Long Memory in the Volatility of Indian Financial Market: An Empirical Analysis Based on Indian Data
1st Edition
Published in February 2015
104 pages
978-3-95489-745-2 (ISBN)
Description
This book examines the long memory characteristics in the volatility of the Indian stock market, the Indian exchange rates and the Indian banking sector. This book also reviews the chain of approaches to estimate the long memory parameter. The long memory characteristics of the financial time series are widely studied and have implications for various economics and finance theories. The most important financial implication is related to the violation of the weak-form of market efficiency which encourages the traders, investors and portfolio managers to develop models for making predictions and to construct and implement speculative trading and investment strategies. In an efficient market, the price of an asset should follow a random walk process in which the price change is unaffected by ist lagged price changes and has no memory.
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Dilip Kumar
Long Memory in the Volatility of Indian Financial Market
An Empirical Analysis Based on Indian Data
Book
04/2014
Anchor Academic Publishing
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Dilip Kumar works in the area of asset pricing. His areas of interest includes Long memory in financial markets, Market efficiency, Extreme value volatility estimator, Bias correction in extreme value volatility estimators.
Content
Text Sample:
Chapter 2.1., Long range dependence in the financial time series:
The study of long-range dependence in financial time series has a long history and has remained an active topic of research in economics and finance. See, for instance, Mandelbrot (1971), Greene and Fielitz (1977) and Cutland, Kopp, and Willinger (1995). Mandelbrot (1972) finds that the R/S analysis shows superior properties over autocorrelation and variance analysis (because it can work with distributions with infinite variance) and spectral analysis (because it can detect non-periodic cycles). Greene and Fielitz (1977) utilize the Hurst rescaled-range (R/S) method and provide evidence in support of long memory in the daily stock return series. With the development of the log periodogram regression estimator by Geweke and Porter-Hudak (1983), based on the order of integration parameter d in the ARFIMA model of Granger and Joyeux (1980) and Hosking (1981), triggered the literature of the fractionally integrated models. Diebold and Rudebusch (1989) explore the long memory characteristics of the US real GNP data. Lo (1991) find that the classical R/S test used by Mandelbrot and Green and Fielitz suffers from a drawback in that it is unable to distinguish between long memory and short range dependence. Lo (1991) proposes a modified test of the R/S statistic which can distinguish between short term dependence and long memory and finds that daily stock returns do not show long-range dependence properties. Cheung and Lai (1995) analyze data from Austria, Italy, Japan and Spain and detect long memory in these markets. In addition, this finding was invariant to the choice of estimation methods employed. In particular, results from both the modified 'rescaled range' and the spectral regression method, which was used to model an ARFIMA process indicated the presence of long memory dynamics in the data. Willinger, Taqqu, and Teverovsky (1999) empirically find that Lo's modified R/S test leading to the acceptance of the null hypothesis of no long-range dependence for CSRP (Center for Research in Security Prices) data is less conclusive than it appears. This is so because of the conservative nature of the test statistic in rejecting the null hypothesis of no long-range dependence, by attributing what is found in the data to short-term dependence instead. Peters (1991) use R/S approach to study the long memory characteristics of daily exchange rates data of US dollars, Japanese yen, British pounds, Euros and Singapore dollars, and finds evidence that support the presence of long memory properties in exchange rates. Baillie, Chung, and Tieslau (1996) investigate the long-range dependence properties in inflation time series and find positive results. Corazza and Malliaris (2002) carry out a study on foreign currency markets and find evidence of long memory. They also find that Hurst exponent does not remain fixed but changes dynamically with time. In addition, they provide evidence that foreign currency returns follow either a fractional Brownian motion or a Pareto-Levy stable distribution. Cajueiro and Tabak (2004) use the rolling sample approach to calculate Hurst exponents over the period October 1992 to October 1996 and provide evidence of long-range dependence in Asian markets. Carbone, Castelli, and Stanley (2004) propose the detrending moving average (DMA) algorithm to estimate the Hurst exponent, which does not require any assumption regarding the underlying stochastic process or the probability distribution function of the random variable. Matteo, Aste, and Dacorogna (2005) study the scaling properties of daily foreign exchange rates, stock market indices and fixed income instruments by using the generalized Hurst exponent approach and find that the scaling exponents can be used to differentiate markets in their stage of development. Cajueiro and Tabak (2005) study the possible sources of long-range dependence in returns of Brazilian stocks and find that firm specific variables can partially explain the long-range dependence measures, such as the Hurst exponent. Souza, Tabak, and Cajueiro (2008) study the evolution of long memory over time in returns and volatilities of British pound futures contracts by using the classic R/S approach, the detrended fluctuation analysis (DFA) approach and the generalized Hurst exponent (GEHE) approach and find a change in the long memory characteristics of the British pound around the time of the European financial crisis. Serletis and Rosenberg (2009) use the detrending moving average (DMA) approach to calculated the Hurst exponent and find evidence in support of anti-persistence (mean reversion) in the US stock market. They also estimate the local Hurst exponent (on non-overlapping windows of 50 observations) to examine the evolution of efficiency characteristics of index returns over time. Kristoufek (2010) re-examines the results of Serletis and Rosenberg (2009) and finds that there are no signs of anti-persistence in the US stock market.
