Exponential GARCH Model Research Articles

Forecasting volatility of wind power production

Given the increasing share of wind energy in the portfolio of energy sources, there is the need for a more thorough understanding of its uncertainties due to changing weather conditions. To account for the uncertainty in predicting wind power production, this article examines the volatility forecasting abilities of different GARCH-type models for wind power production. Moreover, due to characteristic features of the wind power process, such as heteroscedasticity and nonlinearity, we also investigate the use of a Markov regime-switching GARCH (MRS-GARCH) model on forecasting volatility of wind power. Realized volatility, which is derived from lower-scale data, serves as a benchmark for latent volatility. We find that the MRS-GARCH model significantly outperforms traditional GARCH models in predicting the volatility of wind power, while the exponential GARCH model is superior among traditional GARCH models.

Asymmetric volatility in European day-ahead power markets: A comparative microeconomic analysis

This paper uses high-frequency spot price data from fourteen wholesale electricity markets in Europe to analyze asymmetric volatility in European day-ahead power markets with Exponential GARCH (E-GARCH) and TARCH models. Our data set ranges from 1992 to 2015 and consists of approximately 926,000 observations. As such, this paper constitutes the most extensive and comprehensive work conducted so far on European power markets, to the best of our knowledge. Unlike most of the literature that treats price as a continuous variable and attempts to model its trajectory, this paper adopts a unique approach and regards each hour in a day a separate market. The results show, in post-2008 period, the most expensive electricity is consumed in Turkey, Ireland, and UK while the cheapest power is in Russia, Nordic countries, and Czech Republic. Russia, Poland, and Czech Republic have the least volatile markets while France, Ireland, and Portugal have the most volatile ones. Volatility has decreased in many European countries in post-2008 period. Besides, we find magnitude effect is usually larger than the leverage effect, meaning that the absolute value of price change is relatively more important than the sign of the change (whether it is an increase or a decrease) to explain volatility in European day-ahead power markets. Moreover, the results imply there is not a uniform inverse leverage effect in electricity prices; that is, price increases are more destabilizing in some European markets (e.g. Poland, Slovenia, Ireland, Netherlands) than comparable price decreases but vice versa also holds true in some other countries (e.g. Portugal and France). Leverage (or inverse leverage) effect in post-2008 period is relatively stronger in Portugal, France, and Ireland, but its impact is quite limited in Turkey and Germany. Furthermore, although the impact of seasonality on prices is obvious, a specific pattern cannot be identified. Finally, large changes in the volatility will affect future volatilities for a relatively longer period of time in Nordic countries, Ireland, and the UK while changes in current volatility will have less effect on future volatilities in Czech Republic, Russia, and Turkey.

Effects of the Japanese Stock Market on Canadian Value Stocks

This paper empirically examines the time-series relationships of value, growth, and standard stock indices in Canadian and Japanese equity markets. More specifically, we investigate the effects of the returns of the Nikkei 225 (the Nikkei), Tokyo stock price index (TOPIX), and Japanese value and growth stock indices on Canadian value, growth, and standard equity index returns. The new evidence from our empirical examinations is as follows. 1) First, our analyses by the exponential generalized autoregressive conditional heteroscedasticity (EGARCH) models find that the returns of the Nikkei and TOPIX most strongly influence value stock index returns in Canada. 2) Second, our examinations by the EGARCH models clarify that the Japanese value and growth equity index return evolution also most strongly affects Canadian value stock returns.

Modelling the Error Term of Australia Gross Domestic Product

The main aim of this study is to model the Gross Domestic Product (GDP) with the new Combine White Noise (CWN) Model and compare the results with the Vector Autoregressive (VAR) Model and Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) Model which are the existing models. The CWN model estimation yields best results with least information criteria and high log likelihood values. While the EGARCH model estimated yields better results with least information criteria and high log likelihood values when compared with VAR model. CWN has the least forecast errors which are indications of best results when compare with the EGARCH and VAR models, dynamic evaluation forecast errors. The minimum forecast error values indicate forecast accuracy. The determinant of the residual of the covariance matrix value indicates that CWN is efficient, while the determinant of the residual of the covariance matrix value indicates that VAR is not efficient. The total results testify that CWN is the most right model. To model the data that exhibit conditional heteroscedasticity with leverage effect in Australia and other societies in the world efficiently, CWN is recommended.

