Autoregressive Conditional Heteroscedasticity Model Research Articles

DYNAMIC LINKS BETWEEN COMMODITY MARKETS & PAKISTANI SECTORAL INDICES: IMPLICATIONS FOR PORTFOLIO DIVERSIFICATION

This research aimed to examine the inter-connections among international commodities markets and sectoral indices of Pakistan over the most recent period ranging from July 19, 2016, to December 29, 2023. This time period is selected based on recent important events of global significance including COVID-19 pandemics and recent geopolitical crisis emerged due to Russia-Ukraine war in Feb, 2022. This study is utilizing Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model for the deeper inquiry of interplay among the variables. The findings of the study indicate significant spillovers among variables with varying degrees of significance. The results show that various sectors of Pakistan economy showed asymmetric behavior indicating that some sectors were the risk transmitters while other were risk recipients. Moreover, volatility linkages are time-varying with heightened transmissions during turbulent periods. The results provide the significant information in reaching the desired conclusion and making decisions. The findings of study thus had important implications for investors (individual & institutional), fund managers and policy makers while devising strategies for diversification and risk mitigation in the Pakistani context especially in stressful periods.

The Effect of Exchange Rate Volatility on Foreign Tourist Visits in Indonesia: GARCH Analysis

In this era of globalization, currency exchange rates are one of the crucial factors affecting a country's economy. The exchange rate of a country's currency plays an important role in economic stability and international trade, especially in the tourism sector. This study aims to conduct an in-depth analysis to identify patterns of rupiah exchange rate volatility using the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, and then examine whether these patterns have a significant correlation with the number of foreign tourist arrivals in Indonesia. In analyzing the data, researchers conducted several classical assumption tests, namely the normality test and the heteroscedasticity test. The test results show that the data used, namely the rupiah exchange rate data and the number of foreign tourist visits, are not normally distributed and heteroscedastic. In this case, it resulted in researchers not use the Pearson correlation test so they used the Kendall-Tau correlation test and Granger Causality test which resulted in the two variables being correlated. Furthermore, GARCH modeling is carried out which provides forecasting on both data to increase in 2024. The results of this study are expected to provide a basis for consideration for stakeholders to determine policies, especially in the financial and tourism sectors.

Modeling Exchange Rate of Naira to Euro with the APLSTAR-GARCH model

Application of the asymmetric power logistic smooth transition autoregressive (APLSTAR) model proposed by [1] to naira/Euro exchange rate spanning from January, 2006 to April, 2021, which is a nonlinear macroeconomic time series was considered. The APLSTAR model was justifiably fitted to the series and the fit of the APLSTAR model compared with the fits of the competing models revealed that the APLSTAR model fits the data exchange rate of naira to Euro better than the other asymmetric STAR models. Lagrange Multiplier tests for autoregressive conditional heteroscedastic (ARCH) effects were carried out and there was no substantial evidence to reject the presence of ARCH effects in the set of residuals used. Hence, we compared hybrid smooth transition autoregressive-generalized ARCH (STAR-GARCH) models using model evaluation criteria. On balance, the APLSTAR-GARCH (0, 1) model outperforms the other models under consideration.

Addressing Loss and Damage from Climate Change Through Tokenized Rainfall Futures

The objective of the study was to explore how finance to cover the cost of loss and damage from climate change can be mobilized through weather derivatives. More specifically, a futures contract was considered as the derivative to mobilize the financing. To integrate the recent advancements in finance and technology, tokenized weather derivatives can be considered. This study contributes to the literature as it proposes a pricing mechanism for the proposed loss and damage futures. The futures price should be a function of the contract size, the difference between the expected rainfall in the future, and the threshold or long-run average rainfall. This pricing approach is adopted since it allows the price to rise when excess rainfall occurs, which in turn is responsible for loss and damage. Therefore, the forecast of the rainfall should be of significant interest of the economic agent seeking to hedge the loss and damage with the futures. A Long Short-Term Memory (LSTM) model was used for forecasting. The LSTM performed better than traditional linear models such as the Autoregressive Integrated Moving Average (ARIMA) and Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) models, as it can capture the non-linear dynamics of the rainfall data.

