TGARCH Models Research Articles

The transformed Gram Charlier distribution: Parametric properties and financial risk applications

In this paper we study an extension of the Gram–Charlier (GC) density in Jondeau and Rockinger (2001) which consists of a Gallant and Nychka (1987) transformation to ensure positivity without parameter restrictions. We derive its parametric properties such as unimodality, cumulative distribution, higher-order moments, truncated moments, and the closed-form expressions for the expected shortfall (ES) and lower partial moments. We obtain the analytic k th order stationarity conditions for the unconditional moments of the TGARCH model under the transformed GC (TGC) density. In an empirical application to asset return series, we estimate the tail index; backtest the density, VaR and ES; and implement a comparative analysis based on Hansen’s skewed-t distribution. Finally, we present extensions to time-varying conditional skewness and kurtosis, and a new class of mixture densities based on this TGC distribution. • We obtain the parametric properties of the transformed Gram–Charlier density. • We study the unimodality and obtain the true ranges for skewness and kurtosis. • Closed-form expressions for asymmetric-risk measures are obtained. • We study the power-law tail property for asymmetric GARCH models under our density. • The model performs well in both in-sample fitting and out-of-sample backtesting.

Stock Market Integration and Volatility Spillover Effects between Nigeria and African Markets: Evidence from CCC-MGARCH and TGARCH Models

Stock Market Integration and Volatility Spillover Effects between Nigeria and African Markets: Evidence from CCC-MGARCH and TGARCH Models

Time series analysis of the number of Covid-19 deaths in Iraq

In this paper, the time series data for the number of deaths from Coronavirus (COVID-19) patients in Iraq were analyzed for the period from 4/3/2020 to 18/2/2021. ARCH, GARCH, and TGARCH models were applied due to the changing volatility of the series leading to a heteroscedastic variance. The appropriate models for the series were diagnosed and the best model was chosen and used for forecasting by the exponential smoothing methods. The comparison criterion used was the Root Mean Squared Error and the Sum of Squared Residuals. The most appropriate model for modeling and forecasting the Coronavirus deaths series in Iraq was diagnosed as TGARCH (1,1). Finally, the method of Holt-winter-additive forecasting was the best method among the

Forecasting Inflation Applying ARIMA Model with GARCH Innovation: The Case of Pakistan

Purpose: The research aims to build a suitable model for the conditional mean and conditional variance for forecasting the rate of inflation in Pakistan by summarizing the properties of the series and characterizing its salient features.
 Design/Methodology/Approach: For this purpose, Pakistan’s Inflation Rate is based upon the Consumer Price Index (CPI), ranging from January 1962 to December 2019 has been analyzed. Augmented Dickey Fuller (ADF) test that was used for testing the stationarity of the series. The ARIMA modeling technique is a conditional mean and GARCH model for conditional variance. Models are selected on AIC and BIC model selection criteria. The estimating and forecasting ability of three ARIMA models with the GARCH (2,2) model has been compared to capture the possible nonlinearity present in the data. To depict the possible asymmetric effect in the conditional variance, two asymmetric GARCH models, EGARCH and TGARCH models have been applied.
 Findings: Based on statistical loss functions, GARCH (2,2) model is the best variance model for this series. The empirical results reveal that the performance of model-2 is best for all the three variance models. However, the GARCH model is the best as the variance model for this series. This shows that the asymmetric effect invariance is not so important for the rate of inflation in Pakistan. 
 Implications/Originality/Value: The current study was based on the least considered variables and the pioneer in testing the complex relationship through the ARIMA model with GARCH innovation.

Forecasting the conditional heteroscedasticity of stock returns usingasymmetric models based on empirical evidence from Eastern Europeancountries: Will there be an impact on other industries?

This empirical study investigates the leverage effect in six Eastern European countries under normal and non-normaldistribution densities for the sample period from January 2020 to August 2020. We find three countries, Bulgaria, CzechRepublic and Russia which are subject to ARCH effect whereas Poland, Romania and Hungary do not exhibit ARCHeffect in daily stock returns. Further, our study finds leverage effect, where past bad news affects is asymmetrical, pastnegative returns cause more volatility in current stock returns as compared to past positive returns, in three EasternEuropean countries. Based on the AIC and BIC model selection criteria we find that the non-normal student t-distributionand GED produce reliable estimates for Bulgaria, Czech Republic and Poland, respectively. The autocorrelation functionQ1 statistic confirms the insignificance of autocorrelation in residuals of TGARCH model. The impact of stock marketdynamics on other industries, such as pharmaceutical industry, textile and clothing industry, automotive industry issignificant, especially in the conditions of COVID-19 pandemic

Does the Pandemic have Greater Impact on World’s Stock Markets?

