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Autoregressive Conditional Heteroscedasticity With Estimates of the Variance of United Kingdom Inflation
... There are two main factors that are discussed in the literature that determine the composition of a portfolio. These two factors are in line with observations by Engle (1982) about the determinants of portfolio decisions, which are the mean return of a portfolio and the variance of a portfolio. Black and Litterman (1992) outline that from an investor's view, the objective of appropriate asset allocation is to maximize expected return for a given level of risk. ...
... This allows us to determine the stability of our estimated optimal portfolio weights. To estimate the volatility of real returns, we estimate a non-constant variance which is conditioned on past information such as that presented by Engle (1982), namely the Autoregressive Conditional Heteroscedasticity (ARCH) model and Bollerslev's (1986) Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. For the purposes of our analysis, we only test for linear ARCH and GARCH effects on the real returns rather than examine the extensive volatility measures which would constitute as another research question. ...
... To model the thick tails in the estimated white noise we follow the work of Brenner et al. (1996) and Koedijk et al. (1997). They employ the autoregressive conditional heteroscedastic (ARCH) model suggested by Engle (1982) and Bollerslev (1986). In addition, they keep the dependence of the conditional variance on the leverage of short term rates as in the diffusion coefficient of SDE model (7.1). ...
The global economy experienced a worldwide meltdown of asset markets in the
years 2007–2009. This posed great challenges for asset and portfolio managers.
Many funds such as university endowments, sovereign wealth funds, and pension
funds were overexposed to risky returns and suffered considerable losses. On the
other hand, the long-run upswing in the stock market since 2010, induced by a
monetary policy of quantitative easing in the USA, and later in Europe and Asia,
led to asset price booms and new wealth formation. In both cases quite significant
differences in asset management and wealth accumulation were visible. Our book
aims at dealing with sustainable wealth formation and dynamic decision making.
We have three perspectives in mind.
A first perspective is how wealth formation and the proper management of
financial funds can help to buffer income risk sufficiently and to obtain adequate
risk-free income at a later stage of life. This is an important concern in the current
public debate on asset accumulation and wealth disparity. In whatever institutional
form saving takes place, in mutual funds, public pension funds, corporate pension
funds, or private saving accounts, the generic issue is how much to save and invest
and how to make proper asset allocation decisions.
A second important issue for sustainable wealth accumulation is that many
agents and institutions in financial markets tend to put some constraints on the
accumulation and allocation of assets—following some rules, guidelines and restrictions concerning risk-taking, safeness of investments, as well as social, ethical,
environmental, and climate change aspects. Thus investments are often restricted
to certain risk classes, classes of assets or particular assets. Much investment and
asset allocation decisions are therefore made following behavioral and institutional
rules, responding to some given constraints and guidelines, without necessarily
being optimal in the narrow sense.
A third perspective of sustainable wealth formation is that we want to move more
toward dynamic decision making and dynamic re-balancing of portfolios. Portfolio
decisions are frequently modeled as static decisions problems. Yet, how should the
investors respond to expected future returns, changing return differentials, global or
idiosyncratic risk, change of inflation rates, affecting the real value of their assets,
and so on? In standard literature, the modeling of savings and wealth accumulation
are often separated from asset allocation decisions. We pursue a simultaneous and
dynamic treatment of both savings behavior and portfolio decision making, taking
into account expected returns. Expected returns are evaluated here, using a new
method—harmonic estimations of returns.
In order to solve such dynamic decision problems in portfolio theory and
portfolio practice—solving saving as well as asset accumulation problems
simultaneously—we put forward dynamic programming as a procedure for dynamic
decision making that allows to integrate sustainable wealth accumulation as well as
asset allocation decisions. Although some shortcomings of this procedure exist, a
careful use of it can help to not only undertake dynamic modeling but also aid online
decision making once some pattern of expected returns of different asset classes,
for example estimated through using harmonic estimations, has been recognized.
The book is written in a way that it can be used by researchers and in graduate
classes on financial economics, asset pricing and portfolio theory, finance and
macro, portfolio theory and practice, pension fund theory and management, socially
responsible investment decisions, financial market and wealth disparities, methodology of dynamic portfolio theory, intertemporal asset allocation and households’saving, and applied dynamic programming.
Parts of the book are based on lectures delivered at the University of Bielefeld,
Germany, the University of Technology, Sydney, Australia, The New School for
Social Research, New York City, USA, and University of Economics, Vienna,
Austria, as well as conferences and workshops at the ZEW, Mannheim, Germany.
We are very grateful to our colleagues at those institutions as well as to several
generations of students who took our classes in this area and gave comments on
these lectures in their formative stages. We are also grateful for discussions with
Hans Amman, Lucas Bernard, Raphaele Chappe, Peter Flaschel, Lars Gruene,
Stefan Mittnik, Unra Nyambuu, Eckhard Platen, and James Ramsey.
Individually, many of the chapters of the book have been presented at conferences, workshops, and seminars throughout the United States, Europe, and
Australia. Many chapters of this book are also based on previous article by the
authors, published with a variety of different coauthors. Each chapter acknowledges
the particular coauthors involved, and a general acknowledgment can be found
below.
In preparing this manuscript, we in particular relied on the help of Tony Bonen
and Uwe Koeller whom we want to thank for extensive assistance in editing this
volume. Willi Semmler wants to thank the Fulbright Foundation for a Fulbright
Professorship at the University of Economics, Vienna, in the Winter Term 2011, as
well as the German Research Foundation for financial support.
... Selain itu, pendekatan metodologis dalam memperkirakan volatilitas saham serta korelasinya masih heterogen. Beberapa penelitian menggunakan model GARCH untuk menganalisis volatilitas (Engle, 1982;Bollerslev, 1986), dan penelitian lainnya menggunakan DCC-GARCH untuk mengamati pergeseran korelasi antar saham selama periode pandemi (Engle & Sheppard, 2001). Oleh karena itu, diperlukan penelitian yang lebih spesifik dan komprehensif dengan pendekatan kuantitatif yang relevan untuk mengetahui pola arah pergerakan saham perbankan Indonesia sebelum dan di awal pandemi. ...
... Yarovaya, Elsayed, & Hammoudeh (2022) melaporkan sebuah studi yang menggunakan pendekatan ketergantungan jaringan dan entropi transfer untuk memeriksa fenomena penularan di pasar saham selama pandemi COVID-19. Selain itu, Engle (1982) dan Bollerslev (1986) memperkenalkan model heteroskedastisitas bersyarat (ARCH dan GARCH) yang tetap populer untuk estimasi volatilitas pasar. Meningkatnya volatilitas pasar, beberapa penelitian meneliti mata uang kripto sebagai aset safe haven. ...
Penelitian ini mengkaji return volatility lima saham bank di Indonesia, yaitu BBCA, BBNI, BBRI, BMRI, dan BJBR menggunakan alaisis korelasi dan analisis Komponen Utama (PCA) untuk mengetahui korelasi dan struktur varians pada data saham perbankan. Hasil penelitian menunjukan return saham BBCA, BBNI, BBRI, BMRI stabil mengikuti tren volatilitas dalam kisaran -0,1 hingga 0,1 sedangkan BJBR lebih volatil. Saham BBCA, BBNI, BBRI, dan BMRI berkorelasi tinggi dengan nilai korelasi diatas 0,6. Korelasi BJBR 0,4 dengan saham-saham bank besar lainnya di bawah 0,4. Hasil Principal Component Analysis (PCA) menunjukkan bahwa komponen PC1 berpengaruh signifikan sebesar 66,04% terhadap trend keseluruhan pasar saham perbankan. PC2 sebagai faktor khusus untuk BJBR, berbeda secara signifikan dari yang lain dengan nilai PC2 yang tinggi 0,95. Hal ini menunjukkan bahwa BJBR memiliki komponen khusus yang tidak terkait dengan saham bank besar lainnya, seperti atribut bisnis yang lebih lokal atau fokusnya yang berbeda dalam strategi perbankan.
... The ARCH and the GARCH models formulated by Engle (1982) and Bollerslev (1986), respectively are used to study volatility clustering and model uncertainty accordingly. Generally the GARCH model is specified in terms of two equations namely the conditional mean equation (ARMA), and conditional variance equation. ...
... Therefore GARCH model is considered with first difference of the log of real exchange rate (growth rate of real exchange rate). Before fitting the GARCH process, we have tested the presence of ARCH process (volatility clusters) using Lagrange Multiplier (LM) ARCH test [Engle (1982)] and serial correlation in using Ljung-Box Q-Stat. The results presented in Appendix confirm the presence of significant ARCH effects and serial correlation in data. ...