Estimated Value-at-Risk Using the ARIMA-GJR-GARCH Model on BBNI Stock

Stocks are investment instruments that are much in demand by investors as a basis in financial storage. Return and risk are the most important things in investing. Return is a complete summary of investment and the return series is easier to handle than the price series. The movement of risk of loss is obtained from stock investments with profits. One way to calculate risk is value-at-risk. The movement of stocks is used to form a time series so that the calculation of risk can use time series. The purpose of this study was to find out the Value-at-Risk value of BBNI Shares using the ARIMA-GJR-GARCH model. The data used in this study was the daily closing price for 3 years. The time series method used is the model that will be used, namely the Autoregressive Integrated Moving Average (ARIMA)-Glosten Jagannathan Runkle - generalized autoregressive conditional heteroscedastic (GJR-GARCH) model. The stage of analysis is to determine the prediction of stock price movements using the ARIMA Model used for the mean model and the GJR-GARCH model is used for volatility models. The average value and variants obtained from the model are used to calculate value-at-risk in BBNI shares. The results obtained are the ARIMA(1,0,1)-GJR-GARCH(1.1) model and a significance level of 5% obtained value-at-risk of 0.0705.

Hybrid Fourier asymmetric-garch estimation of value at risk and expected shortfall: Empirical evidence from crude oil prices

We propose a hybrid Fourier approximation in an autoregressive fractional integrated moving average (ARFIMA) model, to account for periodic unoberved components in financial time series. We apply this hybrid model on parametric estimation of value at risk (VaR) and expected shortfall (ES). Using crude oil returns, we show that Fourier approximation inclusion significantly accounts for unobserved periodic components in a VaR estimation using exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model under generalized error distribution (GED). Similarly, in VaR estimation, Fourier approximation inclusion significantly accounts for unobserved periodic components using asymmetric power generalized autoregressive conditional heteroscedasticity (APARCH) model under skewed normal distribution (SNORM). For ES estimation, Fourier approximation inclusion only significantly accounts for unobserved periodic components of APARCH under SNORM.

Equilibrium bifurcation and extreme risk in the EU carbon futures market

Considering the long-term memory and volatility clustering of the European Union (EU) Carbon Emission Allowances (EUA) futures returns, based on the economy–energy–environment system perspective and the assumption of investors' heterogeneity, this study proposes a joint modeling approach combining the fractionally integrated generalized autoregressive conditional heteroscedasticity model (FIGARCH) and the stochastic cusp catastrophe model (SCC) to examine the equilibrium bifurcations and extreme risks in the EU carbon futures market. The relevant results are threefold. (1) The SCC model has good fitting effect and interpretability, and is an effective method for investigating catastrophe reactions under time-varying volatility conditions. (2) In the EUA futures market, chartists are mainly affected by short-term price and trading volume changes, which leads to the emergence of equilibrium bifurcations, while fundamentalists make investment decisions based on the economy, the energy market, and market supply–demand, which affects the asymmetry of equilibrium bifurcations. (3) Using the catastrophe criterion (i.e., Cardan's discriminant of the equilibrium surface equation), we identify148 equilibrium bifurcation time points in the EUA futures market from December 3, 2009 to September 16, 2020, most of which are concentrated in two upward periods with an average scale of extreme risks is about 32.51 %. Our analysis provides theoretical support for regulatory authorities to stabilize the carbon futures market and build a collaborative extreme risk management framework covering energy and macroeconomics, also proposing suggestions for traders to effectively prevent extreme risks.

Testing ARCH effect of high-dimensional time series data

Testing for the autoregressive conditional heteroscedasticity (ARCH) effect is an important problem in economic and financial time series. In this article, we consider the ARCH effect test for high-dimensional time series. Our test statistic is built based on the maximum element of Spearman’s rank correlation at different lags. The bootstrap methods are used to approximate the null distribution of the proposed test statistics. We also consider the goodness-of-fit test for ARCH models by applying the test to the residuals of fitted models. Simulation results show that the proposed test statistics enjoy good properties of size in finite samples. Compared to the existing methods, the new test possesses much better power. Moreover, the test is not sensitive to the underlying distribution of the time series. The proposed method is illustrated via two real data.

Comparative Analysis of Gold, Bitcoin and Gold-backed Cryptocurrencies as Safe Havens During Global Crises: A Focus on G7 Stock Market and Banking Sector Indices

In this article, we attempt to analyze and compare the safe-haven features of gold, Bitcoin and gold-backed cryptocurrency against the stock and banking indices of G7 countries during the outbreak of adverse events. To do so, we examine dynamic relationships between different assets and we compute optimal hedge ratios for different couples using the corrected Asymmetric Dynamic Conditional Correlation-Exponential Generalized Autoregressive Conditional Heteroscedasticity and corrected Asymmetric Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroscedasticity models. We clearly show that gold and gold-backed cryptocurrency maintain higher weights in optimal portfolios compared to Bitcoin. We also report that shocks due to unexpected events increasingly affect dynamic correlations, asset weights and hedge ratios. This underscores the need for regular demand for rebalancing the hedge positions and effective risk management. We thereafter show that the relationship between Bitcoin (gold-backed cryptocurrency) and G7 indices is highly affected by the outbreak of COVID-19 pandemic. Such findings highlight the hedging and safe-haven features of different asset classes against stock markets. They could have insightful implications for investors who want to minimize investment risks and policymakers who are worried about the financial consequences of different unexpected events.

