Log-Periodogram Estimation of Long Memory Volatility Dependencies with Conditionally Heavy Tailed Returns

32 Pages Posted: 8 Nov 2000

See all articles by Jonathan H. Wright

Jonathan H. Wright

Johns Hopkins University - Department of Economics

Date Written: November 2000

Abstract

Many recent papers have used semiparametric methods, especially the log-periodogram regression, to detect and estimate long memory in the volatility of asset returns. In these papers, the volatility is proxied by measures such as squared, log-squared and absolute returns. While the evidence for the existence of long memory is strong using any of these measures, the actual long memory parameter estimates can be sensitive to which measure is used. In Monte Carlo simulations, I find that the choice of volatility measure makes little difference to the log-periodogram regression estimator if the data is Gaussian conditional on the volatility process. But, if the data is conditionally leptokurtic, the log-periodogram regression estimator using squared returns has a large downward bias, which is avoided by using other volatility measures. In U.S. stock return data, I find that squared returns give much lower estimates of the long memory parameter than the alternative volatility measures, which is consistent with the simulation results. I conclude that researchers should avoid using the squared returns in the semiparametric estimation of long memory volatility dependencies.

Keywords: Semiparametric Methods, Fractional Integration, Stochastic Volatility, Stock Returns, Heavy Tails.

Suggested Citation

Wright, Jonathan H., Log-Periodogram Estimation of Long Memory Volatility Dependencies with Conditionally Heavy Tailed Returns (November 2000). Available at SSRN: https://ssrn.com/abstract=249308 or http://dx.doi.org/10.2139/ssrn.249308

Jonathan H. Wright (Contact Author)

Johns Hopkins University - Department of Economics ( email )

3400 Charles Street
Baltimore, MD 21218-2685
United States

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