This study analyses the effect of political stability and macroeconomic uncertainty on aggregate investment behaviour in Pakistan over the period 1960–2015. The Auto-Regressive Distributed Lags (ARDL) methodology is applied to explore both the long-run equilibrium relationship and short-run behaviour of investment. The macroeconomic uncertainty variable is derived from real exchange rate and is computed by the best-fitted GARCH model. The results reveal robust effects of political stability and macroeconomic uncertainty on overall investment activity in Pakistan. The government nationalisation policy, GDP growth, user cost of capital, credit availability and degree of openness are found to be the other key determining factors for investment both in long- and short-run. However, the favourable impact of physical infrastructure on investment holds in long-run only, while its effect is adverse though insignificantly in short-run. The findings support the neoclassical flexible accelerator principle and are consistent with economic theory. The volume of available funds is the binding constraint for investment and the McKinnon-Shaw hypothesis is validated in the short-run. Keywords: Aggregate Investment, Irreversibility, Macroeconomic Uncertainty, Political Stability, GARCH, ARDL, Bound Testing Approach, Pakistan
... Segundo Morettin & Toloi (2020), os modelos ARCH (modelos autorregressivos com heterocedasticidade condicional) foram introduzidos por Engle (1982), com o objetivo de estimar a variância da inflação. Esses modelos tem como base a ideia de que o retorno r t não é correlacionado ao longo do tempo, porém, a volatilidade condicional depende de retornos passados por meio de uma função quadrática. ...
... Para verificar a heterocedasticidade condicional e efeitos ARCH na série, investiga-se se as variações nos retornos exibem dependência de variância (efeitos ARCH), justificando assim a utilização de um modelo GARCH. Para esse propósito, são implementados os testes estatísticos ARCH-LM (Engle, 1982). ...
O cenário financeiro global, marcado por considerável volatilidade nos últimos anos, especialmente durante eventos econômicos, geopolíticos e de saúde, destaca a urgência de estratégias robustas de gestão de riscos. A volatilidade nos mercados financeiros, evidenciada pela pandemia da COVID-19, reforça a importância da análise de séries temporais financeiras. Essas teorias oferecem uma visão temporal dos dados, permitindo a identificação de tendências e padrões nos mercados. Este estudo emprega os modelos GARCH(1,1) e EGARCH(1,1) para analisar a série de retornos de uma carteira de investimentos, destacando suas performances significativas na compreensão da volatilidade condicional. O modelo GARCH(1,1) apresenta resultados robustos, indicando aumento gradual na volatilidade condicional, orientando estratégias cautelosas de mitigação de riscos. Por outro lado, o modelo EGARCH(1,1) prevê um leve decréscimo na volatilidade, permitindo estratégias assertivas em um ambiente de menor variabilidade. Essas projeções proporcionam insight(s) essenciais para a gestão de carteiras, destacando a importância de decisões informadas e estratégias adaptativas no cenário dinâmico dos investimentos.
... Besides, several diagnostic and stability techniques are implemented to ascertain whether the coefficients of the determined NARDL model are confirmed, foolproof, and stable or not. Engle, 83 Breusch and Pagan, 84 and Godfrey 85 tests are executed to analyze the possibility of the residuals existence including the serial correlation autoregressive conditionally heteroscedastic and autocorrelation, for instance, autoregressive conditional heteroscedasticity. Moreover, Ramsey regression equation specification error test (RESET) test 86 is performed to analyze the residual terms, its distribution and determination of the model, for instance, choosing convenient models is employed as well. ...
... When each of the variables' series are adapted at the similar in order of integration according to Engle 83 and Engle and Granger, 88 the Johansen cointegration test 81 is one of the most convenient analyses to comprehend the series in terms of fluctuation concerning records across the lengthy. Supposing the findings regarding the stability assessment within detail, cointegration test is an appropriate method at the next stage to find out the long-term linkage among EF (dependent variable) and independent variables of this paper. ...
This manuscript investigates the interplay between energy dynamics, economic growth, and environmental sustainability, offering a comprehensive analysis of Türkiye's long-term ecological and economic trends. In this sense, the research elaborates the long-run linkage among natural gas import, energy usage, economic growth, trade openness, urbanization and ecological footprint (EF) by implementing the Johansen cointegration test, fully modified ordinary least squares (FMOLS) analysis, nonlinear distributed lag autoregressive model (NARDL) model, and wavelet analyses from 1980 to 2022 for Türkiye. Furthermore, when the contributions and novelties of this paper to the existing academic literature are considered, time series models comprehending the Johansen cointegration test, FMOLS analysis, and NARDL model point out the long-run relationship between natural gas import, economic growth, and EF, which is confirming the Environmental Kuznets Curve hypothesis for Türkiye in short term. Considering the coefficients of the FMOLS model, 1% increases in gross domestic product increases EF by 0.1972% and a 1% increase in natural gas import increases EF by 0.0369% as negatively. In addition, according to FMOLS test, it should be stated that a 1% increase in energy use increases EF by 0.7600%. When all remaining independent variables are examined deeply and thoroughly, there is a long-term positive effect between them. Empirical findings reveal that natural gas imports ( p = .0428) and energy consumption ( p < .0001) are major contributors to ecological degradation. Conversely, urbanization ( p = .3999) demonstrates potential for mitigating environmental pressure in the long term. The study highlights the need for transitioning to renewable energy, enhancing energy efficiency, and adopting sustainable urban development practices. These findings emphasize the importance of aligning economic growth with ecological sustainability through targeted policy interventions. Unlike previous studies that predominantly concentrate on renewable energy with CO 2 emissions, this paper dissimilarly highlights the overlooked environmental effects of natural gas imports. These insights not only expand the understanding of Türkiye's energy and environmental dynamics but also challenge the common perception of natural gas as an eco-friendly energy source. To sum up, the research includes empirical results which patronizes the necessity for a transition to renewable resources and cleaner technologies to mitigate environmental costs.
... Traditional econometric approaches, particularly the Autoregressive Conditional Heteroskedasticity (ARCH) model introduced by Engle (1982) and its generalization, the Generalized ARCH (GARCH) model proposed by Bollerslev (1986), laid the foundation for modern volatility modeling. These models, grounded in strong statistical theory, have proven effective in modeling time-varying conditional variance and capturing volatility clustering. ...
... Classical econometric models, such as the Autoregressive Conditional Heteroskedasticity (ARCH) model introduced by Engle (1982) and its generalization, the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model by Bollerslev (1986), laid the groundwork for capturing time-varying volatility and volatility clustering in asset returns. These models are grounded in a well-defined probabilistic framework and have served as the benchmark in both academic and applied settings. ...
In this study, we propose a novel integrated Generalized Autoregressive Conditional Heteroskedasticity-Gated Recurrent Unit (GARCH-GRU) model for financial volatility modeling and forecasting. The model embeds the GARCH(1,1) formulation directly into the GRU cell architecture, yielding a unified recurrent unit that jointly captures both traditional econometric properties and complex temporal dynamics. This hybrid structure leverages the strengths of GARCH in modeling key stylized facts of financial volatility, such as clustering and persistence, while utilizing the GRU's capacity to learn nonlinear dependencies from sequential data. Compared to the GARCH-LSTM counterpart, the GARCH-GRU model demonstrates superior computational efficiency, requiring significantly less training time, while maintaining and improving forecasting accuracy. Empirical evaluation across multiple financial datasets confirms the model's robust outperformance in terms of mean squared error (MSE) and mean absolute error (MAE) relative to a range of benchmarks, including standard neural networks, alternative hybrid architectures, and classical GARCH-type models. As an application, we compute Value-at-Risk (VaR) using the model's volatility forecasts and observe lower violation ratios, further validating the predictive reliability of the proposed framework in practical risk management settings.
... The results from early studies are attributed and affected by the methodology used in the analysis. More recent studies have typically employed most popular techniques such as the Auto regressive Conditional Heteroscedasticity process (ARCH) which was proposed by Engle (1982), and General Auto regressive Conditional Heteroscedasticity (GARCH) which was initially proposed by Bollerslev (1986). Panait and Slavescu (2012) used the GARCH-in-mean model to compare the volatility for seven Romanian companies traded on Bucharest Stock Exchange (BSE) and three market indices, during the period from 1997 to 2012. ...
... 167 index exhibit volatility clustering over time and whether they are predictable. This is the most prominent feature of the time series of DSE, and to achieve this effect, we used up to date time series models proposed initially by Engle (1982) and then extended by Bollerslev (1986). These models are the family of Autoregressive Conditional Heteroscedastic (ARCH). ...