Exponential GARCH Modeling With Realized Measures of Volatility

We introduce the realized exponential GARCH model that can use multiple realized volatility measures for the modeling of a return series. The model specifies the dynamic properties of both returns and realized measures, and is characterized by a flexible modeling of the dependence between returns and volatility. We apply the model to 27 stocks and an exchange traded fund that tracks the S&P 500 index and find specifications with multiple realized measures that dominate those that rely on a single realized measure. The empirical analysis suggests some convenient simplifications and highlights the advantages of the new specification.

Modeling the Asymmetric in Conditional Variance

The purpose of this study is to model the asymmetric in conditional variance of Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) with Combine White Noise (CWN) model to obtain suitable results. Combine white noise has the minimum information criteria and high log likelihood when compare with EGARCH estimation.The determinant of the residual covariance matrixvalue indicates that CWN estimation is efficient. Combine white noise has minimum information criteria and high log likelihood value that signify suitable estimation. Combine white noise has a minimum forecast errors which indicates forecast accuracy.Combine white noise estimation results have proved more efficient when compared with EGARCH model estimation

Dynamics of volatility spillover between stock market and foreign exchange market: evidence from Asian Countries

Abstract Background The purpose of this study is to examine volatility spillover effects between stock market and foreign exchange market in selected Asian countries; Pakistan, India, Sri Lanka, China, Hong Kong and Japan. This study considered daily data from 4th January, 1999 to 1st January, 2014. Methods This study opted EGARCH (Exponential Generalized Auto Regressive Conditional Heteroskedasticity) model for the purpose of analyzing asymmetric volatility spillover effects between stock and foreign exchange market. Results The EGARCH analyses reveal bidirectional asymmetric volatility spillover between stock market and foreign exchange market of Pakistan, China, Hong Kong and Sri Lanka. The results reveal unidirectional transmission of volatility from stock market to foreign exchange market of India. The analysis reveals no evidence of volatility transmission between the two markets in reference to Japan. Conclusions The result of this study provide valuable insights to economic policy makers for financial stability perspective and to investors regarding decision making in international portfolio and currency risk strategies.

HOW DOES PATENT LITIGATION INFLUENCE DYNAMIC RISK FOR MARKET COMPETITORS?

Many recent studies have discussed the appropriateness of various patent measurement indicators, as well as the differences in the positioning of patented technologies, while there is little discussion on the risk transmission of enterprises when faced with infringement litigation. This study used the bivariate EGARCH (Exponential Generalized Autoregressive Conditional Heteroskedasticity) model with DCC (Dynamic Conditional Correlations) to investigate the dynamic risk transmission of patent litigation between market competitors in the smartphone industry. Empirical results revealed that when facing lawsuits from market challengers, the market leader faces fewer risks when handling patent infringement litigations. In addition, the risk reactions of competitors during patent wars may widely differ. Investors should consider the patent infringement litigations when measuring the dynamic risks of share prices, and determining the optimal configuration of asset portfolios in response.

Stock Market Volatility and Equity Trading Volume: Empirical Examination from Brazil, Russia, India and China (BRIC)

This study empirically examines the relationship between equity market volatility and trading volume using equity market indices of four emerging economies, such as, Brazil, Russia, India and China (BRIC) over the period from 2008 to 2013. Using daily data of their respective stock market indices, we estimate an exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model to confirm the volatility asymmetry, and then we examine the volume–volatility relationship by augmenting contemporaneous and lagged trading volume in the EGARCH model. The results indicate substantial volatility asymmetry across the BRIC equity markets. We find that contemporaneous trading volumes are significantly associated with equity market volatility for all the four markets studied, supporting the mixture of distribution hypothesis. Lagged trading volumes are found to be insignificant in explaining conditional volatility. However, it is evident that trading volume fails to attenuate the degree of volatility persistence. The persistence level remains high across the BRIC markets even after incorporating trading volumes in the volatility model.