This study examines the pandemic impact on world’s top forty-five stock markets along with memory analysis and leverage effect. The study is based on time-series data from January 1, 2020 to September 30, 2020 using scaling analysis by means of Hurst exponent and GARCH family models. Memory analysis suggests that all the stock markets are persistent in nature with a shade of uncertainty in the New Zealand stock market. GARCH family models show that volatility is present in some of the stock markets. Both EGARCH and TGARCH models clarified that the leverage effect is present in the BSE-India, Bangladesh, Egypt, Euronext Stock Exchange, New Zealand, and Canada stock markets; Negative information influences the stock market more than positive information for these stock markets. Nevertheless, in consideration of several limitations, an indicator to the future research is designated as well.

The impact of COVID-19 shocks on the volatility of stock markets in technologically advanced countries

This study examines the volatility of China and the most advanced countries of the world stock markets due to the pandemic of COVID-19 using the TGARCH model. This research study presents empirical support for the TGARCH specification for explaining the daily time dependence in the rate of information arrival to the market for stocks traded on China stock market. Using the sample containing closing stock market returns from 05 January 2015 to 04 April 2020 of sample countries, we found that through the COVID-19, there is no significant impact of returns volatility coming from advanced countries towards the China stock market. Further, results state that China has a significant impact on explaining the volatility of the most advanced countries of the world (Switzerland, Sweden, Netherlands, and the UK) except the U.S.A. during COVID-19. We found no significant impact of China stock market returns on the U.S.A.'s volatility, but there is a presence of leverage effect during COVID −19.

An Estimation of the Volatility in the Demand for Malaysian Tourists Visiting Korea

Purpose: With the rapid growth of Muslim tourists visiting Korea in recent years, Southeast Asia countries’ Muslims are emerging as new Korea inbound markets. In particular, Malaysia has the largest number of tourists to Korea among 57 countries belonging to the Organization of the Islamic Conference, making it a bridgehead for the Muslim tourism market. The purpose of this study is to derive an optimal volatility estimation model for more accurate predictions of the demand for Malaysian tourists visiting Korea Research design, data, and methodology: This study conducted empirical analysis on the volatility of the demand for Malaysian tourists visiting Korea using GARCH, EGARCH and TGARCH models using the monthly series data from June 2006 to November 2019. Results: The research results are as follows. First, it was found that symmetrical GARCH model, asymmetrical TGARCH model were identified to be appropriate in estimating the volatility of the demand for Malaysian tourists visiting Korea. Second, it was found that TGARCH(1,1)model is better than GARCH(1,1) models in estimating of the volatility in the demand for Malaysian tourists visiting Korea. Third, according to the estimation results of volatility in the demand for Malaysian tourists visiting Korea, the impact to volatility persists for a while following the news shock. and bad news seemed to show a greater impact to volatility than good news. Implications: The implication of this study lies in that it has derived an optimal model of volatility for the demand of Malaysian tourists visiting Korea, which has been drawing attention due to the growing importance of Muslim tourists in the Korean tourism market. and the research results also provide basic materials to improve the real condition of accepting Muslim tourists visiting Korea by making it possible to predict more accurately the demand for Malaysian tourists visiting Korea.

Information-Theoretic Measures and Modeling Stock Market Volatility: A Comparative Approach

The volatility analysis of stock returns data is paramount in financial studies. We investigate the dynamics of volatility and randomness of the Pakistan Stock Exchange (PSX-100) and obtain insights into the behavior of investors during and before the coronavirus disease (COVID-19 pandemic). The paper aims to present the volatility estimations and quantification of the randomness of PSX-100. The methodology includes two approaches: (i) the implementation of EGARCH, GJR-GARCH, and TGARCH models to estimate the volatilities; and (ii) analysis of randomness in volatilities series, return series, and PSX-100 closing prices for pre-pandemic and pandemic period by using Shannon’s, Tsallis, approximate and sample entropies. Volatility modeling suggests the existence of the leverage effect in both the underlying periods of study. The results obtained using GARCH modeling reveal that the stock market volatility has increased during the pandemic period. However, information-theoretic results based on Shannon and Tsallis entropies do not suggest notable variation in the estimated volatilities series and closing prices. We have examined regularity and randomness based on the approximate entropy and sample entropy. We have noticed both entropies are extremely sensitive to choices of the parameters.

