искусственной нейронной сети и, по сути, относящейся к классу координатно-операторных систем. Полученное методом условной минимизации, решение первой задачи является обобщением известной задачи минимизации на конечном интервале, дополненной условиями гладкого согласования в точках сопряжения различных решений. Приводятся также упрощенные, не оптимальные методы решения этой задачи, а также схематически показаны иные обобщающие подходы. Результатом работы является разработка алгоритма сглаживания данных в классе гладких во всех точках временной оси функций и выводы по моделированию системы предсказания
In many theoretical and applied sciences, practically in all areas of human activity, particularly in economics, there is a need for setting and solving problems of analyzing time series and dynamic processes, as a rule, with uncertain parameters. The purpose of this work is to consider two problems arising in this case. Namely, the problem of smoothing a time series or a process, more precisely, of representing it as a smooth function at all points of the time axis. Another task is to analyze the results of modeling a prediction system based on an artificial neural network and, in fact, belonging to the class of coordinate-operator systems. The solution of the first problem obtained by conditional minimization method is a generalization of the well-known minimization problem on a finite interval augmented by smooth matching conditions at conjugation points of different solutions. Simplified, non-optimal methods for solving this problem are also given, and other generalizing approaches are schematically shown. The result is the development of an algorithm for data smoothing in a class of functions smooth at all points of the time axis and conclusions on the modeling of the prediction system.
... Moreover, these models also elevate the accuracy of the forecast by keeping the Principle of Parsimony i.e., the number of parameter should be minimum. Box and Jenkins (1976) argued that parsimonious ARIMA models give better forecasts than over parametrized models. Forecasting power of ARIMA model was observed better than the regression model for future decision-making (Afzal, Rehman & Butt, 2002). ...
The utmost interest of any state is to strength her control over natural resources and maximize security to protect these resources in her national interest. Water is key to economic growth and development. The rising trend of global water demand and declining freshwater availability have created an issue of water scarcity and warned the world. Pakistan, being a South Asian country is also facing the threat of water scarcity. So this study is planned to first assess the status of water scarcity in Pakistan using various well-defined water indices for the year 1972-73 to 2022-23. ARIMA time series model was used to forecast water scarcity in Pakistan. Pakistan which was once water abundant country is now a water scarce country both in terms of physical and social scarcity. The results depict that Pakistan will fall in the category of absolute water scarce countries in near future either in terms of declining per capita freshwater availability, increased withdrawals to availability ratio, high environmental water scarcity or reduced social adaptive capacity. Some effective measures must be taken to address the problem of water scarcity in Pakistan. It is high time regional forces must initiate regional trans-boundary dialogues and cooperative measures to the optimal use of available freshwater to bring peace, prosperity and economic integration in the region.
... The LSTM model is an important method for deep learning and is particularly suitable for dealing with time series tasks. As a special form of recurrent neural network, it introduces a system of gated units, including input gates, forgetting gates and output gates [1][2]. These gates control the update and output of the memory unit state through current and historical data, selectively controlling the information, forgetting the old information and updating the unit state based on the new information.The structure of the LSTM model is shown in Figure 1. ...
This study explores stock price forecasting, a critical topic for economic stability and investor decision-making. Traditional models like ARIMA struggle with stock market complexity due to their linear assumptions. To address this, the study examines advanced methods, focusing on deep learning techniques such as CNNs and LSTMs for their predictive strengths. It proposes a hybrid model combining Variational Mode Decomposition (VMD) and Bi-directional Long Short-Term Memory Networks (BiLSTM). VMD reduces time series non-stationarity, while BiLSTM captures sequence features via bi-directional processing. Empirical results show the VMD-BiLSTM model outperforms others in RMSE, MAE, and R² metrics, achieving higher forecasting accuracy. Although performance decreases during extreme price fluctuations, it effectively captures main trends. This research highlights the practical value of deep learning in handling complex financial time series and provides innovative methods for stock price prediction.
... Research methods for predicting stock prices include traditional statistical models, machine learning techniques, deep learning approaches, and sentiment analysis methods. Traditional statistical models primarily include the autoregressive integrated moving average(ARIMA) (Box et al., 1976) and the generalized autoregressive conditional heteroskedasticity (GARCH) (Bollerslev, 1986) models. However, these traditional statistical models are inadequate for fitting nonlinear, high-dimensional data and are prone to noisy data, resulting in significant prediction errors when forecasting real-time, dynamic stock prices. ...
With the rapid growth of economic globalization and digital economics, accurately predicting stock price fluctuations has become crucial yet challenging due to high volatility and market noise. Existing forecasting methods, relying primarily on time-series data, technical indicators, and sentiment analysis, often fail to capture the semantic depth of background knowledge, particularly the influence of real-time events. To address this limitation, we propose MoF, a background-aware multi-source fusion mechanism for financial trend forecasting. MoF integrates stock price data with background knowledge on the impact of real-time events on stock trends, which includes key information from policy documents and stock commentaries, and subsequently leverages the MacBERT model to generate feature vectors for stock prediction. Our results show that MoF, by incorporating the influence of real-time events, improves accuracy and interpretability in stock trend forecasting, surpassing LSTM-based models with over 90% accuracy in predicting market fluctuations and providing reliable directional predictions.