THE HOLIDAY EFFECTS ON AMUSEMENT AND THEME PARK COMPANIES’ STOCK PRICES

This study offers further evidence of the holiday effect on excess stock returns and volatility, and additional insights into its impact on the amusement park and attractions industry in the United States. The generalized auto-regressive conditional heteroscedasticity (GARCH) model and dummy variables are adopted to investigate pre- and post-holiday excess returns and volatility. Empirical results suggest the following: (1) both excess returns and excess volatility happen more frequently in pre-holidays than post-holidays; (2) the frequency of excess volatility is higher than excess returns for the holiday effect; and (3) nearly all significant excess volatilities are negative. We, therefore, conclude that the holiday effect exists in publicly traded amusement and theme parks.

Forecasting tail risk of skewed financial returns having exponential‐polynomial tails

AbstractAggregated long and short trading risk positions of speculative assets over time are likely to be unequal. This may be because of irrational decisions of traders and investors as well as catastrophic events that lead to pronounce or salient market crashes. Returns of such assets are therefore more likely to have one polynomial tail and one exponential tail. The generalized hyperbolic (GH) skewed Student‐t distribution is known to handle such situations quite well. In this paper, we use generalized autoregressive conditional heteroscedasticity (GARCH) models to empirically show the superiority of the GH skewed Student‐t distribution in forecasting the extreme tail risks of cryptocurrency returns in the presence of substantial skewness in comparison with some competing distributions. Furthermore, we show the practical significance of the GH skewed Student‐t distribution‐based risk forecasts in computing daily capital requirements. Evidence from the study suggests that the GH skewed Student‐t distribution model tends to be superior in forecasting volatility and expected shortfall (ES) but not value‐at‐risk. In addition, the distribution yields higher value‐at‐risk (VaR) exceptions but surprisingly avoids the red zone of the Basel II accord penalty zones and produces lower but optimal daily capital requirements. Therefore, in the presence of substantially skewed returns having exponential‐polynomial tails, we recommend the use of the GH skewed Student‐t distribution for parametric GARCH models in forecasting extreme tail risk.

Threshold Network GARCH Model

Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its variations have been widely adopted in the study of financial volatilities, while the extension of GARCH‐type models to high‐dimensional data is always difficult because of over‐parameterization and computational complexity. In this article, we propose a multi‐variate GARCH‐type model that can simplify the parameterization by utilizing the network structure that can be appropriately specified for certain types of high‐dimensional data. The asymmetry in the dynamics of volatilities is also considered as our model adopts a threshold structure. To enable our model to handle data with extremely high dimension, we investigate the near‐epoch dependence (NED) of our model, and the asymptotic properties of our quasi‐maximum‐likelihood‐estimator (QMLE) are derived from the limit theorems for NED random fields. Simulations are conducted to test our theoretical results. At last we fit our model to log‐returns of four groups of stocks and the results indicate that bad news is not necessarily more influential on volatility if the network effects are considered.

Comparative Analysis of Bilinear Time Series Models with Time-Varying and Symmetric GARCH Coefficients: Estimation and Simulation

This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive Conditional Heteroscedastic (GARCH) models serve as the white noise component. The methodology involves applying the Klimko–Nilsen theorem, which plays a crucial role in extracting the asymptotic behavior of the estimators. In this context, the Generalized Autoregressive Conditional Heteroscedastic model of order (1,1) noted that the GARCH (1,1) model is defined as the white noise for the coefficients of the example models. Notably, this GARCH model satisfies the condition of having time-varying coefficients. This study meticulously outlines the essential stationarity conditions required for these models. The estimation of coefficients is accomplished by applying the least squares method. One of the key contributions lies in utilizing the fundamental theorem of Klimko and Nilsen, to prove the asymptotic behavior of the estimators, particularly how they vary with changes in the sample size. This paper illuminates the impact of estimators and their approximations based on varying sample sizes. Extending our study to include the estimation of bilinear models alongside GARCH and GARCH symmetric coefficients adds depth to our analysis and provides valuable insights into modeling financial time series data. Furthermore, this study sheds light on the influence of the GARCH white noise trace on the estimation of model coefficients. The results establish a clear connection between the model characteristics and the nature of the white noise, contributing to a more profound understanding of the relationship between these elements.