After the Autoregressive Conditional Heteroskedasticity (ARCH) model and the Generalized ARCH (GARCH) model were introduced by Engle (1982) and Bollerslev (1986) respectively, numerous extensions of ARCH models have been proposed in the literature, by specifying the conditional mean and conditional variance equations, which are potentially helpful in forecasting the future volatility of stock prices. Engle and Bollerslev (1986) propose the Integrated GARCH (IGARCH) model to capture the impact of a shock on the future volatility over an infinite horizon. However, these GARCH and IGARCH models are not able to capture the long memory property of volatility satisfactorily. To deal with this shortcoming, Baillie et al. (1996) propose the fractionally integrated GARCH (FIGARCH) model to allow for fractional orders I(d) of integration, where 0 < d < 1. This model estimates an intermediate process between GARCH and IGARCH. They apply the FIGARCH model to examine the persistence in Deutschmark - U.S. dollar exchange rates volatility. Vilasuso (2002) obtains the exchange rate volatility forecast by using FIGARCH model and finds that the FIGARCH model produces significantly better volatility forecasts (for 1-day and 10-days ahead) compared to GARCH and IGARCH. Kang and Yoon (2006) investigate the asymmetric long memory features in the volatility of Asian stock markets. Cheong, Nor and Isa (2007) investigate the asymmetry and long memory volatility behavior of the Malaysian Stock Exchange daily data by considering the financial crisis between 1991 to 2006 on various sub-periods (pre-crisis, crisis and post-crisis) and find mixed results.
Granger and Ding (1995) utilize the Geweke and Porter-Hudak (1983) test to examine the presence of long-memory in absolute returns of the S&P 500 Index. The estimation of the long memory parameter d in the volatility series as per the Geweke and Poter-Hudak test involves an ordinary linear regression of the log periodogram of a volatility series (with the proxy being the absolute return or the squared return) with the log frequency as the explanatory variable. Lobato and Velasco (2000) apply a two-step semi-parametric estimator to obtain the long-memory parameter of stock market volatility and trading volume. They conduct their analysis in the frequency domain which involves tapering the data. Assaf and Cavalcante (2005) use the modified rescaled range (R/S) statistic of Lo (1991), the rescaled variance measure of Giraitis et al. (2000), and the semi-parametric estimator proposed by Robinson (1995) and the Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity (FIGARCH) by Baillie et al. (1996) to estimate the fractional parameter d for the Brazilian stock market. Kilic (2004) makes use of both parametric and nonparametric methods to examine the long memory characteristics in the volatility of the Istanbul Stock Exchange National 100 Index.
Gu and Zhou (2007) apply Detrended Fluctuation Analysis (DFA), R/S analysis and modified R/S analysis to study the long memory property of the volatility of 500 stocks traded on the Shanghai Stock Exchange (SHSE) and Shenzhen Stock Exchange (SZSE) and find strong evidence in support of long memory in the volatility of the 500 stocks. Dionisio et al. (2007) analyze the behavior of volatility for various international stock market indices in the context of non-stationarity and prefer the FIGARCH model over the GARCH and the IGARCH models for capturing the behavior of volatility. Bentes et al. (2008) use the FIGARCH model and entropy measures to study the long memory property of the volatility time series for S&P 500, NASDAQ 100 and Stoxx 50 indices to compare US and European Markets and find that both perspectives show nonlinear dynamics in the volatility time series. Oh et al. (2008) study the long-term memory in the KOSPI 1 - minute market index and exchange rates of six countries relative to US dollar (5-minutes data of exchange rates are used for Euro, UK GBP, Japanese Yen, Singapore SGD, Switzerland CHF and Australia AUD) using DFA and the FIGARCH model. Their findings are supportive of long memory in the volatility series which can be attributed to the volatility clustering observed in the series. Di Sario et al. (2008) utilize approaches based on wavelets and aggregate series to test for long memory in the volatility of the Istanbul Stock Exchange National 100 Index. They make use of absolute returns, squared returns and log squared returns as proxies of volatility and find that all volatility series display long memory property. Kang et al. (2010) utilize two semi-parametric tests (the Geweke and Porter-Hudak (GPH) test and the Local Whittle (LW) test) and the FIGARCH model to examine the long memory property in the volatility of the Chinese stock market and find evidence of long memory features in the volatility time series and suggest that the assumption of non-normality provides better specifications regarding the long memory volatility processes. Fleming and Kirby (2011) apply fractional-integrated time series models on realized volatility and trading volume of 20 firms to investigate the joint dynamics of the trading volume of stocks and their volatility and find a strong degree of correlation between the innovations to volume and volatility. They suggest that trading volume can be used to obtain more precise estimates of daily volatility for cases in which high-frequency returns are unavailable.
