GARCH Effects Research Articles

A Wavelet-Based Approach of Testing for Granger Causality in the Presence of GARCH Effects

The size and power of the most commonly used tests and a new wavelet-based approach of testing for Granger causality is evaluated by means of a Monte Carlo study in which the error term follows a generalized autoregressive conditional heteroscedasticity consistent (GARCH) process. In the simulation study it is shown that the commonly used causality tests tend to overreject the true null hypothesis in the presence of GARCH errors and that the new wavelet-based approach improves the size properties of the Granger causality test for all of the different situations evaluated.

The empirical relationship between stock returns volatility and trading volume: evidence on the Tunis stock market

The purpose of this paper is to study the relationship between stock returns volatility and trading volume for the main 20 Tunisian stocks listed in the Tunis stock market. We test the effect of trading volume on the persistence of the time-varying conditional volatility of returns. Our empirical results show that in the majority of cases volatility persistence vanish when trading volume is included as an explanatory variable in the conditional variance equation. It implies that the mixture of distribution hypothesis (MDH) explain the autoregressive conditional heteroskedasticity (ARCH) phenomenon. In addition, we use tow different proxies for information arrival to the market, intra-day volatility and overnight indicators. We found that these are good proxies for information arrival and are important in explaining GARCH effect in stock returns.

TESTING THE GARCH MODEL IN THE VIETNAMESE STOCK MARKET

An important factor of interest of investors on stock markets is investment risk. Risk can undergo a quantitative process through volatility, be measured by conditional variance of stock returns. GARCH is an effective and popularly used model for volatility effect on stock returns. This study tests the GARCH model and analyzes other aspects of volatility on stock returns on the two stock markets of Vietnam. In addition, the study provides evidence of the existence of GARCH effect on Vietnamese stock markets. Besides, the study also assesses price margin policy, trading volume and leverage effects on volatility of stock returns.

FINANCIAL CRISES AND INTERNATIONAL STOCK MARKET VOLATILITY TRANSMISSION

This paper examines the interplay between stock market returns and their volatility, focusing on the Asian and global financial crises of 1997–98 and 2008–09 for Australia, Singapore, the UK, and the US. We use a multivariate generalised autoregressive conditional heteroskedasticity (MGARCH) model and weekly data (January 1992–June 2009). Based on the results obtained from the mean return equations, we could not find any significant impact on returns arising from the Asian crisis and more recent global financial crises across these four markets. However, both crises significantly increased the stock return volatilities across all of the four markets. Not surprisingly, it is also found that the US stock market is the most crucial market impacting on the volatilities of smaller economies such as Australia. Our results provide evidence of own and cross ARCH and GARCH effects among all four markets, suggesting the existence of significant volatility and cross volatility spillovers across all four markets. A high degree of time‐varying co‐volatility among these markets indicates that investors will be highly unlikely to benefit from diversifying their financial portfolio by acquiring stocks within these four countries only.

Impact of Index Futures on the Index Spot Market: The Indian Evidence

The study is an empirical work conducted to assess the impact of trading of index futures on the returns and volatility of the index by examining the nature and strength of relationship that exists between Nifty Index and Nifty futures. The test statistics decisively accept the null hypothesis of equal returns, providing strong evidence of the inter linkages between two markets for CNX Nifty. Nifty Futures exhibit slightly higher volatility. The contemporaneous correlation of 0.9413 of Nifty and its futures suggests that the two time series are highly correlated. The lagged futures returns have forecasting power in explaining current spot index returns as the lag one coefficient is 0.1103. The subsequent lead/lag coefficients are diminishing and the results suggest that the cross correlation coefficients at longer leads/lags are not significant. The cross correlation coefficients indicate that the current spot returns are correlated to the current future returns and one-lead/lag futures returns. Futures thus lead the Index by one lead/lag in Nifty market. Granger Causality shows that returns on Nifty Futures cause returns on Nifty Index while the reverse is not true. Regressions run using GARCH (1,1) Model show that the interrelationships between the two markets are strong. There exists both the ARCH Effect (due to recent news) and GARCH effect (due to old news). GARCH effects are stronger in spot index markets for Nifty. ARCH effects are stronger in Index futures market. This implies that futures absorb recent information whereas index markets absorb old information. Thus, empirically it may be concluded that there is a bi-directional flow of information from futures market to the index market and vice versa.