Evaluating the performance of futures hedging using multivariate realized volatility

This paper investigates the performance of a conditional hedging model using the realized covariance measure (RCM) with noisy high-frequency data. We employ a bivariate realized exponential GARCH (BREG) model with some RCMs to estimate conditional optimal hedge ratios in the Japanese stock and futures markets. The bivariate Student’s t-distribution as well as the bivariate normal distribution are used for the return distribution. The out-of-sample results show that the BREG model outperforms the DCC-EGARCH model and the OLS approach using daily returns for a short hedge in the period without unpredictably large fluctuations in returns such as the Lehman aftermath and the economic impact of the Great East Japan Earthquake. The BREG model with a Student’s t-distribution is likely to be superior to that with a normal distribution. The use of RCMs with methods reducing bias induced by microstructure noise and non-synchronous trading improves the performance. We also find that the joint model of returns and RCM such as the BREG model yields better performance for a short hedge than a model in which RCM is included as an exogenous variable.

Nature of Energy Index Volatility in Post Financial Crisis Period: Evidences from India

Abstract This study looks into the nexus between energy index, utility prices, and exchange rate for India, considering weekly data from June, 2008 to May, 2014. Generalized autoregressive conditional heteroskedasticity (GARCH) and exponential GARCH (EGARCH) models have been applied to scrutinize the effect of utility price and exchange rate behaviors on the energy index. The study discloses that rise in the global oil price, traded energy price and depreciation of exchange rate in turn leads to reduction of returns on energy index. It also tells that the impacts of positive and negative shocks on utility price and exchange rate volatility have symmetric consequences, and utility price and exchange rate fluctuations have enduring effect on energy index volatility.

Volatility and efficiency of the world crude oil market

Purpose – The purpose of this paper is to examine volatility and the weak-form efficient market hypothesis (random walk) of world spot crude oil market. Design/methodology/approach – The study uses the generalized autoregressive conditional heteroskedasticity (GARCH-M), exponential generalized autoregressive conditional heteroskedasticity (EGARCH), and threshold GARCH (TGARCH) models. The data are selected from three markets: Dubai Vetch (DV), West Texas Intermediate, and Europe Brent Spot Price. Findings – The weak-form efficient market (random walk) hypothesis was rejected for all estimated GARCH-M, EGARCH, and TGARCH models, indicating that these markets are inefficient and predictable. For daily data, the empirical results showed the presence of asymmetric effects, and the conditional variance process was found to be highly persistent. Originality/value – This study is unique in its nature as it examines three markets on three continents. In addition, one of these markets (DV) was not carried out by the previous study. This work takes into account the market location.

An Almost Closed Form Estimator for the EGARCH Model

The exponential GARCH (EGARCH) model introduced by Nelson (1991) is a popular model for discrete time volatility since it allows for asymmetric effects and naturally ensures positivity even when including exogenous variables. Estimation and inference is usually done via maximum likelihood. Although some progress has been made recently, a complete distribution theory of MLE for EGARCH models is still missing. Furthermore, the estimation procedure itself may be highly sensitive to starting values, the choice of numerical optimization algorithm, etc. We present an alternative estimator that is available in a simple closed form and which could be used, for example, as starting values for MLE. The estimator of the dynamic parameter is independent of the innovation distribution. For the other parameters we assume that the innovation distribution belongs to the class of Generalized Error Distributions (GED), profiling out its parameter in the estimation procedure. We discuss the properties of the proposed estimator and illustrate its performance in a simulation study and an empirical example.

