Autoregressive Conditional Heteroscedasticity Model Research Articles

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 historical transition of return transmission, volatility spillovers, and dynamic conditional correlations: A fresh perspective and new evidence from the US, UK, and Japanese stock markets

<abstract> <p>This paper quantitatively investigated the historical transition of return transmission, volatility spillovers, and correlations between the US, UK, and Japanese stock markets. Applying a vector autoregressive (VAR)-dynamic conditional correlation (DCC)-multivariate exponential generalized autoregressive conditional heteroscedasticity (MEGARCH) model, we derived new evidence for four historical periods between 1984 and 2024. First, we found that the return transmission from the US to the other markets has historically become stronger, whereas recently, the return transmission from the UK to the US has disappeared. Second, we clarified that volatility spillovers from the US to the other markets have historically become stronger, whereas recently, volatility spillovers from the UK to the US have also disappeared. Third, our analyses of the historical constant correlations and DCCs revealed that stock market connectedness has gradually tightened between the US and Japan and between the UK and Japan, whereas recently, the connectedness between the US and UK has weakened. Fourth, our VAR-DCC analyses also revealed that volatility spillovers between the US, UK, and Japanese stock markets have been asymmetric. Fifth, we further showed that the skew-<italic>t</italic> errors incorporated into our VAR-DCC model are effective in estimating the dynamic stock return linkages between the US, the UK, and Japan. Finally, based on our findings, we derived many significant and beneficial interpretations and implications for historically and deeply considering return transmission, volatility spillovers, and DCCs between international stock markets.</p> </abstract>

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.

Haftanın Günü Anomalisi ile Dünya Deniz Ticareti Oynaklığının Tahmini: Baltık Kuru Yük Endeksi Uygulaması

The shipment of raw materials in the world by sea and the volatility in the Baltic Dry Index (BDI), which is the subject of this trade, and the day anomaly are two important issues. Although there are studies on BDI volatility in the literature, there are not many studies on the day anomaly related to BDI. The aim of this study is to reveal the volatility of the BDI variable used in determining the volume of world maritime trade and to determine the day of the week that causes this volatility. Data of the study includes the observation values for 262 working days for the period of 01 July 2021 – 01 July 2022. By taking the natural logarithmic differences of BDI data, the rate of return of the BDI index was obtained. Using these rates of return, experiments were conducted with various autoregressive conditional heteroscedasticity models and according to the findings obtained, it was concluded that there was an ARCH effect in the BDI variable, that Tuesday had an effect on increasing the volatility in the index and Friday had a decreasing effect.

COMPARATIVE PERFORMANCE OF ARIMA, SARIMA AND GARCH MODELS IN MODELLING AND FORECASTING UNEMPLOYMENT AMONG ASEAN-5 COUNTRIES

Unemployment, especially after the COVID-19 pandemic, is a critical issue for any country as it has economic and social ramifications. Consequently, forecasting unemployment becomes an essential task as it can guide government policy. Time series data are frequently influenced by outliers (unexpected events), and some outliers may exist with extreme observation to reduce the forecasting effectiveness of robust estimators. This study compared the performance of Autoregressive Integrated Moving Average (ARIMA), Seasonal Autoregressive Integrated Moving Average (SARIMA) and Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models in modelling and forecasting unemployment rates during the COVID-19 pandemic among the ASEAN-5 countries. These countries include Malaysia, Singapore, Thailand, the Philippines and Indonesia. The monthly unemployment data from January 2010 to December 2021 were applied for all cases, except Thailand, until December 2020. Each adequate model from both forecasting mechanisms underwent forecasting. Their performance was compared based on root mean squared error (RMSE), mean absolute error (MAE), Theil inequality coefficient and symmetric mean absolute percentage error (SMAPE). Static forecasting from the ARIMA and SARIMA models was found to perform better than the GARCH model in modelling and forecasting the unemployment rate among ASEAN-5 countries during the pandemic period.