Volatility persistence and trading volume in an emerging futures market

PurposeThe purpose of this paper is to estimate time‐varying conditional volatility, and examine the extent to which trading volume, as a proxy for information arrival, explain the persistence of futures market volatility using National Stock Exchange S&P CRISIL NSE Index Nifty index futures.Design/methodology/approachTo estimate the volatility and capture the stylized facts of fat‐tail distribution, volatility clustering, leverage effect, and mean‐reversion in futures returns, appropriate ARMA‐generalized autoregressive conditional heteroscedastic (GARCH) and ARMA‐EGARCH models with generalized error distribution have been used. The ARMA‐EGARCH model is augmented by including contemporaneous and lagged trading volume to determine their contribution to time‐varying conditional volatility.FindingsThe paper finds evidence of leverage effect, which indicates that negative shocks increase the futures market volatility more than positive shocks of the same magnitude. In addition, the results indicate that inclusion of both contemporaneous and lagged trading volume in the GARCH model reduces the persistence in volatility, but contemporaneous volume provides a greater reduction than lagged volume. Nevertheless, the GARCH effect does not completely vanish.Practical implicationsResearch findings have important implications for the traders, regulatory bodies, and practitioners. A positive volume‐price volatility relationship implies that a new futures contract will be successful only to the extent that there is enough price uncertainty associated with the underlying asset. Higher trading volume causes higher volatility; so, it suggests the need for greater regulatory restrictions.Originality/valueEquity derivatives are relatively new phenomena in Indian capital market. This paper extends and updates the existing empirical research on the relationship between futures price volatility and volume in the emerging Indian capital market using improved methodology and recent data set.

Fundamental and Behavioural Drivers of Electricity Price Volatility

The stochastic properties of volatility in spot electricity prices are only partially understood and present substantial modelling challenges. This paper develops and applies three complementary modelling approaches in order to uncover its fundamental and behavioural drivers over time and across intra-day trading periods. First, intra-day prices are related to systematic components, including economic fundamentals, strategic and market design effects. Then, residual volatility is attributed to: i) regular, non-linear agent reactions to market fundamentals (covariates of heteroscedasticity), ii) the adaptation of price formation due to substantial agent learning (time-varying effects), and iii) the transient extreme pricing in periods of scarcity (regime-switching dynamics). We find that, i) GARCH effects diminish, when each of the above sources of volatility is accounted for, and ii) allowing for the time-varying responses of prices to fundamentals can yield more precise volatility estimates than an explicit GARCH specification.

Wavelet Improvement of the Over-Rejection of Unit Root Test Under GARCH Errors: An Application to Swedish Immigration Data

In this article, we use the wavelet technique to improve the over-rejection problem of the traditional Dickey–Fuller tests for unit root when the data is associated with volatility like the GARCH(1, 1) effect. The logic of this technique is based on the idea that the wavelet spectrum decomposition can separate out information of different frequencies in the data series. We prove that the asymptotic distribution of the test in the wavelet environment is still the same as the traditional Dickey–Fuller type of tests. The finite sample property is improved when the data suffers from GARCH error. The investigation of the size property and the finite sample distribution of the test is carried out by Monte Carlo experiment. An empirical example with data on the net immigration to Sweden during the period 1950–2000 is used to illustrate the performance of the wavelet improved test under GARCH errors. The results reveal that using the traditional Dickey–Fuller type of tests, the unit root hypothesis is rejected while our wavelet improved test do not reject as it is more robust to GARCH errors in finite samples.

The Dynamic Relationship between Price and Trading Volume: Evidence from Indian Stock Market

This study investigates the nature of relationship between price and trading volume for 50 Indian stocks. Firstly the contemporaneous and asymmetric relation between price and volume are examined. Then we examine the dynamic relation between returns and volume using VAR, Granger causality, variance decomposition (VD) and impulse response function (IRF). Mixture of Distributions Hypothesis (MDH), which tests the GARCH vs. Volume effect, is also studied between the conditional volatility and volume. The results show that there is positive and asymmetric relation between volume and price changes. Further the results of VAR and Granger causality show that there is a bi-directional relation between volume and returns. However, the results of VD imply weak dynamic relation between returns and volume which becomes more evident from the plots of IRF. On MDH, our results are mixed, neither entirely rejecting the MDH nor giving it an unconditional support.

Modeling conditional correlations for risk diversification in crude oil markets

This paper estimates univariate and multivariate conditional volatility and conditional correlation models of spot, forward and futures returns from three major benchmarks of international crude oil markets, namely Brent, WTI and Dubai, to aid in risk diversification. Conditional correlations are estimated using the CCC model of Bollerslev (1990), VARMA-GARCH model of Ling and McAleer (2003), VARMA-AGARCH model of McAleer et al. (2009), and DCC model of Engle (2002). The paper also presents the ARCH and GARCH effects for returns and shows the presence of significant interdependences in the conditional volatilities across returns for each market. The estimates of volatility spillovers and asymmetric effects for negative and positive shocks on conditional variance suggest that VARMA-GARCH is superior to the VARMA-AGARCH model. In addition, the DCC model gives statistically significant estimates for the returns in each market, which shows that constant conditional correlations do not hold in practice.

