Autoregressive Conditional Heteroscedasticity Model Research Articles

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.

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.

A Study on the Nature of Complexity in the Spanish Electricity Market Using a Comprehensive Methodological Framework

The existence of chaos is particularly relevant, as the identification of a chaotic behavior in a time series could lead to reliable short-term forecasting. This paper evaluates the existence of nonlinearity and chaos in the underlying process of the spot prices of the Spanish electricity market. To this end, we used daily data spanning from 1 January 2013, to 31 March 2021 and we applied a comprehensive framework that encompassed a wide range of techniques. Nonlinearity was analyzed using the BDS method, while the existence of a chaotic structure was studied through Lyapunov exponents, recurrence plots, and quantitative recurrence analysis. While nonlinearity was detected in the underlying process, conclusive evidence supporting chaos was not found. In addition, the generalized autoregressive conditional heteroscedastic (GARCH) model accounts for part of the nonlinear structure that is unveiled in the electricity market. These findings hold substantial value for electricity market forecasters, traders, producers, and market regulators.

Fluctuations and Forecasting of Carbon Price Based on A Hybrid Ensemble Learning GARCH-LSTM-Based Approach: A Case of Five Carbon Trading Markets in China

Carbon trading risk management and policy making require accurate forecasting of carbon trading prices. Based on the sample of China’s carbon emission trading pilot market, this paper firstly uses the Augmented Dickey–Fuller test and Autoregressive conditional heteroscedasticity model to test the stationarity and autocorrelation of carbon trading price returns, uses the Generalized Autoregressive Conditional Heteroscedasticity family model to analyze the persistence, risk and asymmetry of carbon trading price return fluctuations, and then proposes a hybrid prediction model neural network (generalized autoregressive conditional heteroscedasticity–long short-term memory network) due to the shortcomings of GARCH models in carbon price fluctuation analysis and prediction. The model is used to predict the carbon trading price. The results show that the carbon trading pilots have different degrees of volatility aggregation characteristics and the volatility persistence is long, among which only the Shanghai and Beijing carbon trading markets have risk premiums. The other pilot returns have no correlation with risks, and the fluctuations of carbon trading prices and returns are asymmetrical. The prediction results of different models show that the root mean square error (RMSE) of Hubei, Shenzhen and Shanghai carbon trading pilots based on the GARCH-LSTM model is significantly lower than that of the single GARCH model, and the RMSE values are reduced by 0.0006, 0.2993 and 0.0151, respectively. The RMSE in the three pilot markets improved by 0.0007, 0.3011 and 0.0157, respectively, compared to the standalone LSTM model. At the same time, compared with the single model, the GARCH-LSTM model significantly increased the R^2 value in Hubei (0.2000), Shenzhen (0.7607), Shanghai (0.0542) and Beijing (0.0595). Therefore, compared with other models, the GARCH-LSTM model can significantly improve the prediction accuracy of carbon price and provide a new idea for scientifically predicting the fluctuation of financial time series such as carbon price.

Robust monitoring conditional volatility change for time series based on support vector regression

This study considers a robust monitoring procedure aimed at detecting an anomaly of conditional volatility from sequentially observed time series following a (nonlinear) generalized autoregressive conditional heteroscedastic (GARCH) model. We employ a specifically designed cumulative sum (CUSUM) method hybridized with the asymmetric Huber support vector regression, named AHSVR. AHSVR-GARCH model provides an effective way to model nonlinear GARCH time series while significantly augmenting the performance of the proposed monitoring process in terms of stability and detection ability. Monte Carlo simulations illustrate the functionality of AHSVR-GARCH monitoring scheme, demonstrating AHSVR-GARCH model’s superiority over the standard SVR-GARCH model when monitoring GARCH-type time series. Data analysis using the S&P 500, NASDAQ index, and Korea Composite Stock Price Index (KOSPI) also affirms our method’s efficacy in real-world applications.