The existing empirical literature has extensively explored stock market return volatility in various emerging and developing markets; however, limited attention has been given to the Dar es Salaam Stock Exchange (DSE). This study seeks to address this gap by analyzing the volatility dynamics of stock returns in the DSE. The analysis is based on a dataset comprising 1,846 daily observations spanning the period from June 2014 to November 2021. Consistent with prior studies, the findings reveal a significant negative relationship between returns and risk, as modeled using the AR(1)-GARCH(1,1)-M framework. The application of the GARCH(1,1) model effectively captures volatility clustering, following the confirmation of heteroscedasticity in the return series. However, due to the GARCH model’s limitations in capturing asymmetries in volatility (i.e., the leverage effect), the analysis was extended using the AR(1)-EGARCH model. The results support the presence of a leverage effect in the DSE, indicated by a negative and statistically significant leverage coefficient. This suggests that negative shocks have a greater impact on volatility than positive shocks of the same magnitude. Moreover, the study confirms a negative correlation between stock returns and volatility. These findings imply that higher levels of risk may lead to disproportionately larger losses for investors in the DSE. Therefore, market participants, policymakers, and portfolio managers must exercise caution and implement robust risk management strategies to safeguard investments against unexpected market fluctuations. The results also offer valuable insights for investors, scholars, and researchers interested in understanding the behavior of stock return volatility in frontier markets such as Tanzania.
... This sudden change otherwise referred to as volatility has significant impact on risk control, asset pricing, and portfolio optimization in the financial markets. Engle (1982) with the introduction of the Autoregressive Conditional Heteroscedastic (ARCH) model, pioneered the study of conditional heteroscedasticity of asset returns. Engle (1982) model expressed conditional variance of returns as a weighted average of previous innovations, making it suitable for describing volatility clustering. ...
... Engle (1982) with the introduction of the Autoregressive Conditional Heteroscedastic (ARCH) model, pioneered the study of conditional heteroscedasticity of asset returns. Engle (1982) model expressed conditional variance of returns as a weighted average of previous innovations, making it suitable for describing volatility clustering. Notwithstanding the success of ARCH model, it has faced criticism due to various weaknesses including difficulties in parameter estimation and the assumption of equal effects for both negative and positive shocks on volatility, among others. ...
The accurate modelling of return unpredictability remains a pivotal challenge in financial econometrics. Traditional models often assume a normal distribution for error terms, which fails to capture the leptokurtic and skewed nature of financial returns. This paper introduces the odd generalized exponential Laplace distribution (OGELAD) as an error distribution tailored for modelling asset return unpredictability. The proposed distribution addresses the limitations of conventional error distributions such as normal (NORM), skew normal (SNORM), normal inverse Gaussian (NIG), and skew generalized error distribution (SGED) in capturing key characteristics of financial returns, such as asymmetry and heavy tails. Using simulated data, the study evaluates the performance of the OGELAD within symmetric and asymmetric volatility models, demonstrating its effectiveness in modelling and forecasting return volatility. Diagnostic tests confirm that all error distributions, including the OGELAD, successfully eliminate ARCH effects from residuals, ensuring robust model performance. Notably, the positive and significant asymmetry parameter in the selected model highlights that positive shocks exert a smaller influence on volatility compared to negative shocks of the same magnitude. This finding underscores the relevance of the proposed distribution in capturing leverage effects observed in financial data. The OGELAD distribution consistently outperformed existing distributions in modelling and forecasting volatility, showcasing its potential for broader applications. It can be Royal Statistical Society Nigeria Local Group 2025 Conference Proceedings 126 extended to multivariate settings for portfolio risk management and applied to high-frequency financial data to test its robustness under varying market conditions.
... The paper proposes the general concept for constructing the family of martingale measures equivalent to a given measure for a wide class of evolutions of risky assets. In particular, it also contains the description of the family of martingale measures for the evolution of risky assets given by the ARCH [18] and GARCH [19], [20] models. In section 2, we formulate the conditions relative to the evolution of risky assets and give the examples of risky asset evolution satisfying these conditions. ...
... The evolution of risky assets, given by the formula (176), includes a wide class of evolutions of risky assets, used in economics. For example, under an appropriate choice of probability spaces {Ω 0 i , F 0 i , P 0 i } and a choice of sequence of independent random values ε i (ω i ) with the normal distribution N (0, 1), we obtain ARCH model (Autoregressive Conditional Heteroskedastic Model) introduced by Engle in [18] and GARCH model (Generalized Autoregressive Conditional Heteroskedastic Model) introduced later by Bollerslev in [19]. In these models, the random variables σ i (ω 1 , . . . ...
The general method is proposed for constructing a family of martingale measures for a
wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent martingale measures to the original measure is a non-empty set. The set of martingale measures is constructed from a set of strictly nonnegative random variables, satisfying certain conditions. The inequalities are obtained for the non-negative random variables satisfying certain conditions. Using these inequalities, a new simple proof of optional decomposition theorem for the nonnegative super-martingale is proposed. The family of spot measures is introduced and the representation is found for them.
The conditions are found under which each martingale measure is an integral over the set of spot measures. On the basis of nonlinear processes such as ARCH and GARCH, the parametric family of random processes is introduced for which the interval of non-arbitrage prices are found. The formula is obtained for the fair price of the contract with option of European type for the considered parametric processes. The arameters of the introduced random processes are estimated and the estimate is found at which the fair price of contract with option is the least.
... Recognizing the pervasive issue of time-varying volatility (i.e., periods of high volatility followed by periods of relative calm, known as volatility clustering) in financial and commodity markets, Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models were developed [12,29]. GARCH and its numerous extensions specifically aim to model and forecast the conditional variance of price returns. ...
Commodity price volatility creates economic challenges, necessitating accurate multi-horizon forecasting. Predicting prices for commodities like copper and crude oil is complicated by diverse interacting factors (macroeconomic, supply/demand, geopolitical, etc.). Current models often lack transparency, limiting strategic use. This paper presents a Regularized Sparse Autoencoder (RSAE), a deep learning framework for simultaneous multi-horizon commodity price prediction and discovery of interpretable latent market drivers. The RSAE forecasts prices at multiple horizons (e.g., 1-day, 1-week, 1-month) using multivariate time series. Crucially, L1 regularization () on its latent vector enforces sparsity, promoting parsimonious explanations of market dynamics through learned factors representing underlying drivers (e.g., demand, supply shocks). Drawing from energy-based models and sparse coding, the RSAE optimizes predictive accuracy while learning sparse representations. Evaluated on historical Copper and Crude Oil data with numerous indicators, our findings indicate the RSAE offers competitive multi-horizon forecasting accuracy and data-driven insights into price dynamics via its interpretable latent space, a key advantage over traditional black-box approaches.
... As an alternative, stochastic volatility models allow for changes in variance and provide a conventional regression framework for modeling volatility (Engle, 1982). Recent research has shifted to stochastic volatility models treating inflation uncertainty as a latent variable with an AR(1) process (Chan, 2017). ...
Inflation is a critical global issue and also a significant challenge in Ethiopia. Despite its profound impact on the economy, research on inflation volatility in Ethiopia remains limited and insufficient. This paper aims to address these gaps by employing BEKK (Baba, Engle, Kraft, and Kroner) and DCC (Dynamic Conditional Correlation) - GARCH (Generalized Autoregressive Conditional Heteroscedasticity) models and analyze the characteristics of inflation trends, which supports informed economic decision making. We focus on four key inflation indicators: the Consumer Price Index (CPI), the Non-Food Price Index (NFPI), the Food Price Index (FPI), and the Exchange Rate (ER), which were compiled from the National Bank of Ethiopia (NBE) from January 2010 to December 2020. The study confirms inflation volatility, supported by the ARCH effect and Ljung-Box Q(m) statistics, along with conditional heteroscedasticity tests. This study demonstrates that, unlike previous approaches that neglected dynamic correlations in inflation volatility, the DCC-GARCH model decisively outperforms the BEKK-GARCH model in both parameter estimation and forecasting accuracy, as evidenced by significantly better Akaike Information Criterion (AIC), Schwarz Bayesian Information Criterion (SBIC), and Hannan-Quinn Information Criterion (HQIC) metrics. Our findings revealed that the DCC (1,1) model effectively captured volatility clustering without being persistent or explosive, as the sum of coefficients is less than 1, confirming mean reversion. In contrast to previous studies, our approach provided a more robust understanding of inflation dynamics, identifying CPI and FPI as the most volatile indicators. The study reveals significant correlations among inflation indicators-CPI, FPI, NFPI, and ER indicating a cohesive inflationary pattern. The coefficients show that past volatility and shocks persistently influence current volatility, underscoring their interdependence. The forecast from the best model reveals substantial instability is observed in CPI and FPI returns. It suggests a sharp increase in FPI and a rise in ER. The better method captured inflation volatility more effectively than other competent models. The DCC-GARCH model offered deeper insights into volatility dynamics, revealing the shortcomings of earlier time series models in addressing inflation volatility.