Simple, Skewness-Based GMM Estimation of the Semi-Strong GARCH(1,1) Model

I propose closed-form estimators for the GARCH(1,1) model that are based on second-order covariances. The ability to obtain closed-form estimates derives from skewness in the sequence being modeled, which permits separate identification and estimation of the ARCH and GARCH effects. I show these estimators to be CAN under weak stationarity using Martingale limit theory. I also demonstrate conditions under which an iterative GLS estimator reliant on these closed-form estimates as starting values shares the same asymptotic distribution with the QMLE. This asymptotic equivalence is achieved given only third moment existence, which substantially relaxes the moment existence criteria generally required for OLS- and TSLS-style estimators of GARCH processes. The proposed estimators are studied in Monte Carlo experiments and applied to a suite of financial data.

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This paper adopts the GM(1, 1) model to predict the rates of return of nine major index futures in the American and Eurasian markets. In a further step, by means of local grey relational analysis and by employing the GM(1, N) model for the first time, the variation relatedness and the main influencing factor among the above mentioned targeted markets is determined. Then, a comparison between GARCH/TGARCH and the grey theory with regard to predictive power is conducted. The findings reveal that the GARCH/TGARCH model performs better than the GM(1, 1), including the optimal α method, in terms of forecasting capabilities. Meanwhile, it is also found that GARCH and spillover effects indeed exist. Moreover, GM(1, N) also reveals that the daily rate of return of the Dow Jones index futures has the most influence on the rates of return of the other index futures.

Estimation and forecasting in first‐order vector autoregressions with near to unit roots and conditional heteroscedasticity

AbstractThis paper investigates the effects of imposing invalid cointegration restrictions or ignoring valid ones on the estimation, testing and forecasting properties of the bivariate, first‐order, vector autoregressive (VAR(1)) model. We first consider nearly cointegrated VARs, that is, stable systems whose largest root, lmax, lies in the neighborhood of unity, while the other root, lmin, is safely smaller than unity. In this context, we define the ‘forecast cost of type I’ to be the deterioration in the forecasting accuracy of the VAR model due to the imposition of invalid cointegration restrictions. However, there are cases where misspecification arises for the opposite reasons, namely from ignoring cointegration when the true process is, in fact, cointegrated. Such cases can arise when lmax equals unity and lmin is less than but near to unity. The effects of this type of misspecification on forecasting will be referred to as ‘forecast cost of type II’. By means of Monte Carlo simulations, we measure both types of forecast cost in actual situations, where the researcher is led (or misled) by the usual unit root tests in choosing the unit root structure of the system. We consider VAR(1) processes driven by i.i.d. Gaussian or GARCH innovations. To distinguish between the effects of nonlinear dependence and those of leptokurtosis, we also consider processes driven by i.i.d. t(2) innovations. The simulation results reveal that the forecast cost of imposing invalid cointegration restrictions is substantial, especially for small samples. On the other hand, the forecast cost of ignoring valid cointegration restrictions is small but not negligible. In all the cases considered, both types of forecast cost increase with the intensity of GARCH effects. Copyright © 2009 John Wiley & Sons, Ltd.

Modeling and forecasting stock return volatility using a random level shift model

We consider the estimation of a random level shift model for which the series of interest is the sum of a short-memory process and a jump or level shift component. For the latter component, we specify the commonly used simple mixture model such that the component is the cumulative sum of a process which is 0 with some probability (1 − α) and is a random variable with probability α. Our estimation method transforms such a model into a linear state space with mixture of normal innovations, so that an extension of Kalman filter algorithm can be applied. We apply this random level shift model to the logarithm of daily absolute returns for the S&P 500, AMEX, Dow Jones and NASDAQ stock market return indices. Our point estimates imply few level shifts for all series. But once these are taken into account, there is little evidence of serial correlation in the remaining noise and, hence, no evidence of long-memory. Once the estimated shifts are introduced to a standard GARCH model applied to the returns series, any evidence of GARCH effects disappears. We also produce rolling out-of-sample forecasts of squared returns. In most cases, our simple random level shift model clearly outperforms a standard GARCH(1,1) model and, in many cases, it also provides better forecasts than a fractionally integrated GARCH model.

Long-Range Dependence in U.S. Home Price Volatility

The existence of GARCH effects in a financial price series means that the probability of large losses is much higher than standard mean-variance analysis suggests. Accordingly, several recent papers have investigated whether GARCH effects exist in the U.S. housing market, as changes in house prices can have far-ranging impacts on defaults, foreclosures, tax revenues and the values of mortgage-backed securities. Some research in finance indicates that the conditional variance of some assets exhibits far greater persistence, or even “long memory”, than is accounted for in standard GARCH models. If house prices do indeed have this very persistent volatility, properly estimating the conditional variance to allow for such persistence is crucial for optimal portfolio management. We examine a number of U.S. metropolitan areas, and find that, for those with significant GARCH effects, more than half indeed exhibit the very high persistence found in other assets such as equities. We also find that, for those markets exhibiting such persistent volatility, C-GARCH models typically do a better job in forecasting than standard GARCH models. Moreover, there is some tentative evidence that metro areas with the fastest appreciation may be most likely to have such long memory conditional variance. These findings should help in improving risk management, through, for instance the construction of better-specified value-at-risk models.