... Such traces are time series, which are commonly modelled accurately and in a parsimonious way by a Hidden Markov Model (HMM). Whilst there are many other approaches to time series analysis, such as the famed Box-Jenkins method and spectral techniques [1,14], a HMM is particularly effective when it is known that the dynamics of the series is strongly influenced by switching between modes, each of which has a particular charcteristic; these modes are represented by the hidden state which evolves as a Markov chain. Consequently, we focus our attention on identifying a hidden Markov chain that describes the modulation (usually assumed to be Markovian a priori) of the workload's characteristics at the particular timescale of interest. ...
A workload analysis technique is presented that processes data from operation type traces and creates a Hidden Markov Model (HMM) to represent the workload that generated those traces. The HMM can be used to create representative traces for performance models, such as simulators, avoiding the need to repeatedly acquire suitable traces. It can also be used to estimate directly the transition probabilities and rates of a Markov modulated arrival process, for use as input to an analytical performance model of Flash memory. The HMMs obtained from industrial workloads are validated by comparing their autocorrelation functions and other statistics with those of the corresponding monitored time series. Further, the performance model applications are illustrated by numerical examples.
... Average (HA), Vector Auto-Regression (VAR) (Hamilton 1994), and Autoregressive Integrated Moving Average (ARIMA) (Box 1976), but their ability to capture nonlinear relationships is insufficient. have also been widely adopted in traffic prediction (Li, Guo, et al. 2021;Zheng et al. 2020), and (Guo et al. 2019) utilized attention to achieve traffic prediction by considering and extracting periodic data, but such work usually requires a large number of training samples. ...
Traffic forecasting is crucial for intelligent transport systems (ITS). Existing methods typically model spatial correlation at the node level, neglecting the spatial correlation at the regional level (such as residential areas to commercial areas). In addition, most studies capture temporal dependencies unidirectionally, ignoring the contextual information of the time step. This article proposes a traffic prediction model called Multi-grained Graph Convolutional Network with Time-step Attention (MGCN-TSA) to address these two types of issues. The model is mainly composed of three modules. The Graph Construction module builds graphs from both the node and regional levels; The Multi-grained Graph Convolutional Fusion module (MGCF) uses a 3D CNN approach to indicate the importance of graphs at different levels. High-level spatial information is obtained by fusing the results of multi-grained graph convolution. The Time-step Attention module (TSA) accomplishes time-step contextual information extraction through time-step self-attention. To achieve sufficiently accurate long-term predictions, we adopt a multi-model recursive prediction strategy to complete the multi-step prediction task. Experiments on two large-scale public datasets demonstrate that the Mean Absolute Error (MAE) is reduced by 1.69%-3.10% and 8.98%-13.53%, respectively, compared to the state-of-the-art methods.
... Cross-spectrum analysis allows you to analyze two time series at the same time. Scientists Box and Jenkins 1976;Brillinger 1975;Elliott and Rao 1982;Priestley 1981;Shumway and Stoffer 2017;Wei 1989) consider cross-spectrum analysis to be more advanced than single-spectrum (Fourier) analysis. ...
This article is devoted to the analysis of the impact of socio-economic shocks on the dynamics of higher education development. It is substantiated that, on the one hand, higher education influences the development of society and the economy, on the other hand, the development trends of a country provide both opportunities and limitations for its development. An algorithmic model for studying the impact of social and economic shocks on the development of the higher education system (HES) has been developed. To diagnose the relationship between higher education and the socio-economic development of Ukraine and Slovakia, the following indicators were used: GDP per capita, the Human Development Index, school enrollment, tertiary, and net migration. The presence of nonlinear trends in the change in indicators has been shown and portraits of the socio-economic development of the countries have been constructed. To assess the impact of socio-economic shocks on the HES, the time-series decomposition method and cross-spectral analysis were used. The time-series decomposition allowed us to identify cyclical components of indicators, based on applying cross-spectral analysis, and the most significant local harmonics and the lag of their influence on the occurrence of shocks in the HES were determined. The use of the developed models allows us to predict periods of shock points in the HES depending on shocks in the tendencies of GDP per capita and net migration.
... This three-step process of selecting the ARIMA model develops it as one of the most sophisticated time series models, since ARIMA is even suitable for autoregressive, non-stationery and data with autocorrelation issue. Box et al. (2015) identified the procedure for the selection of (p), the number of previous observations to be included in the model. This method is called the autoregressive process (AR). ...
Purpose:This study examines the impact of withholding tax on banking transactions and its effect on financial inclusion in Pakistan—where the hidden economy is large.Design/Methodology/Approach: The study utilizes monthly time-series data from January 2005 to June 2022 and employs the Autoregressive Integrated Moving Average (ARIMA) intervention model to analyze the effects of six withholding tax interventions on financial inclusion.Findings: The results indicate that withholding tax interventions generally reduced financial inclusion in Pakistan. Specifically, withholding tax increases in 2008 and 2015 reduced the private sector deposit ratio and increased currency in circulation, while a tax reduction in 2012 temporarily improved financial inclusion. However, subsequent reductions in 2018 and 2021 again led to a decline in financial inclusion, suggesting that such interventions either had a negative impact or were irrelevant to financial inclusion.Implications/Originality/Value: The findings of this study highlight the ineffectiveness of withholding tax on banking transactions as a tool for enhancing financial inclusion—with implications for fiscal policy in Pakistan and other emerging economies such as Argentina and India. The study suggests that the finance divisions of these countries should reconsider the implementation of banking transaction taxes, as they may hinder progress toward sustainable development goals.