... Geleneksel ekonometrik modellerin aksine, Engle (1982) koşulsuz varyansın sabit olduğu ancak koşullu varyansın zamana bağlı olarak değiştiği bir yapı ortaya koymuş ve bu koşullu varyansı, hata terimlerinin karelerinin bir fonksiyonu olarak tanımlamıştır. Otoregresif Koşullu Varyans (ARCH) olarak tanımlanan bu yaklaşım, finansal ve iktisadi zaman serilerindeki oynaklığı modellemek ve tahmin etmek için önemli bir adım olmuştur. ...
... Geleneksel ekonometrik modellerin aksine, Engle (1982) koşulsuz varyansın sabit olduğu ancak koşullu varyansın zamana bağlı olarak değiştiği bir yapı ortaya koymuş ve bu koşullu varyansı, hata terimlerinin karelerinin bir fonksiyonu olarak tanımlamıştır. Otoregresif Koşullu Varyans (ARCH) olarak tanımlanan bu yaklaşım, finansal ve iktisadi zaman serilerindeki oynaklığı modellemek ve tahmin etmek için önemli bir adım olmuştur. ...
... Estas técnicas tienen como base el trabajo seminal de Box & Jenkins (1970) utilizando modelos autorregresivos de media móvil (ARMA), autorregresivos integrados de media móvil (ARIMA) y función de transferencia. A estas técnicas se han incorporado modelos multivariados de series temporales tales como los vectores autoregresivos (VAR) (Sims, 1980) o los modelos autorregresivos con heterocedasticidad condicional (ARCH) y autorregresivos generalizados con heterocedasticidad condicional (GARCH) (Engle, 1982) que permiten sobreponerse a algunas de las limitaciones presentes en modelos univariados. Para que estos modelos puedan utilizarse se requiere el cumplimiento de ciertos supuestos y la estabilidad de los parámetros, pero de acuerdo a las ya mencionadas características del fenómeno inflacionario en Uruguay, esto podría no cumplirse en ciertos períodos de estudio. ...
Entender y predecir el fenómeno inflacionario es un problema central para los economistas y agentes tomadores de decisiones. Tradicionalmente se han utilizado técnicas econométricas de series de tiempo para estudiar este fenómeno; pero, ¿puede la economía de la complejidad aportar una visión complementaria a los estudios anteriores? Este trabajo busca estudiar la dinámica de la estructura de precios de la economía uruguaya desde la perspectiva de la economía de la complejidad, utilizando técnicas de análisis de redes que permitan estudiar la relación entre los bienes y servicios que componen el IPC. En el presente trabajo se estudian los agrupamientos de bienes y servicios a partir del comportamiento dinámico de las series temporales de precios, detectando a su vez variaciones de precios relevantes en esta red. Los resultados muestran que los precios relevantes no están asociados a las divisiones de bienes del IPC y que los agrupamientos son consistentes con estudios anteriores para Uruguay.
... Methodologically, time series forecasting frameworks are broadly categorized into linear and nonlinear paradigms. Linear models, such as the Autoregressive Moving Average (ARMA), Autoregressive Integrated Moving Average (ARIMA), and their heteroskedasticity-aware extensions-the Autoregressive Conditional Heteroskedasticity (ARCH) [3] and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) [4] models-leverage historical linear dependencies for prediction. For instance, adaptive feature fusion mechanisms integrated with ARIMA have enhanced remaining useful life predictions for high-speed train bearings [5], achieving significant improvements in forecasting accuracy. ...
GARCH-type time series (characterized by Generalized Autoregressive Conditional Heteroskedasticity) exhibit pronounced volatility, autocorrelation, and heteroskedasticity. To address these challenges and enhance predictive accuracy, this study introduces a hybrid forecasting framework that integrates the Interval Type-2 Fuzzy Inference System (IT2FIS) with the GARCH model. Leveraging the interval-based uncertainty representation of IT2FIS and the volatility-capturing capability of GARCH, the proposed model effectively mitigates the adverse impact of heteroskedasticity on prediction reliability. Specifically, the GARCH component estimates conditional variance, which is subsequently incorporated into the Gaussian membership functions of IT2FIS. This integration transforms IT2FIS into an adaptive variable-parameter system, dynamically aligning with the time-varying volatility of the target series. Through systematic parameter optimization, the framework not only captures intricate volatility patterns but also accounts for heteroskedasticity and epistemic uncertainties during modeling, thereby improving both prediction precision and model robustness. Experimental validation employs diverse datasets, including air quality concentration, urban traffic flow, and energy consumption. Comparative analyses are conducted against models: the GARCH-Takagi-Sugeno-Kang (GARCH-TSK) model, fixed-variance time series models, the GARCH-Gated Recurrent Unit (GARCH-GRU), and Long Short-Term Memory (LSTM) networks. The results indicate that the proposed model achieves superior predictive performance across the majority of test scenarios in error metrics. These findings underscore the effectiveness of hybrid approaches in forecasting uncertainty for GARCH-type time series, highlighting their practical utility in real-world time series forecasting applications.
... The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, proposed by Bollerslev (1986) as a generalization of the ARCH model introduced by Engle (1982), assumes that the conditional variance at time t is fully determined by past squared returns and its own past values. In its simplest form, the model is specified as: ...
Forecasting volatility plays an important role in a number of economic and financial applications , including portfolio allocation, risk management, option pricing, trading strategies , and monetary policy. Traditional models such as GARCH, Stochastic Volatility (SV), Markov-Switching GARCH (MSGARCH), and the more recent Generalised Autoregressive Score (GAS) have been widely used in several empirical applications. However, little effort has been devoted to understanding the results of comparative studies-whether they favour one model over others or show no clear preference. In this paper, we address this gap in the literature by systematically evaluating the forecasting performance of these models in controlled environments using Monte Carlo experiments, as well as empirical data. Our results indicate that, as expected, when the forecasting model coincides with the data-generating process, it achieves the highest predictive accuracy. However, especially in cases where the sample size of the estimation period is small, competing models may still perform competitively. Furthermore, under additive outliers, GAS and SV models with Student-t innovations consistently outperform their counterparts, even under misspecifica-tion. Additionally, in the presence of structural breaks, the MSGARCH model emerges as a competitive option when the sample size is sufficiently large. These findings reinforce existing empirical evidence supporting the practical relevance of GAS models in volatility forecasting, highlight the importance of SV models in empirical applications, and raise caution regarding the use of MSGARCH models with small sample sizes. To promote transparency and reproducibility, all code and materials from this study are publicly available in our GitHub repository.
... The available tools provided to researchers by artificial intelligence include genetic algorithms, fuzzy networks, and artificial neural networks, which were one of the most suitable of these tools, and many researchers have used this method in their research. In 2004, Hamid and Eqbal used a hybrid GARH-artificial neural network model to study the fluctuations of the S&P 500 index in Istanbul stock in 2009 [6] [7]. In 2008, Parizi and Diaz predicted the price of gold using an improved old neural network technique and two newer techniques in artificial networks [8]. ...
Predicting the price that has the least error and can provide the best and highest accuracy has been one of the most challenging issues and one of the most critical concerns among capital market activists and researchers. Therefore, a model that can solve problems and provide results with high accuracy is one of the topics of interest among researchers. In this project, using time series prediction models such as ARIMA to estimate the price, variables, and indicators related to technical analysis show the behavior of traders involved in involving psychological factors for the model. By linking all of these variables to stepwise regression, we identify the best variables influencing the prediction of the variable. Finally, we enter the selected variables as inputs to the artificial neural network. In other words, we want to call this whole prediction process the "ARIMA_Stepwise Regression_Neural Network" model and try to predict the price of gold in international financial markets. This approach is expected to be able to be used to predict the types of stocks, commodities, currency pairs, financial market indicators, and other items used in local and international financial markets. Moreover, a comparison between the results of this method and time series methods is also expressed. Finally, based on the results, it can be seen that the resulting hybrid model has the highest accuracy compared to the time series method, regression, and stepwise regression.