Forecasting realized volatility: a Bayesian model‐averaging approach

AbstractHow to measure and model volatility is an important issue in finance. Recent research uses high‐frequency intraday data to construct ex post measures of daily volatility. This paper uses a Bayesian model‐averaging approach to forecast realized volatility. Candidate models include autoregressive and heterogeneous autoregressive specifications based on the logarithm of realized volatility, realized power variation, realized bipower variation, a jump and an asymmetric term. Applied to equity and exchange rate volatility over several forecast horizons, Bayesian model averaging provides very competitive density forecasts and modest improvements in point forecasts compared to benchmark models. We discuss the reasons for this, including the importance of using realized power variation as a predictor. Bayesian model averaging provides further improvements to density forecasts when we move away from linear models and average over specifications that allow for GARCH effects in the innovations to log‐volatility. Copyright © 2009 John Wiley & Sons, Ltd.

Liquidity-Adjusted VaR Measurement based on High-Frequency Data: Model Constructing and Backtest

Abstract This article constructed a WACD(1,1)-UHF-GARCH(1,1)-IVaR Model to the stock market of China with the theory of ACD and UHF-GARCH, and took Shanghai Pudong Development Bank as an example, gave an empirical analysis to the intraday Value at Risk adjusted by liquidity in our stock market combining the liquidity indicators designed by price impact model. The result shows that: first, the transactions duration has strong clustering character; second, there is also strong GARCH effect on high-frequency data, and good news will come out more volatility than bad news, but the effect of both news impacting on the market have obviously reduced after considering the influence of liquidity; finally, Monte Carlo simulation shows that the Value at Risk will underestimate the real losses without considering the liquidity effects.

Breaking down the non-normality of stock returns

This paper investigates whether the non-normality typically observed in daily stock-market returns could arise because of the joint existence of breaks and GARCH effects. It proposes a data-driven procedure to credibly identify the number and timing of breaks and applies it on the benchmark stock-market indices of 27 OECD countries. The findings suggest that a substantial element of the observed deviations from normality might indeed be due to the co-existence of breaks and GARCH effects. However, the presence of structural changes is found to be the primary reason for the non-normality and not the GARCH effects. Also, there is still some remaining excess kurtosis that is unlikely to be linked to the specification of the conditional volatility or the presence of breaks. Finally, an interesting sideline result implies that GARCH models have limited capacity in forecasting stock-market volatility.

Modeling Conditional Correlations for Risk Diversification in Crude Oil Markets

This paper estimates univariate and multivariate conditional volatility and conditional correlation models of spot, forward and futures returns from three major benchmarks of international crude oil markets, namely Brent, WTI and Dubai, to aid in risk diversification. Conditional correlations are estimated using the CCC model of Bollerslev (1990), VARMA-GARCH model of Ling and McAleer (2003), VARMA-AGARCH model of McAleer et al. (2009), and DCC model of Engle (2002). The paper also presents the ARCH and GARCH effects for returns and shows the presence of significant interdependences in the conditional volatilities across returns for each market. The estimates of volatility spillovers and asymmetric effects for negative and positive shocks on conditional variance suggest that VARMA-GARCH is superior to the VARMA-AGARCH model. In addition, the DCC model gives statistically significant estimates for the returns in each market, which shows that constant conditional correlations do not hold in practice.

Modeling the Intraday Return Volatility Process in the Australian Equity Market: An Examination of the Role of Information Arrival in S&P/ASX 50 Stocks

This paper examines the intraday return volatility process in Australian company stocks. The data set employed consists of five-minute returns, trading volumes and bid-ask spreads over the period 31 December 2002 to 4 March 2003 for the fifty national and multinational stocks comprising the S&P/ASX 50 index. The GARCH and asymmetric GARCH namely Threshold ARCH (TARCH) processes are used to model the time-varying variance in the intraday return series and the inclusion of news arrival as proxied by the contemporaneous and lagged volume of trade and bid-ask spread together with day-of-week effects are used as exogenous explanatory variables. The results indicate strong persistence in volatility for the fifty stocks even with the day-of-week effects and contemporaneous and lagged volume of trade and bid-ask spread included as explanatory variables in the models. Overall, while there is much variation among the stocks included in terms of the role of the irregular arrival of new information in generating GARCH effects and the degree of persistence, all of the volatility processes are mean reverting.