Asymmetric beta-binomial GARCH models for time series with bounded support

In this paper, we introduce a new class of asymmetric beta-binomial generalized autoregressive conditional heteroscedastic (GARCH) models for bounded integer-valued time series, which can capture the asymmetric impact of positive and negative observations. We study the stationarity conditions of the process and derive the moment and covariance functions. Furthermore, we estimate the unknown parameters using the conditional maximum likelihood (CML) method. The asymptotic properties of the estimators are discussed, as well as their finite-sample performance. Finally, we illustrate the model to real time series data in the field of meteorology.

Performance of crypto-Forex portfolios based on intraday data

This study identifies and assesses the diversification benefits of including large-cap and highly liquid cryptocurrencies into portfolios comprised of major fiat currencies quoted against the USD. We employ hourly data over the period from January 01, 2019 to May 31, 2021. We identify hedging properties across crypto-currency pairs based on intraday volatility fitting through multiplicative component Generalized Autoregressive Conditional Heteroscedasticity (mcGARCH) models and the estimation of Dynamic Conditional Correlation (DCC) Skew Student Copulas. We find that the optimal diversified crypto-Forex portfolio outperforms the actively and passively managed Forex portfolios based on both total risk and downside and upside risk performance measures. Outperformance is robust to different market conditions and optimization methods.

Modeling the Volatility of Daily Listed Real Estate Returns during Economic Crises: Evidence from Generalized Autoregressive Conditional Heteroscedasticity Models

In this paper, we focus on the dynamic volatility behavior of the daily Swedish Real Estate Sector Index and analyze the existence and degree of a long-range dependence or asymmetric news effect since 2003. More specifically, we give extra attention to the 2007–2008 financial crisis, the 2009–2012 European debt crisis, and the first two years of the global COVID-19 pandemic era (2020–2021). We examine changes in volatility during these extreme events. We apply standard GARCH models, asymmetric GARCH models, and long-memory GARCH models with various error distributions to identify the most accurate volatility models of the daily returns of the Swedish Real Estate Sector Index for the full sample period, January 2003 to June 2021. Our results show that the volatility of the Swedish Real Estate Sector Index is time-varying and highly volatile. The impacts of the global financial crisis, European debt crisis, and COVID-19 pandemic are noticeable. Moreover, the volatility pattern during COVID-19 displays significant time-varying long-range dependence and an asymmetrical news impact, which lead to market inefficiency. Finally, the volatility pattern shows a tendency towards increasing leverage effects and less persistent behavior, indicating that the market stakeholders are highly sensitive to negative returns and becoming quicker to respond to market changes.

Do crude oil, gold and the US dollar contribute to Bitcoin investment decisions? An ANN-DCC-GARCH approach

PurposeBitcoin (BTC) is significantly correlated with global financial assets such as crude oil, gold and the US dollar. BTC and global financial assets have become more closely related, particularly since the outbreak of the COVID-19 pandemic. The purpose of this paper is to formulate BTC investment decisions with the aid of global financial assets.Design/methodology/approachThis study suggests a more accurate prediction model for BTC trading by combining the dynamic conditional correlation generalized autoregressive conditional heteroscedasticity (DCC-GARCH) model with the artificial neural network (ANN). The DCC-GARCH model offers significant input information, including dynamic correlation and volatility, to the ANN. To analyze the data effectively, the study divides it into two periods: before and during the COVID-19 outbreak. Each period is then further divided into a training set and a prediction set.FindingsThe empirical results show that BTC and gold have the highest positive correlation compared with crude oil and the USD, while BTC and the USD have a dynamic and negative correlation. More importantly, the ANN-DCC-GARCH model had a cumulative return of 318% before the outbreak of the COVID-19 pandemic and can decrease loss by 50% during the COVID-19 pandemic. Moreover, the risk-averse can turn a loss into a profit of about 20% in 2022.Originality/valueThe empirical analysis provides technical support and decision-making reference for investors and financial institutions to make investment decisions on BTC.