... One of the most important issues before applying the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) methodology is to first examine the residuals for evidence of heteroscedasticity. To test for the presence of heteroscedasticity in residuals of KSE index return series, the Lagrange Multiplier (LM) test for ARCH effects proposed by Engle (1982) is applied. In summary, the test procedure is performed by first obtaining the residuals t e from the ordinary least squares regression of the conditional mean equation which might be an autoregressive (AR) process, moving average (MA) process or a combination of AR and MA processes; (ARMA) process. ...
it is about the interrelationship between Indian knowledge system and mgt.
... To capture the time-varying conditional variance phenomenon, Engle (1982) proposed the Autoregressive Conditional Heteroscedastic (ARCH) model. Although the ARCH model is a considerable contribution to the econometric literature, it has some problems including long lag length and non-negativity restriction on parameters. ...
Dictatorship has been one of the most persistent regimes types in history. Different dictators have applied different strategies for maintaining political support across different societies. We discuss and empirically estimate the hypothesis that states that dictators rely more on patronage as compared to the general provision of public goods for political support. Our results, based on the data from cross-section of the countries from all continents, confirm this hypothesis. We use military spending as an indicator of the patronage to military and the secondary school enrolment as an indicator of the provision of public goods. In the separate sets of regressions, we conclude that dictatorship has a significant negative effect on the secondary school enrolment rate and a significant positive effect on military expenditure as percentage of GDP. These effects, in turn, might have caused the persistent of dictatorships in many societies. In order to generalise these findings, we also check robustness of the findings with respect to other variables like infant mortality rate, average life expectancy, Human Development Index (HDI), corruption, rule of law, ease of doing business and competitiveness. The robustness analysis confirms our findings. JEL Classification: P16, H11, H41, H42 Keywords: Dictatorship, Patronage, Public Goods Provision, Military Spending, Secondary School Enrolment Rate, Robustness Analysis
... This volatility is reflected in the residual variance that does not meet the homoscedasticity assumption. The ARCH test developed by Engle (1982) is used to test the existence of the heteroskedasticity of the residuals and the autocorrelation of the squared residuals. The variance consists of two components. ...
This study examines how livestock ships affect price volatility and disparity at the producer and consumer levels. East Nusa Tenggara (ENT) is one of the provinces in Indonesia that experiences a beef surplus. Nationally, Jakarta and East Kalimantan are the provinces that experience the 2nd and 4th beef deficits. Livestock distribution is an expected method to reduce the volatility and disparity of live cattle and beef prices. The ARCH/GARCH model is used in analyzing volatility and forecasting food and agricultural commodity prices. Based on the results of the ARCH/GARCH analysis, livestock ships have not been effective in reducing producer price volatility in East Nusa Tenggara and consumer prices in Jakarta and East Kalimantan before the presence of livestock ships (January 2010-December 2015) and after the presence of livestock ships (January 2016-December 2023). The results show that CN Livestock Ships have not been effective in reducing consumer price volatility in both Jakarta and East Kalimantan and also producer prices in ENT and East Kalimantan. Based on the results of the variation coefficient analysis, livestock ships are effective in reducing price disparities between producers (in ENT) and consumers (in East Kalimantan) centers. The smaller the coefficient of variance of a data group, the more homogeneous the data is and this means that the price is more stable or does not fluctuate This ineffectiveness is influenced by the conditions of the COVID-19 pandemic and ship docking. The price disparity decreased due to lower transportation costs using livestock ships. Referring to this, efforts to increase the effectiveness of the Camara Nusantara livestock ship must be viewed comprehensively. In addition to increasing the operational capacity of livestock ships by increasing the number of fleets and improving ports and other supporting infrastructure, the government also needs to look at the role of inter-island livestock traders, slaughterhouse facilities and wholesalers (distributors, importers) to jointly utilize the Camara Nusantara livestock ship in order to stabilize beef prices both at the producer and consumer levels. Keywords: Camara Nusantara livestock ship, beef price, volatility, disparity, ARCH, GARCH.
... Pengukuran dan pemodelan volatilitas harga dilakukan dengan model ARCH GARCH (Engle 1982, Bollerslev 1986 ...
... These models struggle to capture nonlinear dependencies, dynamic patterns and regime changes, making them less effective for modeling complex systems (Smets and Wouters 2003). Classical time-series models such as ARIMA (Box and Jenkins 1976), GARCH (Engle 1982;Bollerslev 1986), and LSTM (Hochreiter and Schmidhuber 1997) assume linearity and focus exclusively on time sequences often failing to capture structural complexity and nonlinear interactions. Classical Machine Learning methods, including Support Vector Machines (SVM) (Cortes and Vapnik 1995), Random Forests (Breiman 2001), and simple neural networks, generally treat data as independent samples, ignoring temporal and structural dependencies. ...
A novel approach based on unsupervised Machine Learning techniques is proposed to explore the complex interconnections between the dynamics of energy commodity prices, such as oil, gas and electricity prices in the USA, and the dynamics of certain macroeconomic variables that reflect the behavior of the US economy, such as interest rates and the Standard and Poor’s index. This methodology combines the Wasserstein barycenter with Graph Machine Learning and Manifold Learning techniques to identify common stochastic factors that drive the dynamics of energy commodity prices. Our analysis reveals the presence of a well-defined group of energy commodity markets that share similar characteristics. To study common stochastic factors, a Gaussian Mixture Model is fitted to the Wasserstein barycenter of the discovered cluster. The fitting is performed by maximum likelihood using the Expectation–Maximization algorithm with an initialization strategy based on Graph Machine Learning techniques. A fine-tuning of specific factors affecting the dynamics of energy commodity prices is also discussed.
... Dalam ekonomi makro, in lasi adalah salah satu indikator utama yang mencerminkan stabilitas harga barang dan jasa dalam perekonomian suatu negara. In lasi yang tidak stabil atau ber luktuasi tajam dapat menciptakan ketidakpastian ekonomi yang memengaruhi keputusan investasi dan perilaku pasar saham (Engle, 1982). Sebagai salah satu pilar perekonomian, pasar saham sering kali menjadi re leksi dari sentimen investor terhadap kondisi ekonomi makro, termasuk perubahan in lasi. ...
Abstrak Penelitian ini menganalisis hubungan antara volatilitas inflasi dengan volatilitas harga saham United Tractors (UNTR) selama periode 2009-2018. Dengan menggunakan metode kuantitatif, penelitian ini mengukur standar deviasi sebagai indikator volatilitas untuk kedua variabel. Uji korelasi Pearson menunjukkan bahwa terdapat hubungan positif antara volatilitas inflasi dan volatilitas harga saham UNTR, meskipun dengan tingkat hubungan yang lemah. Hasil ini menunjukkan bahwa kenaikan inflasi sebesar 1% berpotensi meningkatkan harga saham UNTR sebesar 0,311%. Temuan ini menyoroti pentingnya pengelolaan risiko volatilitas, baik oleh perusahaan maupun pemerintah, dalam menciptakan stabilitas pasar dan menarik minat investor. Studi ini memberikan kontribusi pada literatur tentang dinamika makroekonomi dan pasar saham di Indonesia. Abstract This study analyzes the relationship between inflation volatility and the volatility of United Tractors (UNTR) stock prices during the period 2009-2018. Using a quantitative method, this study measures standard deviation as an indicator of volatility for both variables. Pearson's correlation test shows that there is a positive relationship between inflation volatility and UNTR stock price volatility, albeit with a weak level of correlation. This result shows that an increase in inflation of 1% has the potential to increase UNTR's share price by 0.311%. These findings highlight the importance of managing volatility risk, both by companies and governments, in creating market stability and attracting investor interest. This study contributes to the literature on macroeconomic dynamics and the stock market in Indonesia.
... To measure the exploitation and exploration transition, we followed Swift (2016) and looked at the firm's largest one-year change in R&D expenditure between 2009 and 2014, which is normalized with variances for each firm based on the GARCH model (Bollerslev, 1986;Engle, 1982). This model estimates the firm's R&D expenditure trend over time and generates residuals that indicate the frequency and extent to which R&D investment differs from the predicted trend. ...
Prior research presents mixed findings on the impact of temporal shifting between exploration and exploitation on organizational performance. Our study seeks to further clarify these effects and explore the moderating role of environmental scarcity. By analyzing 1,247 firm-year observations from publicly traded U.S. high-tech firms (2009–2014), we find that temporal transitioning from exploitation to exploration negatively affects firm performance, whereas time shifting from exploration to exploitation has a positive impact. Moreover, environmental scarcity intensifies the negative performance consequences of moving from exploitation to exploration. Our findings contribute to the literature on organizational ambidexterity and learning.
... Stylized facts regarding exchange rate returns are often explained through various models within the ARCH family. Engle (1982) proposed its use, and later, Bollerslev (1986) further developed its application. These models offer a framework for describing and analyzing exchange rate return features. ...