... The ARIMA (AutoRegressive Integrated Moving Average) model was initially formulated by Box & Jenkins (1976). In recent decades, the ARIMA model and its derivatives have been extensively employed, predominantly attributed to their mathematical simplicity and adaptable applicability. ...
The urgent need to address global climate change and promote sustainable development highlights the growing demand for renewable energy sources. Solar energy, in particular, holds significant importance due to its widespread availability and environmentally friendly characteristics. For Azerbaijan, a country dedicated to sustainable development and actively contributing to environmental conservation efforts, renewable energy assumes a central role in its strategic agenda. The objective of this study is to evaluate the historical trajectory of solar energy production in Azerbaijan over the past decade and forecast its future trends until 2030. Utilizing the Autoregressive Integrated Moving Average (ARIMA) model, this study utilizes time series analysis to examine the overall development trends within the solar energy sector. By analyzing past data and using forecasting model, this research endeavors to offer valuable insights to guide policy decisions and strategic planning initiatives concerning renewable energy development in Azerbaijan ABSTRACT JEL Classification: C22, F64, O44, Q20, Q42, Q56.
... In the equation four ∆ = --1. But if p = q = 0, then the model become a random walk form and classified as ARIMA (0, 1, 0).(Jenkins & P, 1976) Box-Jenkins ApproachTo determine which parameter of the time series model is fitted for the historical values of a given time series perfectly, statisticians George Box and Gwilym Jenkins developed theBox-Jenkins (1970) technique, which uses ARIMA models. The Box-Jenkins analysis is a systematic method for detecting, fitting, approving, and applying the ARIMA time series model. ...
The basic economic condition of a country is measured and presented by Gross Domestic Product (GDP). Government’s high officials, Business owners or managers, rely on forecasting of GDP, to determine fiscal year monitory policy and operating activities. This paper has collected GDP data from 1971 to 2021 from an international website. Exploratory analysis has performed for trend, seasonality & outlier detection. Augmented Dickey-Fuller test, Phillip Peron and Kwiatkowski-Phillips-Schmidt-Shin test has performed to check seasonality and stationary. To determine the best fitted model for GDP, ARIMA models (Autoregressive integrated Moving Average) have constructed using Box-Jenkins technique. Considering all statistical criterions this paper has determined ARIMA (4, 2, 1) isthe best fitted model and forecasted for the next ten years. Finally, residual test has performed to determine reliable forecasting.
... While stationarity is important to the predictability of time series (Kim et al. 2021;Liu et al. 2022), real-world series always present non-stationarity. To tackle this problem, the classical statistical method ARIMA (Box 1976) stationarizes the time series through differencing. As for deep models, since the distribution-varying problem accompanied by nonstationarity makes deep forecasting even more intractable, stationarization methods are widely explored and always adopted as the pre-processing for deep model inputs. ...
The forecasting of Multivariate Time Series (MTS) has long been an important but challenging task. Due to the non-stationary problem across long-distance time steps, previous studies primarily adopt stationarization method to attenuate the non-stationary problem of original series for better predictability. However, existed methods always adopt the stationarized series, which ignore the inherent non-stationarity, and have difficulty in modeling MTS with complex distributions due to the lack of stochasticity. To tackle these problems, we first develop a powerful hierarchical probabilistic generative module to consider the non-stationarity and stochastity characteristics within MTS, and then combine it with transformer for a well-defined variational generative dynamic model named Hierarchical Time series Variational Transformer (HTV-Trans), which recovers the intrinsic non-stationary information into temporal dependencies. Being an powerful probabilistic model, HTV-Trans is utilized to learn expressive representations of MTS and applied to the forecasting tasks. Extensive experiments on diverse datasets show the efficiency of HTV-Trans on MTS forecasting tasks.
... A process-driven model, such as conceptual rainfall runoff, explains how watershed systems work (Sudheer et al. 2002). Using simple mathematical methods and intelligent algorithms, data-driven models forecast future streamflow without analyzing physical processes (Box and Jenkins 1976). ...
The growing population and the rise in urbanization have made managing water a critical concern around the world in recent years. Globally, flooding is one of the most devastating natural disasters. Flood risk mitigation relies heavily on accurate and consistent streamflow forecasts. Pakistan Upper Indus Basin (UIB) is most vulnerable to flooding. Floods have become more frequent in recent decades. UIB can be divided into sub-regions due to its landscape variability, and its collective impact is most prominent in the Massam region. UIB hydrological and meteorological station observations have been used to study seasonal hydro-meteorological variations. To predict flooding, this study proposes a hybrid model combining artificial neural networks as multi-layer perceptron (MLPs) in feed-forward mode, along with empirical mode decomposition (EMD). Data collected by the surface-water hydrology project and Pakistan Meteorological Department from 1960 to 2012, 1969 to 2012, and 1972 to 2012 have been utilized from 17 locations. Statistical parameters and Nash–Sutcliffe Efficiency were measured to analyze the model’s prowess. As a result, decomposition-based models perform better than AI-based models when it comes to prediction accuracy. MLPQTP-EMD performed exceptionally better than competing AI models. The results are further validated by performing a peak value analysis during the flooding season (June–September) achieving a remarkable 91.3% score adding a 5.6% increase by EMD for input data achieving 39.3–32.3% statistical indices scores.