THE ASYMMETRIC VOLATILITY OF THE ISLAMIC CAPITAL MARKET DURING THE COVID-19 PANDEMIC

This study attempts to identify the existence of asymmetric volatility in the Islamic capital market in Indonesia during the Covid-19 pandemic. The paper employs the symmetric analysis of the GARCH (1,1) model and the asymmetric analysis of the TGARCH (1,1) model in order to identify Islamic capital market behaviour duringthe first 200 days after the first Covid-19 cases were confirmed. We used the daily closing prices of the Indonesia Sharia Stock Index (ISSI). The symmetric analysis of the GARCH (1,1) model revealed that the current value of return on the ISSI does not have a significant impact on its future value. On the other hand, the TGARCH (1,1) model showed that the asymmetric parameter coefficient was positive and statistically significant. Good news and bad news does not have the same level of impact on the volatility of returns on the ISSI. Furthermore, coefficients αi and γi in the variance equation indicate that good news has a higher volatility impact than bad news. The results indicate that investors should not to worry about the bad news effect of theCovid-19 pandemic, while the government should continue the mitigation of the spread of the coronavirus along with its economic recovery policy.

A dynamic factor model applied to investor sentiment in the European context

This paper proposes an Investor Sentiment Index for the European market and tests its predictability power over returns and volatility. The constructed Investor Sentiment Index for Europe draws upon three well-established and two recent individual sentiment proxies through a novel dynamic factor modeling addressed to behavioral finance. The index is obtained through an extended period of analysis and validated with other sentiment index measures. The work relies on individual sentiment proxies based on a dynamic factor model and tests it using a TGARCH model for volatility and returns. It carries out an in-sample and out-of-sample analysis to examine this sentiment index’s forecasting power over returns sustained on a recursive rolling window prediction against Fama and French’s three-factor model. The findings demonstrate that the proposed index closely predicts STOXX600 variance and returns and confirms a strong spillover effect between European and US stock markets. This study also concludes that the proposed European Sentiment Index is a valid alternative method for investors to monitor and predict market behaviors. The developed sentiment measure is a vital market prediction movement tool for financial information providers, investors, bankers, and financial analysts. The research combines the sentiment index with a TGARCH approach over the extended period of analysis and validates the method with other sentiment index measures. An in-sample and out-of-sample study confirms the predictive power of this work’s sentiment over returns compared to Fama and French’s three-factor model. AcknowledgmentThis work is funded by National Funds through the FCT – Foundation for Science and Technology, I.P., within the scope of the project Refª UIDB/05583/2020. Furthermore, we would like to thank the Research Centre in Digital Services (CISeD) and the Polytechnic of Viseu for their support.

Contribution to the analysis of the Moroccan dirham exchange rate volatility : Econometric modeling using the asymmetric TGARCH model

Resume Le contexte generale de cette etude est lie directement a la reforme du regime de change applique au Maroc en passant vers la flexibilite graduelle basee sur l’elargissement des bandes de fluctuation du taux de change. L’objectif principal de ce travail est de modeliser les previsions de la volatilite des taux de change bilateraux du dirham marocain EUR/MAD et USD/MAD tout en se basant sur la methodologie empirique des modeles econometriques de familles ARCH. L’analyse empirique a porte sur des donnees allant du 30/11/2001 au 30/11/2020, avec un echantillon de 4800 observations journalieres. Les resultats ont montre que la serie temporelle etudiee est caracterisee par le phenomene de volatilite, par des specifications asymetriques et l’existence d’une kurtosis excessive. Ainsi, le critere de selection AKAIKE Information Critierrium (AIC) nous a amene a choisir le modele asymetrique AR(1)-TGARCH comme modele adequat pour la modelisation et la prevision de la volatilite du taux de change du dirham marocain. Mots cles : Volatilite, taux de change, ARCH, modeles asymetriques TGARCH, Kurtosis, AKAIKE Information Critierrium. JEL : C01, C24, C32, C58, E60, F31, F41. Abstract The general context of this study is directly related to the reform of the exchange rate regime applied in Morocco by moving towards a gradual flexibility based on the widening of the exchange rate fluctuation bands. The objective of this work is modeling the volatility of the bilateral exchange rates of the Moroccan dirham EUR/MAD and USD/MAD while being based on the empirical methodology of the ARCH family econometric models. The empirical analysis covered a period from 30/11/2001 to 30/11/2020, with a sample of 4800 daily observations. The results showed that the time series studied is characterized by the phenomenon of volatility, asymmetric specifications and the existence of excessive kurtosis. Thus, the AKAIKE Information Critierrium (AIC) selection criterion led us to choose the asymmetric AR(1)- TGARCH model as an adequate model to forecast the volatility of the Moroccan dirham exchange rate. Keywords : Volatility, exchange rates, ARCH, asymmetric models TGARCH, Kurtosis, AKAIKE Information Critierrium.