Chapter 2.1., Long range dependence in the financial time series:
The study of long-range dependence in financial time series has a long history and has remained an active topic of research in economics and finance. See, for instance, Mandelbrot (1971), Greene and Fielitz (1977) and Cutland, Kopp, and Willinger (1995). Mandelbrot (1972) finds that the R/S analysis shows superior properties over autocorrelation and variance analysis (because it can work with distributions with infinite variance) and spectral analysis (because it can detect non-periodic cycles). Greene and Fielitz (1977) utilize the Hurst rescaled-range (R/S) method and provide evidence in support of long memory in the daily stock return series. With the development of the log periodogram regression estimator by Geweke and Porter-Hudak (1983), based on the order of integration parameter d in the ARFIMA model of Granger and Joyeux (1980) and Hosking (1981), triggered the literature of the fractionally integrated models. Diebold and Rudebusch (1989) explore the long memory characteristics of the US real GNP data. Lo (1991) find that the classical R/S test used by Mandelbrot and Green and Fielitz suffers from a drawback in that it is unable to distinguish between long memory and short range dependence. Lo (1991) proposes a modified test of the R/S statistic which can distinguish between short term dependence and long memory and finds that daily stock returns do not show long-range dependence properties. Cheung and Lai (1995) analyze data from Austria, Italy, Japan and Spain and detect long memory in these markets. In addition, this finding was invariant to the choice of estimation methods employed. In particular, results from both the modified 'rescaled range' and the spectral regression method, which was used to model an ARFIMA process indicated the presence of long memory dynamics in the data. Willinger, Taqqu, and Teverovsky (1999) empirically find that Lo's modified R/S test leading to the acceptance of the null hypothesis of no long-range dependence for CSRP (Center for Research in Security Prices) data is less conclusive than it appears. This is so because of the conservative nature of the test statistic in rejecting the null hypothesis of no long-range dependence, by attributing what is found in the data to short-term dependence instead. Peters (1991) use R/S approach to study the long memory characteristics of daily exchange rates data of US dollars, Japanese yen, British pounds, Euros and Singapore dollars, and finds evidence that support the presence of long memory properties in exchange rates. Baillie, Chung, and Tieslau (1996) investigate the long-range dependence properties in inflation time series and find positive results. Corazza and Malliaris (2002) carry out a study on foreign currency markets and find evidence of long memory. They also find that Hurst exponent does not remain fixed but changes dynamically with time. In addition, they provide evidence that foreign currency returns follow either a fractional Brownian motion or a Pareto-Levy stable distribution. Cajueiro and Tabak (2004) use the rolling sample approach to calculate Hurst exponents over the period October 1992 to October 1996 and provide evidence of long-range dependence in Asian markets. Carbone, Castelli, and Stanley (2004) propose the detrending moving average (DMA) algorithm to estimate the Hurst exponent, which does not require any assumption regarding the underlying stochastic process or the probability distribution function of the random variable. Matteo, Aste, and Dacorogna (2005) study the scaling properties of daily foreign exchange rates, stock market indices and fixed income instruments by using the generalized Hurst exponent approach and find that the scaling exponents can be used to differentiate markets in their stage of development. Cajueiro and Tabak (2005) study the possible sources of long-range dependence in returns of Brazilian stocks and find that firm specific variables can partially explain the long-range dependence measures, such as the Hurst exponent. Souza, Tabak, and Cajueiro (2008) study the evolution of long memory over time in returns and volatilities of British pound futures contracts by using the classic R/S approach, the detrended fluctuation analysis (DFA) approach and the generalized Hurst exponent (GEHE) approach and find a change in the long memory characteristics of the British pound around the time of the European financial crisis. Serletis and Rosenberg (2009) use the detrending moving average (DMA) approach to calculated the Hurst exponent and find evidence in support of anti-persistence (mean reversion) in the US stock market. They also estimate the local Hurst exponent (on non-overlapping windows of 50 observations) to examine the evolution of efficiency characteristics of index returns over time. Kristoufek (2010) re-examines the results of Serletis and Rosenberg (2009) and finds that there are no signs of anti-persistence in the US stock market.