... The ARIMA model considers the parameterization of the time series through the identification of the autoregressive level, the moving average and the order of integration. Starting from the fact of working with strictly stationary series, the Dickey-Fuller test was previously carried out to identify the differentiation order that will allow working with stationary series [9,10]. The specification of the ARIMA model is presented in Eq. 1. ...
This manuscript addresses the problem of forecasting the demand for innovative products with limited and inhomogeneous sales data over time. The main objective of the study is to use the information available from a group of innovative chlorophyll-based food products to build a coherent demand forecasting system. From a transactional database, time series were constructed for each group of products, analyzing the stationarity and seasonality of the time series through the Dickey–Fuller and Canova–Hansen tests. Likewise, an ARIMA model, a long short-term memory (LSTM) recurrent deep neural network, and a support vector machine (SVM) were trained to select the best model for each product based on a forecast performance metric. A comparison between classical forecasting techniques and machine learning models is shown. The LSTM neural network was the best model for most products because the internal architecture of the network allows not only to capture non-linear relationships between variables but is also capable of controlling the flow of information to preserve characteristics over time that are relevant for forecasts. The second-best model was the SVM, which allows capturing non-linear behaviors through kernel functions and uses a smaller amount of data for its estimation. Finally, the ARIMA model presented the lowest performance for all products. The objective of having various methodologies is that the system allows the best forecast to be selected according to the type of product, availability of information and methodology used, which will allow the company to integrate new products into the system over time.
... The autocovariance function for a stationary autoregressive process of Order , is given by (Box-Jenkins, 1976) as The autocorrelation function of the process is given by ...
This paper assessed comprehensively and systematically the predictive capabilities of the Nigerian Monthly Crude Oil Production forecasting models. To obtain the generality of the empirical results, ARIMA model was used. Some of the frequently used measures of forecast adequacy such as Mean Error (ME), Mean Absolute Error (MAE), Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) were used to evaluate the forecast performance of the chosen models. This study reveals the fact that ARIMA (1, 1, 1) model is the best or optimal model for the period forecasted. The study fitted an appropriate time series models of crude oil production in Nigeria (2005-2022) which provided a useful forecast for quantity of crude oil production and export for the purpose of making reliable budget for the sustenance of the economy. This study reveals the fact that ARIMA (1, 1, 1) model is the best or optimal model for the period forecasted.
Spatial and temporal variation in precipitation over varying seasons impacts multiple parameters. Examining the fluctuations and alterations in rainfall patterns across diverse spatial scales and the identification of trends in rainfall have been fundamental areas of interest in the varying fields globally. Trend analysis helps in comprehending past and current changes in climatic conditions, yet forecasting future scenarios is of immense value to decision-makers, enabling them to make informed decisions by considering anticipated variations in climate variables, such as Precipitation. Despite having various stochastic and statistical models, reliable rainfall forecasting remains a back-breaking issue. This study attempts to model and forecast SWM rainfall (June-September) for the Kutch district over the next 15 years. A five-year moving average of long-term IMD gauge station gridded annual rainfall data (0.25 × 0.25 degree) from 1961 to 2018 has been used. The ADF statistical test was applied to assess the stationarity of the series. A forecast using the univariate ARIMA (2,0,0) model indicates that there is a marked fall in SWM rainfall in upcoming years over the Kutch district, where the mean has fallen by −20.33%. The best fit ARIMA (p, d, q) model for sub-divisions; Abdasa (1,0,0), Anjar (2,0,2), Bhachau (4,0,0), Bhuj (2,0,2), Gandhidham (2,0,1), Lakhpat (5,0,0), Mandvi (2,0,2), Mundra (2,0,2), Nakhatrana (2,0,2) and Rapar (2,0,1). The mean (forecast) for all the Subdivisions has been reduced except Nakhatrana and Lakhpat have slightly increased by 0.60% and 0.29%, respectively.
The study focuses on a detailed assessment of artificial light pollution in three major cities of Gujarat: Ahmedabad, Surat, and Vadodara for year 2014 to 2023. Night light pollution, resulting from the excessive directed use of artificial lighting, is a pressing environmental issue with far-reaching implications. The findings of this study are expected to offer valuable insights into the extent and nature of light pollution in these cities. The research includes the calculation of average night light radiation for urban areas. By employing the Mann Kendall and Sen's Slope, this research also aims to identify trends and patterns in night light pollution over the study period. Moreover, by employing the ARIMA and SARIMA model, this research also aims to identify trends and patterns as well as forecasting in night light pollution for 2024. Vadodara, Ahmedabad, and Surat exhibit distinct seasonal patterns in night light radiance, characterized by peaks during winter and troughs during the monsoon season , influenced by local environmental and climatic factors. From 2014 to 2023, all three cities show a consistent upward trend in radiance, with significant seasonal fluctuations observed from July to September due to monsoonal cloud cover. Surat, in particular, maintains relatively stable radiance levels but experiences reduced trends in July and September. These findings underscore the interplay between seasonal variability and long-term growth, highlighting the severity of light pollution in urban areas and emphasizing the need for data-driven interventions to inform urban planning and resource management strategies.