Research on the Influencing Factors and Fluctuation of Hous-ing price in Jinan City based on GARCH model

For a long time, the real estate industry has been identified as the pillar industry of economic growth, driving the development of the national economy. However, the continuous rise of housing prices has caused many economic and social problems. However, a sTab and healthy development of the real estate market is more conducive to people’s livelihood, so it is particularly necessary to study the factors and fluctuations affecting the real estate price. Prices are affected by multiple factors comprehensive, taking jinan as an example, the selection of 2004-2018 data of commodity house average price and its influencing factors of jinan, modeling by economics method and use the analysis software Eviews econometric analysis, thus the study situation and its changes in 15 years, jinan prices, the relationship between the influencing factors of jinan index and use the 2010-2019 monthly data to establish GARCH, TGARCH model to study the volatility.

Modelling Stock Returns Volatility and Asymmetric News Effect: A Global Perspective

This paper modelled stock returns volatility using daily S&P Global 1200 index from 1st September, 2010 to 30th September, 2020. The S&P 1200 represents a free-float weighted stock market index of global equities covering seven (7) regional stock market indices and approximately 70% of the global market capitalization, hence was used to compute global stock returns. The data analysis was carried out with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) techniques. Of the variant GARCH models specified in this study, the symmetric GARCH-M (1,1) and the asymmetric TGARCH (1,1) models were found suitable for the estimation. The findings from the GARCH-M and TGARCH models revealed explosive volatility persistence and strong asymmetric news effect in the global stock market, respectively. The implication of volatility persistence is that current volatility shocks influenced expected returns over a long period. The asymmetric news effect showed that negative news (bad news) spurred stock returns volatility than positive news (good news) especially in 2020 which was due to the COVID-19 crisis as shown by the plot of the conditional variance. These results were consistent with the empirical findings of a number of studies in emerging markets. Hence, the study concludes that the global stock market exhibited high volatility persistence and leverage effect during the sampled period.

Globalization Effects on Contagion Risks in Financial Markets

Research background: Financial globalization has opened international capital markets to investors and companies worldwide. However, the global financial crisis has created big volatility in the stock prices that induces a restriction in the reflection of full information. We explore ten EU Member States (France, Germany, The United Kingdom, Belgium, Bulgaria, Romania, Greece, Portugal, Ireland, Spain), and the USA. The explored period is 03.03.2003 - 30.06.2016, as it includes the effects of the global financial crisis of 2008. Purpose of the article: To determine if there is a contagion effect between the Bulgarian stock market and the other examined stock markets during the crisis period and whether these markets are efficient. Methods: Argument Dickey-Fuller Test, DCC-GARCH Model, Autoregressive (AR) Models, TGARCH Model, Descriptive Statistics. Findings & Value added: Our results show that a contagion across the Bulgarian capital market and eight capital markets exist during the global financial crisis of 2008. We register the strongest contagion effects from US and German capital markets to the Bulgarian capital market. The Bulgarian capital market is relatively integrated with the stock markets of Germany and the United States. That is the explanation of why the Bulgarian capital market is exposed to financial contagion effects from the US capital market and the capital markets of EU member states during the crisis period. We register statistically significant AR (1) for the UK, Greece, Ireland, Portugal, Romania, and Bulgaria, and we can define these global capital markets as inefficient.