Predicting influenza-like illness trends based on sentinel surveillance data in China from 2011 to 2019: A modelling and comparative study1

BackgroundInfluenza is an acute respiratory infectious disease with a significant global disease burden. Additionally, the coronavirus disease 2019 pandemic and its related non-pharmaceutical interventions (NPIs) have introduced uncertainty to the spread of influenza. However, comparative studies on the performance of innovative models and approaches used for influenza prediction are limited. Therefore, this study aimed to predict the trend of influenza-like illness (ILI) in settings with diverse climate characteristics in China based on sentinel surveillance data using three approaches and evaluate and compare their predictive performance. MethodsThe generalized additive model (GAM), deep learning hybrid model based on Gate Recurrent Unit (GRU), and autoregressive moving average-generalized autoregressive conditional heteroscedasticity (ARMA—GARCH) model were established to predict the trends of ILI 1-, 2-, 3-, and 4-week-ahead in Beijing, Tianjin, Shanxi, Hubei, Chongqing, Guangdong, Hainan, and the Hong Kong Special Administrative Region in China, based on sentinel surveillance data from 2011 to 2019. Three relevant metrics, namely, Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE), and R squared, were calculated to evaluate and compare the goodness of fit and robustness of the three models. ResultsConsidering the MAPE, RMSE, and R squared values, the ARMA—GARCH model performed best, while the GRU-based deep learning hybrid model exhibited moderate performance and GAM made predictions with the least accuracy in the eight settings in China. Additionally, the models’ predictive performance declined as the weeks ahead increased. Furthermore, blocked cross-validation indicated that all models were robust to changes in data and had low risks of overfitting. ConclusionsOur study suggested that the ARMA—GARCH model exhibited the best accuracy in predicting ILI trends in China compared to the GAM and GRU-based deep learning hybrid model. Therefore, in the future, the ARMA—GARCH model may be used to predict ILI trends in public health practice across diverse climatic zones, thereby contributing to influenza control and prevention efforts.

Developing Exp-FIGARCH Hybrid Models for Time Series Modelling

In this paper, we introduced a new hybrid model namely Exponential Autoregressive-Fractional Integrated Generalized Autoregressive Conditional Heteroscedasticity (ExpAR-FIGARCH) model and study financial data. The Daily Nigeria All Share Stock Index that exhibit nonlinear, volatility and long memory effect were analyzed in the study. The existing ExpAR-Generalized Autoregressive Conditional Heteroscedasticity (ExpAR-GARCH) model were estimated and compared with the proposed ExpAR-FIGARCHmodel. Results showed that the new hybrid model is better based on efficient parameters, serial correlation analysis and forecast measures of accuracy. Therefore, as a conclusion, the current study indicates that the ExpAR-FIGARCHmodel performed better compared to the ExpAR-GARCHhybrid model. Therefore, the ExpAR-FIGARCHmodel is a better option for modeling nonlinear, volatility and long memory characteristics of time series. Future study should focus on the application of the developed hybrid ExpAR-FIGARCHmodel using health, meteorological and economic data.

Analysis Volatility Spillover of Stock Index in ASEAN (Case Study: Indonesia, Singapore, Malaysia)

Every country has its own income, including ASEAN countries such as Indonesia, Singapore, and Malaysia. One source of national income can come from stocks, which can be measured by the stock index. The income of each country depends on each other and can be influenced by a phenomenon, such as the Covid-19 pandemic. The Covid-19 pandemic can also cause volatility spillover. This research aims to analyze volatility spillover in ASEAN countries (Indonesia, Singapore, and Malaysia) before and during Covid-19 by looking at the effects of asymmetric volatility. Volatility spillover testing in this study uses the Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) model, starting with creating a time series model and then modeling the residuals from that model, then finding the estimated parameter results of asymmetric volatility effects. The results of this study indicate that during the period before Covid-19, there is volatility spillover for Indonesia and Malaysia. Then, during the Covid-19 period, there is volatility spillover for Indonesia and Malaysia, for Indonesia and Singapore, and for Singapore and Malaysia.