The UK retail landscape has undergone significant changes over the past decade, driven by factors such as the rise of online shopping, economic downturns, and, more recently, the COVID-19 pandemic. Accurately measuring pedestrian flows in retail areas with high spatial and temporal resolution is essential for selecting the most appropriate forecasting model for different retail locations. However, several studies have adopted a one-size-fits-all approach, overlooking important local characteristics that are only occasionally captured by the best global model. In this work, using data generated by the SmartStreetSensor project, a large network of sensors installed across UK cities that collect Wi-Fi probe requests generated by mobile devices, we examine the optimal forecasting method to predict pedestrian footfall in various retail areas across Great Britain. After assessing six representative time series forecasting models, our results show that the LSTM model outperforms traditional methods in most areas. However, pedestrian counts at certain locations with specific spatial characteristics are better forecasted by other algorithms.
The prediction of energy consumption is important for the efficient operation of building air-conditioning systems. Most predicted models are based on historical energy consumption data and the factors influencing air conditioning systems, including weather, time of day, and previous consumption. However, the traditional prediction models, such as the Autoregressive Integrated Moving Average (ARIMA) time series model and back propagation (BP) neural network model, show large errors in their prediction of the energy consumption of air-conditioning systems. To achieve better prediction, the Long Short-Term Memory (LSTM) model of deep learning is adopted in this study based on an air-conditioning system of a University Library in Guangzhou. The results demonstrate that the LSTM model can produce more reliable predictions. The daily energy consumption forecast reduced by 11.2 % compared to that of the Autoregressive Moving Average model (MAPE). The hourly energy consumption forecast reduced by 16.31 %. In addition, compared with the BP neural network model, the MAPE’s daily energy consumption prediction reduced by 49 % and the hourly energy consumption prediction reduced by 36.61 %.
Monitoring crop production has a direct effect on national and global economies and plays a significant role in food security. This study creates a possible autoregressive integrated moving average (ARIMA) model that can estimate the past (2010 to 2022) and future trends (2023 to 2035) for cultivated cropland and fertilizer consumption and their effects on rice and wheat production. The study results demonstrated past and future trends for different variables such as cultivated cropland, fertilizer consumption and rice, and wheat production over time. Based on the ARIMA model analysis, a 2.4% and 113% total reduction in cropland and fertilizer consumption over the next 13 years respectively was predicted. Over the next 13 years, the production of major crops, specifically rice and wheat, is expected to increase by 12.4% and 25.9%, respectively. However, the multiple linear regression model showed a significant change for dependent variables such as cropland and fertilizer consumption, with R² values of 61% and 74%, respectively, for rice and wheat production. The predictive results from the ARIMA model analysis possibly showed an increasing trend for estimating crop yields, with a minor change in cultivated cropland and highly decreased fertilizer consumption. These results highlight that higher crop production can be achieved with less cropland and with minor fertilizer inputs.
Traffic prediction is a pivotal component of intelligent transportation systems (ITS), which can provide effective support for traffic planning and management. Recently, graph convolutional networks (GCNs) have been proposed to model intricate spatio-temporal correlations. However, most GCNs use static graphs, which fail to capture dynamic spatial correlations due to sensor damage. A few studies based on dynamic graph neural networks can model such dynamics but struggle to capture long-term spatio-temporal dependencies because they mainly focus on local and short-term changes in the graph. To overcome these limitations, we propose a time-varying fuzzy graph convolutional network called TFGCN that combines dynamic and static graphs to predict multi-sensor traffic flow. TFGCN uses a gated fuzzy graph to model long-term dynamic spatial correlations adaptively. It also employs a periodic coupled Transformer network that integrates monthly and weekly periodic data to capture global temporal trend information. Extensive experiments conducted on two real-world datasets demonstrate that our proposed model outperforms several state-of-the-art baselines.
Developing feasible study designs that minimize the number of participant responses while retaining acceptable statistical properties has been a challenge in psychological research, thus motivating the developments and use of planned missing designs in longitudinal panel studies. In this study we propose several planned missingness designs for experience sampling/ecological momentary assessment (EMA) studies and evaluate the statistical implications and trade-offs involved in reducing the number of data points collected per person. We consider change trajectories arising from the latent growth curve, multilevel, and time series contexts. A Monte Carlo simulation study revealed that factors such as the type of change trajectory and the placement of data points can greatly affect the estimation results even when the number of time points is held constant. Traditional growth curve models and an autoregressive time series model of order 1 worked well with most planned missingness designs, while a moving average time series model of order 1 required a more careful selection of the planned missingness scheme. Findings also revealed that most planned missingness designs were robust to identifying correctly specified models provided that the correct time intervals are used, thus providing enriched options for researchers and practitioners to collect fewer data points with negligible costs to statistical power.