This study employs a novel approach by using the GARCH-MIDAS model to estimate the volatility of the nominal exchange rate, incorporating variables of the monetary approach as a long-run component. We analyze the daily closing prices of the peso-dollar nominal exchange rate from July 1991 to December 2022 and the quarterly macroeconomic fundamentals from September 1988 to December 2022. Our findings reveal a significant influence of the monetary approach variables on the long-term feature of the exchange rate volatility. We find that the bias of long-term volatility is contingent upon the distinctive functional relationship fundamental to the demand for real money balances. Our investigation concludes that the specification grounded in the monetary approach yields more robust volatility predictions when compared with alternative models.
... Engle [32] proposed the Autoregressive Conditional Heteroskedasticity (ARCH) model as a solution to issues arising from constant variance. ARCH models acknowledge that asset return shocks, though uncorrelated, may still exhibit dependence. ...
This study investigates the volatility dynamics of gold, silver, and platinum prices using daily closing data from the Shanghai Gold Exchange between 2012 and 2020. We employed ARCH and GARCH models to analyze volatility, asymmetry, and spillover effects among these precious metals. Our findings reveal that all three metals exhibit significant price fluctuations and volatility clustering. Silver demonstrated the highest volatility overall. Furthermore, all metals displayed asymmetric responses to market shocks, with gold and platinum demonstrating greater sensitivity to positive shocks (good news) compared to negative ones (bad news). Silver exhibited the opposite behavior. We also observed a one-way directional spillover effect where gold price volatility significantly impacts both silver and platinum, while silver price volatility primarily affects platinum. These results have important implications for investors, portfolio managers, and financial institutions. Understanding the volatility dynamics and spillover effects among these precious metals is crucial for effective risk management, portfolio diversification, and developing robust investment strategies.
... (ARCH) models. These models are based on a series of differences that follow a martingale pattern [2]. The generalized Autoregressive Condition Heteroscedastic (GARCH) model was developed by Bollerslev in 1986 [1]. ...
This research proposes a new model for nonlinear time series called the Secant Double AR model of order k, SecDAR(k), which is based on the double autoregressive model with an augmented secant function. In 2007, Ling introduced this family of double autoregressive models, with the prototype model named DAR(P), where p is the order of the model. This approach addresses data volatility that leads to heteroscedasticity .Using dynamic principles and local linear methods, this research analyzes the stability conditions of the model. First, we approximate the previously mentioned model to a linear difference equation using a local linear strategy. Secondly, the roots of the characteristic equation are used to assess stability. In the end, the stability conditions for the above model are applied using data showing the average monthly closing price of heating oil in US dollars from 1990 to 2024. To evaluate the accuracy and quality of the models' fit on the actual data, we use the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC). In the application section, we use the stability condition to evaluate the stability for each order of SecDAR(k) from 1 to 6.
... The ARCH model was the first volatility model developed by Engle (1982). Later, the author identified a problem with the ARCH specification, highlighting the resemblance to a moving average model rather than an autoregressive specification. ...
The outbreak of COVID-19 sent shockwaves through global markets, where the commodity markets were significantly affected. The main issue of the study highlights the scarcity of past studies on the link between COVID-19 and the volatility of crude palm oil futures (FCPO), intensified by Malaysia's rigorous lockdowns that disrupted supply networks and market sentiments, resulting in significant price changes throughout the pandemic. This study aims to fill this research gap by using the GARCH method to investigate the volatility of FCPO market during the COVID-19 pandemic. Daily time series data of FCPO from 1st March 2019 to 31st December 2020 were used as the sample and divided into two subsample periods covering before and during COVID-19. This research displays unanticipated fluctuations in commodity market prices during crises, emphasizing volatility dynamics amidst external shocks. The results indicated that the GARCH (3,1) model effectively captured the volatility dynamics observed within the full sample period, while the GARCH (1,1) was the best model to explain FCPO volatility during pre-and post-COVID-19. Further, COVID-19 had a positive and significant impact on the volatility of FCPO returns, implying that COVID-19 increased the volatility of the FCPO returns during the pandemic.
... The ARCH model, proposed by [3], was developed to capture the dynamic nature of return volatility, which varies over time rather than remaining constant. Consequently, rather than depending on standard deviations derived from short-or long-term samples, the ARCH model suggests using weighted averages of previous squared forecast errors, effectively serving as a form of weighted variance [35]. ...
In numerous domains of finance and economics, modelling and predicting stock market volatility is essential. Predicting stock market volatility is widely used in the management of portfolios, analysis of risk, and determination of option prices. This study is about volatility modelling of the daily Johannesburg Stock Exchange All Share Index (JSE ALSI) stock price data between 1 January 2014 and 29 December 2023. The modelling process incorporated daily log returns derived from the JSE ALSI. The following volatility models were presented for the period: sGARCH(1,1) and fGARCH(1,1). The models for volatility were fitted using five unique error distribution assumptions, including Student’s t, its skewed version, the generalized error and skewed generalized error distributions, and the generalized hyperbolic distribution. Based on information criteria such as Akaike, Bayesian, and Hannan–Quinn, the ARMA(0,0)-fGARCH(1,1) model with a skewed generalized error distribution emerged as the best fit. The chosen model revealed that the JSE ALSI prices are highly persistent with the leverage effect. JSE ALSI price volatility was notably influenced during the COVID-19 pandemic. The forecast over the next 10 days shows a rise in volatility. A comparative study was then carried out with the JSE Top 40 and the S&P500 indices. Comparison of the FTSE/JSE Top 40, S&P 500, and JSE ALLSI return indices over the COVID-19 pandemic indicated higher initial volatility in the FTSE/JSE Top 40 and S&P 500, with the JSE ALLSI following a similar trend later. The S&P 500 showed long-term reliability and high rolling returns in spite of short-run volatility, the FTSE/JSE Top 40 showed more pre-pandemic risk and volatility but reduced levels of rolling volatility after the pandemic, similar in magnitude for each index with low correlations among them. These results provide important insights for risk managers and investors navigating the South African equity market.
... The exchange rate of the Nigerian Naira to the United States Dollar (EXR) is measurable at high frequency (daily or intra-day) or low frequency (monthly, quarterly, bi-annually, annually, or multi-year). When the EXR is measured at high frequency, it becomes very volatile in such a way that both the seasonal and non-seasonal ARIMA variants fail to capture their forecasting dynamics due to the non-homoscedasticity of the models' residuals (Engle, 1982). As a © 2025 Department of Mathematics, Modibbo Adama University. ...
Over the past eight decades, the United States Dollar has become the vehicle currency driving other major foreign currencies as well as minor currencies emerging in the financial markets. Consequently, the goal of developed and developing countries is to maintain good exchange rates with the USD through effective monetary policy management. To assess the monthly Naira-Dollar exchange rates (EXR) relationship, this study applied the non-seasonal Autoregressive Integrated Moving Average (ARIMA) and Seasonal ARIMA (SARIMA) models to examine the forecasting dynamics of the series. The pre-test results confirmed that EXR is a stationary difference process of order one {I(1)}, contains seasonality. SARIMA (0, 1, 1)(0, 1, 1)12 was observed to outperform its ARIMA (3, 1, 0) counterpart. The preference of the Akaike Information Criterion (AIC) in selecting the model over Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) was highlighted. A diagnostic check was carried out on the identified model and it revealed that the residual of the model is a white noise since it is homoscedastic, stationary, and non-autocorrelated. Findings from this study established that the Naira is projected to continue to fluctuate and further lose value relative to the USD within the forecasted time frame. Based on these findings, both the Government and policymakers need to formulate policies that will further enhance investment incentives, currency stabilization, and local production support. The practical implications of the forecast results on the country’s economy include rising costs of living, higher inflation, reduced foreign direct investment, job losses, worsening trade deficit, and skilled worker migration.
... (ARCH) models. These models are based on a series of differences that follow a martingale pattern [2]. The generalized Autoregressive Condition Heteroscedastic (GARCH) model was developed by Bollerslev in 1986 [1]. ...
This research proposes a new model for nonlinear time series called the Secant Double AR model of order k, SecDAR(k), which is based on the double autoregressive model with an augmented secant function. In 2007, Ling introduced this family of double autoregressive models, with the prototype model named DAR(P), where p is the order of the model. This approach addresses data volatility that leads to heteroscedasticity .Using dynamic principles and local linear methods, this research analyzes the stability conditions of the model. First, we approximate the previously mentioned model to a linear difference equation using a local linear strategy. Secondly, the roots of the characteristic equation are used to assess stability . In the end, the stability conditions for the above model are applied using data showing the average monthly closing price of heating oil in US dollars from 1990 to 2024. To evaluate the accuracy and quality of the models' fit on the actual data, we use the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC). In the application section, we use the stability condition to evaluate the stability for each order of SecDAR(k) from 1 to 6.
