Heteroscedastic Model Research Articles

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.

Partial Derivatives Estimation of Multivariate Variance Function in Heteroscedastic Model via Wavelet Method

For derivative function estimation, conventional research only focuses on the derivative estimation of one-dimensional functions. This paper considers partial derivatives estimation of a multivariate variance function in a heteroscedastic model. A wavelet estimator of partial derivatives of a multivariate variance function is proposed. The convergence rates of a wavelet estimator under different estimation errors are discussed. It turns out that the strong convergence rate of the wavelet estimator is the same as the optimal uniform almost sure convergence rate of nonparametric function problems.

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.

Factors driving FIFA world cup 2022 viewership ratings in mainland China: marketing outlooks for FIFA world cup 2026.

The FIFA World Cup is not only the most lucrative athletic event globally, but it also functions as a platform for promoting peace owing to FIFA's new vision. Nevertheless, the determinants of TV viewership ratings, especially in the Chinese market, which is a critical revenue stream for FIFA TV broadcasting, are still unsolved. Using a distributional regression, this study aimed to quantify the dynamics of viewership ratings for the FIFA World Cup 2022 in mainland China. The CCTV viewership ratings were modeled using 12 covariables related to Chinese TV consumer behavior. Given the data structure, a Logit Normal regression model was chosen to fit the location and dispersion parameters of viewership ratings to explanatory variables. In the fitted heteroscedastic model, the viewership ratings dynamics in mainland China were driven by the match kick-off time: . In addition, the model captures the factors that influence the variations in viewership ratings: (if, FIFA World Cup champion = "Yes") + 0.004 × FIFA world ranking]. Thus, it shows that the FIFA World Cup champions tamp down such variations, leading to a more stable viewing behavior among Chinese consumers. Time- and team-sensitive strategies are proposed to aid in crafting uncertainty-suppressing business decisions for the FIFA World Cup 2026. Ultimately, in the more insecure 2020s, a broader live coverage of the FIFA World Cup would be invaluable for promoting peace.

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.

Hedging performance analysis of energy markets: Evidence from copula quantile regression

AbstractThis study investigates hedging performance with respect to different market structures for energy‐related commodities, including West Texas Intermediate crude oil, Brent crude oil, Chinese crude oil, and Heating oil. Copula quantile regression functions and the generalized autoregressive conditionally heteroscedasticity model are combined to analyze the nonlinear impact of dependence and the heterogeneous impact of market structure changes on hedging performance. Results show that hedging performance presents nonlinearity and market structure changes have surprisingly strong heterogeneous effects on the quantile hedge ratio, where bearish and bullish have lower hedge ratios than normal markets, which is captured better by Clayton copula quantile regression. Additionally, the trend of hedging effectiveness over different market structures also shows an inverted U shape. After changing data frequency or the types of futures contracts, the conclusions remain the same. Our empirical findings imply that hedgers are supposed to adjust the hedging number of futures according to market structure changes to hedge price risk effectively.

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.

Empirical Testing of Models of Autoregressive Conditional Heteroscedasticity Used for Prediction of the Volatility of Bulgarian Investment Funds

The relevance of the development is determined by the possibility of testing a complex analytical methodology for forecasting the daily volatility of Bulgarian investment funds, which will support the investment community in making adequate investment decisions. The used risk attribution quantification models GARCH (1.1), EGARCH (1.1), GARCH-M (1.1) and TGARCH (1.1) are adapted to predict the volatility of investment funds. The current development focuses on forecasting the risk concentration of investment funds (in Bulgaria) through the testing of complex, analytical and specialized models from the GARCH group. The object of the study includes quantitative analysis, estimation and forecasting of daily volatility through the models GARCH, EGARCH, GARCH-M and TGARCH with specification (1.1). The research covers the net balance sheet value of forty-two investment funds for the period from 13 July 2020 to 13 July 2023, where the results of the research show that according to three of the models GARCH, EGARCH and GARCH-M with the highest risk concentration the investment fund “Golden Lev Index 30” stands out. An exception to the thus formed trend is related to the TGARCH model in which the future conditional volatility is with the “EF Rapid” investment fund. When testing the models, we found that the GARCH model and the EGARCH model successfully optimize the regression parameters of the final equation for all analyzed investment funds, and as a result, valid forecasts are formed. In the case of the remaining two GARCH-M and TGARCH models, the impossibility of applicability of the model for some investment funds was found because of the optimization procedure, in which the parameters of the models have a value of zero. The present study is a unique mechanism for forecasting the daily volatility of Bulgarian investment funds, which further assists investors in risk assessment and is a prerequisite for making adequate and responsible investment decisions. The wide-spectrum toolkit of risk forecasting models allows their testing in investment funds with different risk natures (high-risk, balanced and low-risk). From a research point of view, in future research dedicated to modeling the risk attribution of investment funds, the analytical toolkit can be enriched with the following models: QGARCH, PGARCH, GJR-GARCH, IGARCH, SGARCH, AVGARCH, NGARCH and GAS. From a statistical point of view, we can apply the analyzed models to different probability distributions in order to describe the risky nature of investment funds.

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.