India is poised to reach the ambitious target of becoming a USD 5 trillion economy by 2027 and become the third largest economy of the world by 2032. This trajectory is fuelled by a youthful population, a burgeoning middle class, and robust digital infrastructure. Indian Prime Minister, Narendra Modi, has built his global image with political astuteness, emphasising multilateralism and the rule of law. However, in a world, where nationalism, egotism and authoritarianism are on the rise, India faces a challenging task as a global leader in maintaining world peace, contain global wars and coax others countries to play by the book. India may need to recalibrate its foreign policy in order to align its global political ambitions with its growing economic targets. This paper looks at the factors that have contributed to India's economic growth and its growing international stature. ARIMA (Auto-Regressive Integrated Moving Average) technique has been applied to forecast the GDP growth rates of India until 2035. India is projected to reach a GDP of USD 7 trillion during this period. The paper concludes that with economic growth, India is also likely to increase its influence as a global leader.
Tujuan dari penelitian ini adalah untuk mengetahui pengaruh harga broiler dan harga jagung terhadap harga karkas dengan menerapkan analisis Vector Autoregressive (VAR) serta menerapkan metode VAR dengan ditambahkan calendar effects (VAR-X) dan jika data tidak stasioner pada level dan terdapat kointegrasi maka digunakan vector error correction model (VECM-X). Hal ini didasarkan pula pada pertimbangan untuk melihat apakah ada perbedaan harga ketika terdapat kejadian hari raya tertentu dan hari biasa. Hasil analisis dengan VECM pada lag 13 untuk harga karkas menyatakan bahwa terdapat beberapa hubungan kausalitas, diantaranya harga broiler mempengaruhi harga karkas. Hari-hari khusus seperti awal tahun, akhir tahun, awal Ramadhan, idul fitri dan idul adha mempengaruhi harga karkas. Sedangkan harga jagung tidak mempengaruhi harga karkas. Uji kelayakan model menunjukkan hasil bahwa sisaan model VECM bersifat whise noise pada tingkat kepercayaan 95%. Oleh karena itu dapat disimpulkan bahwa model VECM layak digunakan.
In the past three decades, GNSS-based Integrated Water Vapor (IWV) retrieval has been intensively investigated, and its products have been widely used in meteorology like severe weather event monitoring. The physical model for the inversion of IWV from the tropospheric Zenith Total Delay (ZTD) requires meteorological data at the location of the GNSS station, such as the surface pressure and the atmospheric weighted mean temperature. However, real-time acquisition of the meteorological data is a very challenging task for most GNSS stations. While proposed empirical models such as Global Pressure and Temperature 3 (GPT3) can provide the meteorological data based on their historical information, larger estimation distortions are found in specific mid- and high-latitude regions. Moreover, we analyzed the seasonal variations in GPT3 prediction errors. In view of the above-mentioned problems, this study implements an IWV conversion model based on a feedforward Deep artificial Neural Network (DNN) and Long Short-Term Memory Network (LSTM) network, which learns historical data from GNSS stations and allows real-time ZTD to IWV conversion without the need of actual meteorological observation but of values only GPT3. Results at four selected mid- and high-latitude GNSS stations show that the Root Mean Square Error (RMSE) of the proposed deep learning method decreases from an average of 3.97 mm to 2.84 mm compared to GNSS IWV retrieved from GPT3. The proposed model provides a broad applicability in real-time GNSS IWV prediction without the availability of real-time measured meteorological data.
Background: Buffalo milk production in India plays a significant role in the global dairy market, with a rich history deeply intertwined with the country's economy and culture. Over six decades, the dynamics of buffalo farming have been pivotal in shaping India's dairy landscape.
Methods: This paper delves into the subject by analysing a comprehensive time series dataset spanning six decades. The focus lies on understanding the economic and cultural significance of buffalo farming, particularly in relation to milk production. Four forecasting models-ARIMA, SES, Seasonal Naive and ETS-are employed to discern temporal patterns in buffalo milk production.
Result: The study reveals that the ARIMA and ETS models outperform SES and Seasonal Naive models in capturing and elucidating data behaviour. Their superior performance underscores their efficacy in predicting buffalo milk production trends accurately. These findings offer valuable insights for policymakers and stakeholders aiming to optimize buffalo milk production and foster long-term growth in India's dairy sector.
Tuberculosis remains a global health challenge, predicting its incidences is crucial for effective planning and intervention strategies. This study combines AutoRegressive Integrated Moving Average (ARIMA) and Nonlinear AutoRegressive with exogenous input (NARX) models as an innovative approach for TB incidence rate prediction. The performance of the proposed model (ARIMA-NARX) was evaluated using standard metrics (MSE, RMSE, MAE, and MAPE), and it was refined to achieve the best average predictive accuracies with an MSE: 0.0622, RMSE: 0.0851, MAE: 0.07520, and MAPE: 0.05535 followed by NARX 0.1597, 0.3189, 0.2724, and 0.3366, and ARIMA (2,0,0) 0.7781, 0.5959, 0.6524, and 0.6080 Models. These findings are expected to shed light on the TB incidence rate, providing valuable information to policymakers such as the World Health Organization (WHO) and health professionals. The developed model can potentially serve as a predictive tool for proactive TB control and intervention strategies in the region and the world at large.