Forecasting Volatility in Commodity Market: Application of Select GARCH Models

Commodity prices are volatile and volatility varies over time. Investing in commodities has generated heavy returns and has become increasingly popular, in spite of the high risks associated. The issue of volatility in commodity markets has attracted discussions at international forums too. This study is conducted to assess the volatility related issues of spot and future indices (metal, energy and agriculture) of MCX of India and to gauge the existence of leverage effect in the select commodity indices. It explores various measures of volatility spanning from November 1, 2005 to March 31, 2014. It has applied various ARCH family models such as Generalized Autoregressive Conditional Heteroscedasticity (GARCH), Exponential GARCH (EGARCH) and Component GARCH (CGARCH) models. The results of GARCH indicate high persistence of volatility and news sensitivity. For metal spot, energy spot and metal future persistence is extremely high but for agriculture spot and energy future indices do not portray meaningful result. EGARCH model indicates that there is leverage effect in energy spot, agriculture spot and metal future but other indices do not verify presence of leverage effect. The results of CGARCH model indicate towards subsistence of trend and transitory component of volatility in all the indices except energy future.

A differential harmony search based hybrid interval type2 fuzzy EGARCH model for stock market volatility prediction

In this paper a new hybrid model integrating an interval type2 fuzzy logic system (IT2FLS) with a computationally efficient functional link artificial neural network (CEFLANN) and an Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model has been proposed for accurate forecasting and modeling of financial data with changing variance over time. The proposed model denoted as IT2F-CE-EGARCH helps to enhance the ability of EGARCH model through a joint estimation of the important features of EGARCH like leverage effect, asymmetric shock by leverage effect with the secondary membership functions of interval type2 TSK FLS and the functional expansion and learning component of a CEFLANN. The secondary membership functions with upper and lower limits of IT2FLS provide a forecasting interval for handling more complicated uncertainties involved in volatility forecasting compared to type1 FLS. The performance of the proposed model has been observed with two membership functions i.e. Gaussian with fixed mean, uncertain variance and Gaussian with fixed variance and uncertain mean. The proposed model has also been compared with a few other fuzzy time series models and GARCH family models based on four performance metrics: MSFE, RMSFE, MAFE and Rel MAE. Again a differential harmony search (DHS) algorithm has been suggested for optimizing the parameters of all the fuzzy time series models. The results indicate that the proposed IT2F-CE-EGARCH model offers significant improvements in volatility forecasting performance in comparison with all other specified models over BSE Sensex and CNX Nifty dataset.

Examination of Stock Market Returns Viz-a-Viz Utility Price and Exchange Rate Movements: Evidences from India after Credit Crisis

This paper constitutes an analysis on Indian stock market returns. The conducted study probes the nexus between returns on four stock market indices, namely Sensex (BSE 30), Energy Index (BSE ENERGY), Oil and Gas Index (BSE OIL & GAS), and Capital Goods (BSE CG), and returns on traded energy prices, traded gas prices, global oil prices, and rupee-dollar exchange rates, based on weekly data from June 9, 2008 to May 16, 2014. Generalized autoregressive conditional heteroskedasticity (GARCH) and exponential GARCH (EGARCH) models have been used to examine the impacts of utility price and exchange rate movements on mentioned stock market indices. The study have established that movements of traded energy price, global oil price, and exchange rate have significant impacts on the movements of considered stock market indices, and surprisingly movements in gas price have no significant impact in any of the indices. Span of the study has been selected based on the establishment of Indian Energy Exchange, and in order to rule out the possibilities of volatility clustering, which may possibly probe biasness in the results, data pertaining to lower frequency range have been selected. Data for this study have been collected from Reserve Bank of India, Indian Energy Exchange, Bombay Stock Exchange, Multi Commodity Exchange, and U.S. Energy Information Administration.

