Long-range Dependence in Daily Stock Volatilities

Recent empirical studies show that the squares of high-frequency stock returns are long-range dependent and can be modeled as fractionally integrated processes, using, for example, long-memory stochastic volatility models. Are such long-range dependencies common among stocks? Are they caused by the same sources of variation? In this article, we classify daily stock returns of Standard and Poor 500 companies on the basis of a company's size and its business or industrial sector and estimate the strength of long-range dependence in the stock volatilities using two different methods. Almost all of the companies analyzed exhibit strong persistence in volatility. We then use a canonical correlation method to identify common long-range dependent components in groups of companies, finding strong evidence in support of common persistence in volatility. Finally, we use a chi-squared test to study the effects of company size and sector on the number of common long-range dependent volatility components detected in groups of companies. Our results indicate the existence of some size effects, although they are not related to company size in a monotonic manner. On the other hand, the effects of company sector are pronounced. Randomly selected companies are found to be driven by a significantly larger number of persistent components than companies in certain business sectors, implying that persistence in stock volatility of companies in the same sector is more likely caused by the same source. These results suggest, among other interesting implications, that the volatilities of stocks for companies in the same business sector will be more often tied together in the longer run than will the volatilities of companies grouped only on the basis of size.

[1]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

[2]  Stephen E. Fienberg,et al.  The analysis of cross-classified categorical data , 1980 .

[3]  Eric F. Wood,et al.  IDENTIFYING MULTIVARIATE TIME SERIES MODELS , 1982 .

[4]  J. Geweke,et al.  THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS , 1983 .

[5]  C. Granger,et al.  Co-integration and error correction: representation, estimation and testing , 1987 .

[6]  G. C. Tiao,et al.  Model Specification in Multivariate Time Series , 1989 .

[7]  S. Turnbull,et al.  Pricing foreign currency options with stochastic volatility , 1990 .

[8]  Tim Bollerslev,et al.  Cointegration, Fractional Cointegration, and Exchange Rate Dynamics , 1994 .

[9]  P. Robinson.  Semiparametric Analysis of Long-Memory Time Series , 1994 .

[10]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[11]  N. Shephard,et al.  Multivariate stochastic variance models , 1994 .

[12]  Bonnie K. Ray,et al.  ESTIMATION OF THE MEMORY PARAMETER FOR NONSTATIONARY OR NONINVERTIBLE FRACTIONALLY INTEGRATED PROCESSES , 1995 .

[13]  P. Robinson.  Log-Periodogram Regression of Time Series with Long Range Dependence , 1995 .

[14]  P. Robinson.  Gaussian Semiparametric Estimation of Long Range Dependence , 1995 .

[15]  Y. Tse,et al.  Long memory in interest rate futures markets: A fractional cointegration analysis , 1995 .

[16]  F. Breidt,et al.  Improved Quasi-Maximum Likelihood Estimation for Stochastic Volatility Models , 1996 .

[17]  Richard T. Baillie,et al.  Long memory processes and fractional integration in econometrics , 1996 .

[18]  Improved Quasi-Maximum Likelihood for Stochastic Volatility Models , 1996 .

[19]  Ignacio N. Lobato,et al.  Real and Spurious Long-Memory Properties of Stock-Market Data , 1996 .

[20]  Yuzo Hosoya,et al.  A limit theory for long-range dependence and statistical inference on related models , 1997 .

[21]  Bonnie K. Ray,et al.  Identifying Common Long-range Dependence in a Vector Time Series , 1997 .

[22]  W. Fuller,et al.  Introduction to Statistical Time Series (2nd ed.) , 1997 .

[23]  CONSISTENCY OF THE AVERAGED CROSS‐PERIODOGRAM IN LONG MEMORY SERIES , 1997 .

[24]  F. Breidt,et al.  The detection and estimation of long memory in stochastic volatility , 1998 .

[25]  Domenico Marinucci,et al.  Semiparametric frequency domain analysis of fractional cointegration , 1998 .

[26]  Siem Jan Koopman,et al.  Estimation of stochastic volatility models via Monte Carlo maximum likelihood , 1998 .

[27]  Ignacio N. Lobato.  A semiparametric two-step estimator in a multivariate long memory model , 1999 .

[28]  É. Moulines,et al.  Log-Periodogram Regression Of Time Series With Long Range Dependence , 1999 .

[29]  T. Bollerslev,et al.  Equity trading volume and volatility: Latent information arrivals and common long-run dependencies , 1999 .

[30]  C. Velasco,et al.  Non-stationary log-periodogram regression , 1999 .

[31]  C. Hurvich,et al.  ON THE LOG PERIODOGRAM REGRESSION ESTIMATOR OF THE MEMORY PARAMETER IN LONG MEMORY STOCHASTIC VOLATILITY MODELS , 2001, Econometric Theory.