Usando-se um modelo padrão da literatura de macroeconomia, este artigo avalia qual é o ganho de bem-estar para o Brasil da suavização do ciclo econômico. Nosso procedimento segue a proposta de Lucas (1987) de decompor o consumo agregado em uma parte que representaria a sua tendência e outra que representaria o seu ciclo. Para estimar estes dois componentes do consumo, usa-se aqui um modelo econométrico baseado numa representação estado-espaço para a renda e o consumo, levando em conta o fato de que renda e consumo têm que obedecer uma relação de longo prazo pela Teoria da Renda Permanente, e uma relação de curto prazo caso haja restrições à liquidez. Ambas as relações são testadas empiricamente. A partir das estimativas para o ciclo e a tendência do consumo, calcula-se quanto o consumidor representativo deve ser compensado para ser indiferente entre a sequência de consumo observada e uma sequência modificada onde o ciclo é suavizado. Os resultados apontam para um ganho de bem-estar pequeno da suavização do ciclo econômico para o Brasil, o que é consistente com os resultados da literatura empirica de macroeconomia para o Brasil. Uma decomposição idêntica é implementada para os EUA de forma a comparar os resultados.
Forecasting mortality is challenging. In general, mortality rate forecasting exercises have been based on the supposition that predictors’ residuals are random noise. However, issues regarding model selection, misspecification, or the dynamic behavior of the temporal phenomenon lead to biased or underperformed single models. Residual series might present temporal patterns that can still be used to improve the forecasting system. This paper proposes a new recursive direct multi-step Hybrid System for Mortality Forecasting (HyS-MF) that combines the Autoregressive Integrated Moving Average (ARIMA) with Neural Basis Expansion for Time Series Forecasting (N-BEATS). HyS-MF employs (i) ARIMA to model and forecast the mortality rate time series with a recursive approach and (ii) N-BEATS with the direct multi-step approach to learn and forecast the residuals of the linear predictor. The final output is generated by summing ARIMA with the N-BEATS forecasts in each time horizon. HyS-MF achieved an average Mean Absolute Percentage Error (MAPE) less than 1.34% considering all prediction horizons, beating statistical techniques, machine learning, deep learning models, and hybrid systems considering 101 different time series from the French population mortality rate.
Next-generation wireless network aims to support low-latency, high-speed data transmission services by incorporating artificial intelligence (AI) technologies. To fulfill this promise, AI-based network traffic prediction is essential for pre-allocating resources, such as bandwidth and computing power. This can help reduce network congestion and improve the quality of service (QoS) for users. Most studies achieve future traffic prediction by exploiting deep learning and reinforcement learning, to mine spatio-temporal correlated variables. Nevertheless, the prediction results obtained only by the spatio-temporal correlated variables cannot reflect real traffic changes. This phenomenon prevents the true prediction variables from being inferred, making the prediction algorithm perform poorly. Inspired by causal science, we propose a novel network traffic prediction method based on self-supervised spatio-temporal causal discovery (SSTCD). We first introduce the Granger causal discovery algorithm to build a causal graph among prediction variables and obtain spatio-temporal causality in the observed data, which reflects the real reasons affecting traffic changes. Next, a graph neural network (GNN) is adopted to incorporate causality for traffic prediction. Furthermore, we propose a self-supervised method to implement causal discovery to to address the challenge of lacking ground-truth causal graphs in the observed data. Experimental results demonstrate the effectiveness of the SSTCD method.
Petroleum production forecasting involves the anticipation of fluid production from wells based on historical data. Compared to traditional empirical, statistical, or reservoir simulation-based models, machine learning techniques leverage inherent relationships among historical dynamic data to predict future production. These methods are characterized by readily available parameters, fast computational speeds, high precision, and time–cost advantages, making them widely applicable in oilfield production. In this study, time series forecast models utilizing robust and efficient machine learning techniques are formulated for the prediction of production. We have fused the two-stage data preprocessing methods and the attention mechanism into the temporal convolutional network-gated recurrent unit (TCN-GRU) model. Firstly, the random forest (RF) algorithm is employed to extract key dynamic production features that influence output, serving to reduce data dimensionality and mitigate overfitting. Next, the mode decomposition algorithm, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), is introduced. It employs a decomposition–reconstruction approach to segment production data into high-frequency noise components, low-frequency regular components and trend components. These segments are then individually subjected to prediction tasks, facilitating the model’s ability to capture more accurate intrinsic relationships among the data. Finally, the TCN-GRU-MA model, which integrates a multi-head attention (MA) mechanism, is utilized for production forecasting. In this model, the TCN module is employed to capture temporal data features, while the attention mechanism assigns varying weights to highlight the most critical influencing factors. The experimental results indicate that the proposed model achieves outstanding predictive performance. Compared to the best-performing comparative model, it exhibits a reduction in RMSE by 3%, MAE by 1.6%, MAPE by 12.7%, and an increase in R2 by 2.6% in Case 1. Similarly, in Case 2, there is a 7.7% decrease in RMSE, 7.7% in MAE, 11.6% in MAPE, and a 4.7% improvement in R2.