Exponential GARCH Modeling with Realized Measures of Volatility

We introduce the Realized Exponential GARCH model that can utilize multiple realized volatility measures for the modeling of a return series. The model specifies the dynamic properties of both returns and realized measures, and is characterized by a flexible modeling of the dependence between returns and volatility. We apply the model to 27 stocks and an exchange traded fund that tracks the S&P 500 index and find specifications with multiple realized measures that dominate those that rely on a single realized measure. The empirical analysis suggests some convenient simplifications and highlights the advantages of the new specification.

Asymmetry and Leverage in Conditional Volatility Models

The three most popular univariate conditional volatility models are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). The underlying stochastic specification to obtain GARCH was demonstrated by Tsay (1987), and that of EGARCH was shown recently in McAleer and Hafner (2014). These models are important in estimating and forecasting volatility, as well as in capturing asymmetry, which is the different effects on conditional volatility of positive and negative effects of equal magnitude, and purportedly in capturing leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. As there seems to be some confusion in the literature between asymmetry and leverage, as well as which asymmetric models are purported to be able to capture leverage, the purpose of the paper is three-fold, namely, (1) to derive the GJR model from a random coefficient autoregressive process, with appropriate regularity conditions; (2) to show that leverage is not possible in the GJR and EGARCH models; and (3) to present the interpretation of the parameters of the three popular univariate conditional volatility models in a unified manner.

Price discovery and volatility spillovers in futures and spot commodity markets

Purpose – The purpose of this paper is to investigate empirically the price discovery and volatility spillovers in Indian spot-futures commodity markets. Design/methodology/approach – The study has used four futures and spot indices of Multi-Commodity Exchange, Mumbai. The study also employs vector error correction model (VECM) and bivariate exponential Garch model (EGARCH) to analyze the price discovery and volatility spillovers in Indian spot-futures commodity market. Findings – The VECM shows that agriculture future price index (LAGRIFP), energy future price index (LENERGYFP) and aggregate commodity index (LCOMDEXFP) effectively serve the price discovery function in the spot market implying that there is a flow of information from future to spot commodity markets but the reverse causality does not exist. There is no cointegrating relationship between metal future price index (LMETALFP) and metal spot price index (LMETALSP). Besides the bivariate EGARCH model indicates that although the innovations in one market can predict the volatility in another market, the volatility spillovers from future to the spot market are dominant in the case of LENERGY and LCOMDEX index while LAGRISP acts as a source of volatility toward the agri-futures market. Research limitations/implications – The results are aggregate in nature. Further study at disaggregated level will provide further insights on behavior of specific commodity prices and the price discovery process. Originality/value – The paper provides useful information about the evolution and structures of futures commodity trading in India, related literature and relevant methodology concerning the hypotheses.

Asymmetric cross-market volatility spillovers: evidence from Indian equity and foreign exchange markets

In order to capture the volatility and asymmetric transformation effect in Indian stock and foreign exchange market, two exchange rates [US Dollar (USD) and Euro] were tested with stock index (SENSEX). The study focused on the 2008 US subprime financial crisis period and analyzed data for the two sub periods like pre subprime and post subprime crisis period. The whole of the study period covers from 2nd April 2004 to 30th March 2012 with total of 1,930 daily observations. Descriptive statistics were drawn from the data series to know the nature of the data. All return series were found to be stationary at level. To proceed, for examining the volatility spillover between the variables generalized autoregressive conditional heteroskedasticity (GARCH) and exponential GARCH (EGARCH) models was used. The benefit of using EGARCH model is that, it is able to capture the asymmetric nature or the impact of good and bad news separately. The inferences drawn by applying these models in the two sub periods revealed that post crisis period comprised highest bidirectional volatility and asymmetric spillover effect between these two markets compared to pre-crisis period. The study observed that unlike volatility in Euro currency, volatility in Indian stock market was more caused by volatility in USD. Likewise post crisis period is pronouncing more volatility compared to pre-crisis period. This kind of research is of higher relevance in present day context because it allows the players of the financial markets to hedge their risk accordingly.