Relationships among return and liquidity of cryptocurrencies

The cryptocurrency market is a complex and rapidly evolving financial landscape in which understanding the inter- and intra-asset dependencies among key financial variables, such as return and liquidity, is crucial. In this study, we analyze daily return and liquidity data for six major cryptocurrencies, namely Bitcoin, Ethereum, Ripple, Binance Coin, Litecoin, and Dogecoin, spanning the period from June 3, 2020, to November 30, 2022. Liquidity is estimated using three low-frequency proxies: the Amihud ratio and the Abdi and Ranaldo (AR) and Corwin and Schultz (CS) estimators. To account for autoregressive and persistent effects, we apply the autoregressive integrated moving average-generalized autoregressive conditional heteroscedasticity (ARIMA-GARCH) model and subsequently utilize the copula method to examine the interdependent relationships between the return on and liquidity of the six cryptocurrencies. Our analysis reveals strong cross-asset lower-tail dependence in return and significant cross-asset upper-tail dependence in illiquidity measures, with more pronounced dependence observed in specific cryptocurrency pairs, primarily involving Bitcoin, Ethereum, and Litecoin. We also observe that returns tend to be higher when liquidity is lower in the cryptocurrency market. Our findings have significant implications for portfolio diversification, asset allocation, risk management, and trading strategy development for investors and traders, as well as regulatory policy-making for regulators. This study contributes to a deeper understanding of the cryptocurrency marketplace and can help inform investment decision making and regulatory policies in this emerging financial domain.

The Islamic effect: Exploring the dynamics of Islamic events on sustainable performance of Islamic and conventional stock markets

This study attempts to investigate the effects of Islamic events on both Islamic and conventional stock markets and analyze which market reacts more pronouncedly to these events. From 2012 to 2022, the research used daily stock return data from eight nations: Kuwait, India, Nigeria, Malaysia, Pakistan, Qatar, Saudi Arabia, and the United Arab Emirates. The study examines how Islamic holidays such as Ashura, Eid Meelad ul Nabi, Eid ul Azha, and Ramadan affect both Islamic and Western stock markets. The researchers use the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model to analyze the data. The results of this analysis show that Islamic events in India, Nigeria, Malaysia, Pakistan, and Qatar have a strong and favorable link with Islamic stock returns. However, it was discovered that there is a little correlation between Islamic events and Islamic stock returns in the remaining three nations. The study also reveals a strong and favorable correlation between Islamic events and conventional stock performance in all countries. By offering a comparative analysis of the effect of Islamic events on Islamic stock markets and mainstream stock markets, these findings add to the body of current material. Every religion has its own set of rituals that its adherents observe, and these rituals frequently have an impact on different economic and non-economic activities. This study sheds light on the precise connection between these events and stock market performance by examining the impact of Islamic occasions on both Islamic and conventional stock markets.

Transition E-Garch Model for Modeling and Forecasting Volatility of Equity Stock Returns in Nigeria Stock Exchange

The mean-equations that exhibit unconditional variance do not reflect real-world data characteristics and do not always fully embrace the thick tail properties of high-frequency financial time series. However, there are cases when mean-equations exhibit conditional and unconditional variances, which conventional Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models do not accommodate with assumptions of normal error innovation. The behaviour of equity in stock returns volatility was investigated using mean-equations that reflect both conditional and unconditional variances under the variants innovation distribution. The Nigeria Stock Exchange’s, (NSE’s), daily All Stock Index, (ASI) data from 3rd May 1999 to 18th March 2019 was utilized to characterize the volatility structure of equity in Nigeria Stock returns. The Transition Exponential GARCH Model (TEGM) with non-normal innovations was used to demonstrate the dynamic model performance and predictive power in modeling variances that transit between unconditional and conditional structures. Under various error innovations, the structural characteristics of the TEGM were examined, and the parameters were estimated. The TEGM result under Student’s t innovation distribution was significant for forecasting and predicting random series data. The error distribution has both the minimal and sufficient requirements for the best predictive capacity and forecasting capabilities. Over a longer period, the NSE’s daily ASI showed more unconditional variance than conditional variation. The Transition Exponential GARCH Model was found to be the best model for describing the volatility structure of financial assets in Nigerian stock returns, and is thus recommended for making informed investment decisions with better forecast performance.