This section introduces time series data mining tasks in the sport domain. One of the aspects that are described is the discovering of events or detecting anomalies. These event discovery tools can be applied to time series sport data, for example, for recognition of player activities. Recognizing activities such as passing, shooting, or dribbling in soccer may be quite useful to provide insights into the team’s behavior, which could be also helpful to support decision making in training. Both time series data mining and concepts developed in sport science can go hand in hand to design meaningful analysis.
Accurate performance prediction of cloud workloads is essential for optimizing resource allocation, meeting service level agreements (SLAs), and ensuring efficient cloud service delivery. In this research paper, we conduct a comparative analysis of the ARIMA (Auto Regressive and Integrated Moving Average) time series model with other popular techniques for cloud workloads performance prediction. We evaluate the performance of ARIMA in comparison with other models, including machine learning algorithms and statistical methods, using real-world cloud workload performance data.
This paper defines the unit Burr XII autoregressive moving average (UBXII-ARMA) model for continuous random variables in the unit interval, where any quantile can be modeled by a dynamic structure including autoregressive and moving average terms, time-varying regressors, and a link function. Our main motivation is to analyze the time series of the proportion of stored hydroelectric energy in Southeast Brazil and even identify a crisis period with lower water levels. We consider the conditional maximum likelihood method for parameter estimation, obtain closed-form expressions for the conditional score function, and conduct simulation studies to evaluate the accuracy of the estimators and estimated coverage rates of the parameters’ asymptotic confidence intervals. We discuss the goodness-of-fit assessment and forecasting for the new model. Our forecasts of the proportion of the stored energy outperformed those obtained from the Kumaraswamy autoregressive moving average and beta autoregressive moving average models. Furthermore, only the UBXII-ARMA detected a significant effect of lower water levels before 2002 and after 2013.
Lawrence R. Klein murió a los 93 años, el 20 de octubre de 2013. Su vida profesional ha sido larga y fructífera. Se mantuvo muy activo hasta los 87 años y el autor de este trabajo ha sido testigo directo de ello. Ha sido para él, maestro, mentor y amigo, y la colaboración de los dos se ha mantenido a lo largo de más de cuarenta años. Desde el punto de vista de la economía y de la econometría la carrera de Klein ha sido larga y variada, habiendo trabajado en áreas muy diversas. Como su vida y su obra son muy conocidas, en este trabajo, hecho en su homenaje, se hace referencia a lo que ha sido su última etapa de trabajo, muy relacionada con los modelos econométricos de Alta Frecuencia y con el mantenimiento del Proyecto LINK como un modelo de referencia de predicción económica mundial. Se combina la explicación del papel que tiene la econometría en nuestro mundo avanzado con algunos aspectos técnicos relacionados con las áreas de actividad mencionadas y con lo que podría ser una próxima etapa de evolución de esta disciplina.
The objective of this study is to predict unemployment in Indonesia in the wake of the demographic dividend. The sample used in this study is the unemployment data from 1990 to 2022 from the Indonesian Central Bureau of Statistics database. Using non-seasonal ARIMA (Autoregressive Integrated Moving Average) modeling, this study projected unemployment. It was predicted using six alternative models. With a mean absolute percent error (MAPE) of 9.56% (MAPE ≤10%), the predictions were quite accurate. It indicates that the ARIMA model has a good forecasting capability. According to the dynamic method’s unemployment projection, there will be less unemployment between 2023 and 2050. For Indonesia, maximizing the demographic dividend is both a challenge and an opportunity presented by the decline and stable number in unemployment. The demographic dividend will cause a substantial increase in employment and the creation of various new jobs. Several factors will support the demographic dividend. Thus, it could help governments to make decisions on labor issues. It also highlights a policymaker’s direction to pursue labor development, including employment trends.
Air pollution can have detrimental effects on human health as well as the environment. Particulate Matter (PM), as a global issue, is a type of air pollution that consists of small particles suspended in the air. Therefore, it is crucial to estimate and monitor levels of PM in the air in order to protect public health and the environment. This study proposed a novel hybrid method to apply the capability of two various deep learning models, namely, the encoder-decoder convolutional neural network and the Long Short-Term Memory (LSTM) model for PM10 prediction. The first model was utilized as a data argumentation method to enhance dataset diversity, and the LSTM model employed meteorological parameters and spatiotemporal factors to estimate the PM10 levels. The proposed technique achieved performance resulting in a coefficient of determination value of 0.88 and a mean absolute error value of 7.24. The results confirm that the developed hybrid method as an effective tool of PM prediction can be used to inform decision-making about policies and actions to reduce PM levels.
The forecast of electricity consumption is very important for the energy planning of a country, company, or region. The interest in electricity consumption projections is related, in general, to the financial impact that energy distribution can generate, which can cause immense losses. In this work, we propose a methodology using the bottom-up approach through time series models and cluster analysis to obtain the prediction of electricity consumption. Energy efficiency measures were included in the methodology to evaluate the electric energy savings. In particular, this methodology was applied to electricity consumption data from the Federal Rural University of Rio de Janeiro (UFRRJ). The results show that the proposed methodology presented an average absolute percentage error of approximately 1%. In addition, it showed great potential for reducing the consumption of electricity at UFRRJ for the implementation of energy efficiency measures.
ResearchGate has not been able to resolve any references for this publication.