... High volatility can lead to heteroskedasticity. Engle developed the Autoregressive Conditional Heteroscedasticity (ARCH) model [38], which was later expanded by Bollerslev into the Generalized ARCH (GARCH) model [15] into the Generalized ARCH (GARCH) model. The GARCH process of order ( , ) is formulated in Equation (4) [33]. ...
Indonesia, as the largest Muslim-majority country, has significant potential to enhance its Shariah financial sector, which has been growing rapidly, around 7.43% from 2023 to 2024, and contributing to the national economy. However, political and natural disasters have influenced the economy and Shariah-compliant stocks. This study focuses on forecasting Shariah-compliant stock prices using Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models and estimating investment risks via Value at Risk (VaR) for four Islamic banks listed in IDX: BRIS, BTPS, BANK, and PNBS. The findings indicate that GARCH models effectively capture stock price dynamics and provide accurate 10-day forecasts. Additionally, the models reliably predict VaR, validated through backtesting at various confidence levels. These insights are valuable for financial regulators and risk managers, aiding in policy design to ensure market stability by enabling the implementation of measures such as stricter capital reserve requirements for institutions with high-risk exposure and mandatory adoption of advanced risk management techniques like dynamic stress testing. Such policies not only mitigate systemic risks during periods of financial volatility but also enhance the overall resilience and robustness of the financial system. For investors, accurate risk predictions support informed decision-making, enhance portfolio protection, and optimize risk management.
... where l(.) is a function that depends on a finite number of lagged values of observable and { θ i VaR t− j(θ) } p i=1 are the auto-regressive term ensuring that VaR changes smoothly over the periods. Additionally, among all four CAViaR models proposed by Engle (1982), we adopt asymmetric . However, V's colors are representations of the commodity industries (Energy = "blue", Grain = "orange", Metal = "pink" and Livestock = "yellow"). ...
Utilizing cross-correlation-based Planar Maximally Filtered Graph, and conditional Value-at-Risk-based extreme
risk spillover network approaches, we analyze the structure and dynamics of price contagion and risk trans
mission between different commodity groups in the global commodity futures market during the Global
Financial Crisis (GFC) and different phases of the COVID-19 pandemic. As expected, owing to the fundamental
differences between the two crises, we find very divergent commodity network structures and non-identical
direction of risk transmission between commodities in these two crises. Gold and silver, however, continued
to play their role of risk transmitters based on several factors, including the severity of the economic or political
crisis, prevailing market sentiment, and the distinctive attributes of the affected asset classes in both crisis—right
at the beginning of the GFC but towards the latter part of the COVID19 crisis
Kenyan coffee is globally recognized for its high quality and distinct flavor, securing a strong reputation in international markets. However, it faces growing competition from major producers such as Brazil, Colombia, Vietnam, Cuba, and Ethiopia. This study evaluates Kenya’s competitiveness in the global coffee industry by examining price dynamics and volatility from 1990 to 2022 across 21 coffee-producing countries. Data were sourced from the International Coffee Organization, World Bank, and FAOSTAT. The analysis employed price analysis, hedonic regression, and volatility models (GARCH, TARCH, and EGARCH). Results show Kenya ranks sixth among Arabica coffee producers in terms of production. Hedonic regression reveals that coffee prices are significantly influenced by macroeconomic and supply-side factors. Volatility models confirm the presence of volatility clustering, where high-price volatility persists over time, but show no significant asymmetry—indicating that both positive and negative shocks impact prices similarly. These findings highlight the need for market stabilization strategies, including hedging tools, improved market access, and stable exchange rates, to protect producers from adverse price movements. The study provides vital policy insights for enhancing Kenya’s resilience and long-term competitiveness in the global coffee value chain.
Artificial Intelligence (AI) has emerged as a transformative force in promoting green development by enhancing energy efficiency, optimizing resource utilization, and driving sustainable innovation. This study investigates the impact of AI adoption on green development using a dynamic panel Generalized Method of Moments (GMM) approach, addressing potential endogeneity and reverse causality. The research utilizes panel data from multiple industries from 2013 to 2022, incorporating AI investment, AI patents, and AI-driven sustainability initiatives as key independent variables. Green development is measured through carbon footprint reduction, renewable energy adoption, and environmental efficiency metrics. The findings reveal a significant positive relationship between AI adoption and green development, with AI-driven automation and predictive analytics playing a crucial role in sustainability improvements. These results provide valuable policy insights for integrating AI into global sustainability frameworks and guiding businesses toward environmentally responsible AI implementation.
The study is conducted with aim to analyze and examine the behavior of Asian Pacific stock market by analyzing the volatilities of five chosen stock markets; Karachi Stock Exchange (KSE) 100, Jakarta Stock Exchange (JKSE), Nikkei 225 Stock (N225), Shanghai Stock Exchange (SSE) and Taiwan Stock Exchange (TWSE) indices. This study takes 25 years, 2000 till 2024 of data by taking daily prices of the markets. The prices were transformed to log returns. In the descriptive statistics N225 index had recorded the highest positive return and highest negative return. Similarly, TWSE index recorded the lowest positive and lowest negative returns. Furthermore, modeling the volatilities, the study first estimated the ARCH effect for heteroscedasticity, the results are significant for all the series. The outcomes of GARCH model for all the series are significant. The study finds that past volatilities are significantly affecting the current volatilities and empirically the future returns and volatilities can be predicted by using past volatilities. The EGARCH model found that all the indices are having asymmetric volatilities. Thus, it is concluded that Asian pacific stock markets behave in similar way.
Penelitian ini bertujuan untuk mengetahui bagaimanakah tingkat return saham dan model volatilitas dengan metode ARCH-GARCH pada saham Bank Rakyat Indonesia tahun 2019 sampai dengan 2022. Dalam penelitian ini pendekatan penelitian yang digunakan yaitu pendekatan deskriptif kuantitatif, dimana menggunakan data kuantitatif yang berbentuk angka karena mengacu pada harga saham. Volatilitas menunjukkan fluktuasi pergerakan harga saham, semakin tinggi volatilitas maka semakin tinggi pula kemungkinan mengalami keuntungan dan kerugian. Data time series yang sering memiliki volatilitas tinggi adalah data harga saham. Data time series dibidang keuangan sering memiliki sifat volatility clustering atau disebut dengan heteroskedastisitas sehingga metode ARCH-GARCH layak digunakan pada pemodelan volatilitas saham BBRI tahun 2019 sampai dengan 2022. Pemodelan data daily closing price saham berguna agar investor mampu untuk mempelajari situasi saham, sehingga dapat mengambil keputusan yang tepat ketika melakukan pembelian dan penjualan saham BBRI)
The study aims to investigate the impact of coal and electricity price volatility on Borsa Istanbul (BIST) chemical petroleum plastic index (CPPI) return. Sample of the study spans from August 2009 to December 2020. In this study, volatility in electricity and coal prices are modeled with autoregressive conditional heteroscedasticity models. In the regression model including the BIST CPPI return, it is investigated whether the electricity and coal price volatility coefficients are statistically significant. When we examine the models showing the impact of electricity and coal volatility on BIST CPPI return, we conclude that the electricity and coal price volatility coefficients are statistically insignificant.