After the Autoregressive Conditional Heteroskedasticity (ARCH) model and the Generalized ARCH (GARCH) model were introduced by Engle (1982) and Bollerslev (1986) respectively, numerous extensions of ARCH models have been proposed in the literature, by specifying the conditional mean and conditional variance equations, which are potentially helpful in forecasting the future volatility of stock prices. Engle and Bollerslev (1986) propose the Integrated GARCH (IGARCH) model to capture the impact of a shock on the future volatility over an infinite horizon. However, these GARCH and IGARCH models are not able to capture the long memory property of volatility satisfactorily. To deal with this shortcoming, Baillie et al. (1996) propose the fractionally integrated GARCH (FIGARCH) model to allow for fractional orders I(d) of integration, where 0 < d < 1. This model estimates an intermediate process between GARCH and IGARCH. They apply the FIGARCH model to examine the persistence in Deutschmark - U.S. dollar exchange rates volatility. Vilasuso (2002) obtains the exchange rate volatility forecast by using FIGARCH model and finds that the FIGARCH model produces significantly better volatility forecasts (for 1-day and 10-days ahead) compared to GARCH and IGARCH. Kang and Yoon (2006) investigate the asymmetric long memory features in the volatility of Asian stock markets. Cheong, Nor and Isa (2007) investigate the asymmetry and long memory volatility behavior of the Malaysian Stock Exchange daily data by considering the financial crisis between 1991 to 2006 on various sub-periods (pre-crisis, crisis and post-crisis) and find mixed results.
Granger and Ding (1995) utilize the Geweke and Porter-Hudak (1983) test to examine the presence of long-memory in absolute returns of the S&P 500 Index. The estimation of the long memory parameter d in the volatility series as per the Geweke and Poter-Hudak test involves an ordinary linear regression of the log periodogram of a volatility series (with the proxy being the absolute return or the squared return) with the log frequency as the explanatory variable. Lobato and Velasco (2000) apply a two-step semi-parametric estimator to obtain the long-memory parameter of stock market volatility and trading volume. They conduct their analysis in the frequency domain which involves tapering the data. Assaf and Cavalcante (2005) use the modified rescaled range (R/S) statistic of Lo (1991), the rescaled variance measure of Giraitis et al. (2000), and the semi-parametric estimator proposed by Robinson (1995) and the Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity (FIGARCH) by Baillie et al. (1996) to estimate the fractional parameter d for the Brazilian stock market. Kilic (2004) makes use of both parametric and nonparametric methods to examine the long memory characteristics in the volatility of the Istanbul Stock Exchange National 100 Index.
Gu and Zhou (2007) apply Detrended Fluctuation Analysis (DFA), R/S analysis and modified R/S analysis to study the long memory property of the volatility of 500 stocks traded on the Shanghai Stock Exchange (SHSE) and Shenzhen Stock Exchange (SZSE) and find strong evidence in support of long memory in the volatility of the 500 stocks. Dionisio et al. (2007) analyze the behavior of volatility for various international stock market indices in the context of non-stationarity and prefer the FIGARCH model over the GARCH and the IGARCH models for capturing the behavior of volatility. Bentes et al. (2008) use the FIGARCH model and entropy measures to study the long memory property of the volatility time series for S&P 500, NASDAQ 100 and Stoxx 50 indices to compare US and European Markets and find that both perspectives show nonlinear dynamics in the volatility time series. Oh et al. (2008) study the long-term memory in the KOSPI 1 - minute market index and exchange rates of six countries relative to US dollar (5-minutes data of exchange rates are used for Euro, UK GBP, Japanese Yen, Singapore SGD, Switzerland CHF and Australia AUD) using DFA and the FIGARCH model. Their findings are supportive of long memory in the volatility series which can be attributed to the volatility clustering observed in the series. Di Sario et al. (2008) utilize approaches based on wavelets and aggregate series to test for long memory in the volatility of the Istanbul Stock Exchange National 100 Index. They make use of absolute returns, squared returns and log squared returns as proxies of volatility and find that all volatility series display long memory property. Kang et al. (2010) utilize two semi-parametric tests (the Geweke and Porter-Hudak (GPH) test and the Local Whittle (LW) test) and the FIGARCH model to examine the long memory property in the volatility of the Chinese stock market and find evidence of long memory features in the volatility time series and suggest that the assumption of non-normality provides better specifications regarding the long memory volatility processes. Fleming and Kirby (2011) apply fractional-integrated time series models on realized volatility and trading volume of 20 firms to investigate the joint dynamics of the trading volume of stocks and their volatility and find a strong degree of correlation between the innovations to volume and volatility. They suggest that trading volume can be used to obtain more precise estimates of daily volatility for cases in which high-frequency returns are unavailable.