Return and Volatility Spillover in Equity and Commodity Market: Some Indian Evidence

This study empirically investigates the return and volatility spillover among equity markets, Agro and non-Agro commodity markets. The study has used daily return data of BSE SENSEX as equity index, MCX iCOMEDEX, including Gold, Silver, and Crude oil, as non-agro indices, and NCDEX (AGRIDEX) as agro commodity indices to analyze volatility transmission between assets and markets using Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and Exponential Generalized Autoregressive Conditional Heteroscedastic (EGARCH) model. The study has used dummy variables in the variance equation to identify the structural breaks during the COVID 19 pandemic. Further, Vector Auto Regression (VAR) pair-wise Granger causality test has been used to understand returns’ causality. The study has found a bidirectional and unidirectional causal relationship between variables. The study indicates that NCDEX could influence all the variables except MCX Gold. In structural breaks with deterministic dummy variables during COVID-19, we have found mixed evidence of asymmetric impact on conditional volatility. The study also indicates a positive and significant asymmetric volatility effect in the case of MCX Gold and MCX Silver during the COVID-19 period. The study has specified that SENSEX dominates the inflow of information to all commodity markets. Also, the findings signpost that information flows from NCDEX to MCX Gold, MCX Silver, and MCX Crude Oil. JEL Codes: C32, E30, E44, F41, G15, Q43

Asymmetric Volatility in Stock Market: Evidence from Selected Export-based Countries

In a country, the financial markets depend on several economic factors. One of these important factors is the export of the country. The stock index of the country tends to be raised due to the exports, though it may occur after some time rather than immediately. In this study, an attempt has been made to predict the best model of volatility in top export countries, Germany, China, the United States, Japan and Hong Kong by taking into account the closing price of the stock index of the sampled countries for a period ranging from the year 2000 to 2020. The returns from the stock markets are asymmetric; negative returns are found to be followed by a greater increase in volatility than the corresponding positive returns. Therefore, both symmetric and asymmetric generalised autoregressive conditional heteroscedasticity (GARCH) models have been applied to predict the volatility. The symmetric model used is GARCH (1,1) and asymmetric models used in the study are exponential GARCH (1,1) and GJR-GARCH (1,1). The study shows that EGARCH model has outperformed the GARCH and GJR-GARCH models in estimating the volatility in four stock indices ( Hanif & Pok, 2010 ; Kışınbay, 2010 ; Lin, 2018 ), and GJR-GARCH has outperformed in estimating volatility in one stock index ( Oberholzer & Venter, 2015 ; Shamiri & Hassan, 2007 ). The benefit of this study is to help portfolio managers, investors and corporations in making investment-related decisions. JEL Codes: C20, C31, C58, G12

A multivariate spatial and spatiotemporal ARCH Model

This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects, as they are usually present in geo-referenced data. Furthermore, spatial and temporal cross-variable effects in the conditional variance are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and different error distributions, the performance of the QMLE is analysed in a series of Monte-Carlo simulations. In addition, we illustrate the practical usage of the new model with a real-world example. We analyse the monthly real-estate price returns for three different property types in Berlin from 2002 to 2014. We find weak (instantaneous) spatial interactions, while the temporal autoregressive structure in the market risks is of higher importance. Interactions between the different property types only occur in the temporally lagged variables. Thus, we see mainly temporal volatility clusters and weak spatial volatility spillovers.

Calendar Anomalies in NFT Coins

Abstract 
 This study examines the effect of day-of-the-week, month-of-the-year, and turn-of-the-month anomalies on NFT coins (Stacks, Tezos, and Decentraland) and Bitcoin over the period 2019–2023 by employing the generalized autoregressive conditional heteroscedasticity (GARCH) model. Based on the day-of-the-week anomaly results, Bitcoin has lower returns on Thursdays and Fridays, and Stacks has lower returns on Wednesdays. The remaining coins do not exhibit that anomaly. According to the month-of-the-year effect results, all evaluated coins generated abnormal returns in January. Moreover, positive returns were also reported in February for Tezos, Decentraland, and Bitcoin. Additionally, Bitcoin experienced positive returns in March as well. Furthermore, besides January, Stacks had significantly positive returns in April and May. Finally, the results of the turn-of-the-month anomaly suggest that only Stacks has statistically significant and positive returns on the last day of the month and the next three days. The remaining cryptocurrencies do not have such an anomaly. Overall, the findings of this study suggest the existence of calendar anomalies in the cryptocurrency market that contradict the assumptions of market efficiency. By using these outcomes, investors may develop trading strategies for their portfolio selection; hence, by taking advantage of the market, they could earn unusual profits.