AbstrakPasar keuangan merupakan cerminan dinamika ekonomi global yang seringdiwarnai oleh volatilitas, yaitu fluktuasi signifikan dalam harga aset. Penelitianini bertujuan untuk menganalisis hubungan antara volatilitas pasar, yangdiukur melalui indeks VIX, dan alokasi saham oleh investor dalam rentangwaktu 2015–2024. Metode yang digunakan adalah analisis data historis VIXdan persentase alokasi saham. Hasil penelitian menunjukkan bahwapeningkatan indeks VIX cenderung menyebabkan penurunan alokasi sahamoleh investor, mengindikasikan adanya penghindaran risiko di tengahketidakpastian pasar. Sebaliknya, ketika indeks VIX menurun, alokasi sahammeningkat sebagai respons terhadap kondisi pasar yang lebih stabil. Temuanini menegaskan bahwa volatilitas pasar memainkan peran penting dalampengambilan keputusan investasi. Pemahaman mendalam tentang volatilitasmemungkinkan investor untuk mengelola risiko lebih efektif danmemanfaatkan peluang yang muncul dalam kondisi pasar yang fluktuatif.AbstractThe financial market reflects the dynamics of the global economy, oftencharacterized by volatility, which signifies significant fluctuations in assetprices. This study aims to analyze the relationship between market volatility,measured through the VIX index, and investors' equity allocation from 2015 to2024. The methodology involves analyzing historical data on the VIX index andequity allocation percentages. The results indicate that an increase in the VIXindex tends to lead to a decrease in equity allocation by investors, suggestingrisk aversion amid market uncertainty. Conversely, when the VIX indexdecreases, equity allocation rises in response to more stable marketconditions. These findings confirm that market volatility plays a significant rolein investment decision-making. A deep understanding of volatility enablesinvestors to manage risk more effectively and seize opportunities that ariseunder fluctuating market
Rural economies are largely dependent upon agriculture, which is greatly determined by climatic conditions such as rainfall. This study aims to forecast agricultural production in Maharashtra, India, which utilises annual data from the year 1962 to 2021. Since rainfall plays a major role with respect to the crop yield, we analyze the impact of rainfall on crop yield using four time series models that includes ARIMA, ARIMAX, GARCH-ARIMA and GARCH-ARIMAX. We take advantage of rainfall as an external regressor to examine if it contributes to the performance of the model. 1-step, 2-step, and 3-step ahead forecasts are obtained and the model performance is assessed using MAE and RMSE. The models are able to more accurately predict when using rainfall as a predictor compared to when solely dependant on historical production trends (more improved outcomes are seen in the ARIMAX and GARCH-ARIMAX models). As such, these findings underscore the need for climate-aware forecasting techniques that provide useful information to policymakers and farmers to aid in agricultural planning.
Agricultural commodity markets remain unstable due to climate change, evolving global demand, and disruptions faced due to supply chain. Improved risk management strategies are crucial to establish food security and ensuring proper income of the farmers. In this paper, we examine the application of the renowned newsvendor model to agricultural products. We demonstrate effectiveness of the model to determine optimal procurement quantity and alleviate risks associated with both shortages and overproduction. Newsvendor model has been widely applied in different discipline since its inception, determines optimal quantity by balancing shortage and overage cost. We establish significance of applying the model to India’s agricultural sector to improve procurement decisions, minimizing losses. Additionally, integration of the model into policy planning also improve the effectiveness of government interventions, such as minimum support price (MSP) schemes and buffer stock management. Furthermore, we explore the application of the model to the country’s agricultural export policy, particularly focusing on the African countries affected by droughts, and receive support from the United Nations. The newly developed framework effectively enhance food security in vulnerable regions along with improving India's agricultural trade and global outreach. Our findings indicate that incorporating newsvendor framework contribute towards a more stable and market-driven agricultural economy in India.
This paper examines the forecasting performance of different GARCH models (GRACH, EGARCH, TARCH and APARCH) under the Normal, Student-t and Generalized error distributional assumption. We compare the effect of different distributional assumption on the GARCH models. The data we analyze is the daily stocks index of Islami Bank and Brac bank of Dhaka Stock Exchange during the time period 19.01.2014 to 17.1.2024. We find that improvements of the overall estimation are achieved when asymmetric GARCH models are used with student-t distribution and generalized error distribution. Moreover, it is found that APARCH, EGARCH and TARCH model give better forecasting performance than GARCH model. Our results show that noticeable improvements can be made when using asymmetric GARCH model with non normal distributional assumptions. APARCH model with student-t distribution fit the data well. So we may conclude that APARCH model with student-t distribution is the most suitable model to predict the volatility of Islami bank closing index.
This paper examines different hedging techniques for options written on non-exchange-traded agricultural commodities using the futures markets to hedge, and evaluates the performance using statistical measures. The paper applies the hedging methods to real agricultural commodity data from the USDA. In these markets there are a number of commercial risks, such as weather and supply-chain disruption, which need to be managed by both producers and consumers. Typically, there is no perfectly correlated hedging instrument available for the product being traded, and as such there is basis risk present when trying to find a hedging solution. This highlights the need for empirical studies which address the problem of how to hedge in this environment. We evaluate static and dynamic hedging strategies for European options written on livestock indices using live cattle futures to hedge. Hedging methods based on delta, minimum variance, value-at-risk (VaR), and conditional VaR (C-VaR) are tested. Hedging performance is examined by hedging effectiveness (i.e calculating risk reduction versus an unhedged portfolio) and distribution statistics. Overall, we found that the static minimum-variance technique provided the best hedging performance in terms of risk reduction versus the unhedged portfolio.
Price volatility in grain markets, especially for maize, has substantial socio-economic impacts, particularly in low-income regions where food security remains a critical concern. Accurate forecasting of grain price volatility is therefore crucial in safeguarding the financial interests of commodity traders, as well as shielding consumers from detrimental effects of inflationary food prices. This study proposes a hybrid Bi-directional Long Short-Term Memory (BLSTM) model, integrated with generalised autoregressive conditional heteroscedasticity (GARCH)-type methods, to forecast white maize futures volatility in South Africa. By comparing the forecasting accuracy of the hybrid BLSTM model against several benchmarks, including standard LSTM and BLSTM models, our results demonstrate notable improvements in prediction accuracy, as shown through heteroscedasticity-adjusted performance metrics. The key contribution of this research is its enhancement of volatility forecasting by combining advanced machine learning with traditional econometric approaches, bridging a gap in predictive accuracy for commodity price dynamics. Additionally, this study supports the United Nations Sustainable Development Goals (SDGs), particularly Zero Hunger and Responsible Consumption and Production, by improving food price stability and risk management in agriculture. This approach exemplifies the evolving role of data science in financial analysis, offering market participants an effective tool to manage price risk and improve food security.
Impact Statement
This study introduces a novel hybrid forecasting model that integrates GARCH-type econometric techniques with Bi-directional Long Short-Term Memory (BLSTM) neural networks to predict the realised volatility of white maize futures. As white maize is a staple food, accurate volatility forecasting directly contributes to improved food security and price stability. The model significantly outperforms traditional approaches and standard deep learning models across multiple forecast horizons, offering a powerful risk management tool for farmers, traders, and policymakers. By enhancing the accuracy of agricultural price forecasts, this research supports the United Nations Sustainable Development Goals (SDGs), particularly Zero Hunger (SDG 2) and Responsible Consumption and Production (SDG 12), while also demonstrating the value of advanced data science methods in addressing real-world socio-economic challenges.
Bu çalışmanın amacı, üç farklı geleneksel emtia portföylerinin optimize edilmesi ve kripto para birimleri ile çeşitlendirmenin portföyler üzerindeki etkilerinin incelenmesidir. Araştırmanın veri setini, dört likit kripto para birimi ve üç farklı geleneksel emtiaya ait günlük veriler oluşturmaktadır. Çalışmada her bir emtia için uygun ARMA modelleri belirlenmiştir. Emtia portföylerini optimize etme ve kripto para birimleri ile çeşitlendirmenin etkisini gözlemlemek amacıyla OxMetrics6 programı yardımıyla DCC-GARCH modeli kullanılmıştır. Ulaşılan analiz sonuçlarına göre, kripto para birimlerinden bir kısmı portföy çeşitlendirmesinde yatırımcı riskini azaltmakta bir kısmı da koruma özelliği göstermektedir. Çalışmanın bulgularında, kripto para birimlerinin, geleneksel emtialar ile arasındaki düşük korelasyon ve portföy performansını artırdığına ulaşılmıştır. Bu bağlamda, kripto para birimleri portföy çeşitlendirmesi için iyi bir araç olmakta ve portföy performansını olumlu etkilemektedir.
This study examines the long-and short-term dynamic impacts of participatory investments in infrastructure (Transport and energy) on India's economic growth, as measured by GDP, from 1994 to 2023, employing the Autoregressive Distributed Lag (ARDL) model. The stationarity of time series variables was assessed by unit root tests, namely the Augmented Dickey-Fuller (ADF) test and the Phillips-Perron (PP) test, indicating that all variables are integrated of the first order. The estimation results for both long-and short-term connections demonstrate strong beneficial impacts of participatory investments in transportation and energy on GDP. Over the long term, the effects of participation investment in transportation surpass those of participatory investment in energy; conversely, in the short term, the opposite holds true. Furthermore, a cointegration relationship exists between participation investments in the transport and energy sectors and India's GDP. GDP necessitates roughly six years to revert to its equilibrium value in the long term after experiencing short-term disturbances in participatory investments. Additionally, the Toda-Yamamoto causality test revealed a unidirectional long-term causal relationship between GDP and participatory investment in transport, as well as from participatory investment in energy to GDP.
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