Using Models of the GARCH Family to Estimate the Level of Food and Non-Food Inflation in Ethiopia

An increase in inflation volatility implies higher uncertainty about future prices. As a result, producers and consumers can be affected by the increased inflation volatility, because it increases the uncertainty and the risk in the market. Thus, inflation volatility attracts the attention of researchers to find a suitable model which can predict the future conditions of the market. This study aims to fit appropriate ARMA-GARCH family models for food and non-food inflation rate of from the period January 1971 through June 2020. Since the main objective of the study is identifying an appropriate model for inflation series, the null and alternative hypotheses are defined in comparison of the two types of models. H0: The symmetric GARCH models better capture inflation volatility of Ethiopia. H1: The asymmetric GARCH models better capture inflation volatility of Ethiopia. The ARMA-GARCH family models were applied to capture the stylized facts of financial time series such us leptokurtic, volatility clustering and leverage effects. The mean model results show that, an ARMA (1, 2) and ARIMA (0, 1, 1) models are identified as the best fitted model for food and non-food inflation, respectively. From the estimation results of volatility model, an asymmetric TGARCH (1, 1) model with Student's t- distributional assumptions of the residual is the best model for non-food inflation. Thus, modeling of information, news of events is very significant determinants of volatility and GARCH family models are appropriate for the given series (monthly food-inflation volatility) of Ethiopia under the study period considered.

The Impact of Covid-19 Pandemic on Stock Market Return Volatility: Evidence from Malaysia and Singapore

In this study, the volatility of two Asian stock markets, Bursa Malaysia and Singapore Exchange, is estimated. The analysis used data on daily closing prices of the indices of the respective stock markets between July 1, 2019 and August 31, 2020. The sample is split into two subsample periods: Pre-COVID-19 pandemic and during the COVID-19 pandemic. We estimated a standard GARCH, GARCH-M, TGARCH, EGARCH and PGARCH model for each subsample. We chose the best GARCH that yielded the lowest Schwarz information criterion for the normal, skewed normal, Student’s t-distribution, skewed Student’s t-distribution, generalized error distribution (GED) and skewed GED. The results show that both stock market returns are quite persistent, and the persistence decreases for both stock market returns during the pandemic. Furthermore, the normal distribution performed well for Malaysian and Singaporean stock markets before the pandemic and switched to a Student’s t (skewed normal) during the pandemic. The standard GARCH(1,1), GARCH-M(1,1), and EGARCH(1,1) performed well for both stock market returns, and the EGARCH indicates the presence of the leverage effect when stock market returns are negatively correlated to its volatility.

India VIX and Forecasting Ability of Symmetric and Asymmetric GARCH Models

Volatility forecasting plays an important role in decisions concerning risk assessment, asset valuation and monetary policy formulation. Forecasting implied volatility is a key parameter in pricing of options. Thus, through this paper we attempt to model and test the predictive ability of symmetric GARCH(1,1) and asymmetric TGARCH(1,1) and EGARCH(1,1) models in forecasting the India Volatility Index (VIX). The estimated results confirm the dependency of volatility on its past behavior. It discloses that conditional variance takes longer to disintegrate and the innovations to it are highly persistent in nature. The predictive ability of these models to forecast the direction of the VIX series is evaluated by employing a standard (symmetric) loss function, such as the root mean square error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE) and Theil’s inequality coefficient. The results show that the GARCH(1,1) provides superior forecasts compared to other models.

Moments of Tgarch Models with Gram-Charlier Innovations

Moments of Tgarch Models with Gram-Charlier Innovations

Volatility analysis and volatility spillover across equity markets between India and Europe

This paper is a comparative study of volatility spillover effects in India and European indices. The analysis used various GARCH models, in order to measure conditional volatility (GARCH), asymmetric effect in the conditional volatility (T-GARCH), volatility persistence in conditional volatility (E-GARCH), impact of conditional volatility on conditional returns (M-GARCH) and volatility spillover (GARCH (1, 1), with exogenous variable, for the period 2005 to 2018. The major results, regarding volatility spillover, revealed that Indian stock market had exercised strong impact on selected European indices. Volatility spillover was found to be from Indian stock market to European indices and vice-versa. According to the T-GARCH model, there was significant asymmetric effect on the conditional volatility. The results of E-GARCH model established volatility persistence in conditional volatility.