Diagnostic checks in time series models based on a new correlation coefficient of residuals

For checking time series models, the Ljung–Box, Li–Mak and Zhu–Wang statistics play an important role, which use the Pearson's correlation coefficient to implement (squared) residual (partial) autocorrelation tests. In this paper, we replace the Pearson's correlation coefficient with a new rank correlation coefficient and propose a new test statistic to conduct diagnostic checks for residuals in autoregressive moving average models, autoregressive conditional heteroscedasticity models and integer-valued time series models, respectively. We conduct simulations to assess the performance of the new test statistic, and compare it with existing ones, and the results show the superiority of the proposed one. We use three real examples to exhibit its usefulness.

A time series modeling approach for damage monitoring of concrete dam under seismic effects

In order to improve the applicability of time series models for the diagnosis of concrete dam damage under seismic loading, this paper proposes a diagnostic method for structural damage by combining linear time series modeling and non-linear modeling of model residuals. Starting from the linear structural dynamic response transmissibility function, the expressions of the generalized Auto-Regressive with eXtra inputs (GARX) model for the dynamic response under stationary excitation conditions were derived. The GARX model with dynamic coefficients was extended to model the dynamic response under seismic loading and the generalized Auto-Regressive Conditional Heteroscedasticity (GARCH) model was used to nonlinearly model the model residuals. To track the coefficients of the GARX model, an adaptive least squares recursion method based on fuzzy forgetting factor was studied. The damage indicator of Minkowski distance based on the GARCH model coefficients was proposed. Finally, the effectiveness of the diagnostic methods of the GARX and GARCH models was verified by a numerical calculation of the non-linear damage to a dam. The results showed that GARX can effectively describe the input-output relationship of the dam in the absence of damage. After damage occurs, the GARCH model and the improved Minkowski distance index for the model residuals of GARX can effectively characterize the non-linear damage evolution of the dam.

Mean-Value-at-Risk Portfolio Optimization Based on Risk Tolerance Preferences and Asymmetric Volatility

Investors generally aim to obtain a high return from their stock portfolio. However, investors must realize that a high value-at-risk (VaR) is essential to calculate for this aim. One of the objects in the VaR calculation is the asymmetric return volatility of stocks, which causes an unbalanced decrease and increase in returns. Therefore, this study proposes a mean-value-at-risk (mean-VaR) stock portfolio optimization model based on stocks’ asymmetric return volatility and investors’ risk aversion preferences. The first stage is the determination of the mean of all stocks in the portfolio conducted using the autoregressive moving average Glosten–Jagannathan–Runkle generalized autoregressive conditional heteroscedasticity (ARMA-GJR-GARCH) models. Then, the second stage is weighting the capital of each stock based on the mean-VaR model with the investors’ risk aversion preferences. This is conducted using the Lagrange multiplier method. Then, the model is applied to stock data in Indonesia’s capital market. This application also analyzed the sensitivity between the mean, VaR, both ratios, and risk aversion. This research can be used for investors in the design and weighting of capital in a stock portfolio to ensure its asymmetrical effect is as small as possible.

A comparative study of error distributions in the GARCH model through a Monte Carlo simulation approach

Financial time series data are known to exhibit volatility clustering, which implies that the volatility of financial returns tends to persist over time. This phenomenon has significant implications for risk management and financial decision-making. To capture this volatility clustering effect, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is widely used. Through a Monte Carlo simulation experiment, the performance GARCH-type model with five different error distribution specifications were compared. The study found that the Skewed Generalized Error Distribution (SGED) was the most efficient and consistent distribution for modelling financial time series. The SGED outperformed the Normal, Student's t, GED, and skewed Student's t distributions in terms of goodness-of-fit, MSE, MAE and different sample sizes. The study suggests that the SGED may be more suitable for modelling financial time series with a GARCH-type specification in general contexts.

Conditional-mean multiplicative operator models for count time series

Multiplicative error models (MEMs) are commonly used for real-valued time series, but they cannot be applied to discrete-valued count time series as the involved multiplication would not preserve the integer nature of the data. Thus, the concept of a multiplicative operator for counts is proposed (as well as several specific instances thereof), which are then used to develop a kind of MEMs for count time series (CMEMs). If equipped with a linear conditional mean, the resulting CMEMs are closely related to the class of so-called integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models and might be used as a semi-parametric extension thereof. Important stochastic properties of different types of INGARCH-CMEM as well as relevant estimation approaches are derived, namely types of quasi-maximum likelihood and weighted least squares estimation. The performance and application are demonstrated with simulations as well as with two real-world data examples.