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Log-periodogram estimation of long memory volatility dependencies with conditionally heavy tailed returns

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  • Jonathan H. Wright

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.

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Bibliographic Info

Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 685.

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Date of creation: 2000
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Handle: RePEc:fip:fedgif:685

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Keywords: Rate of return ; Time-series analysis;

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References

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Cited by:
  1. Pierre Perron & Zhongjun Qu, 2008. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Boston University - Department of Economics - Working Papers Series wp2008-004, Boston University - Department of Economics.
  2. Christopher J. Neely, 2004. "Implied volatility from options on gold futures: do statistical forecasts add value or simply paint the lilly?," Working Papers 2003-018, Federal Reserve Bank of St. Louis.
  3. Christopher J. Neely, 2004. "Forecasting foreign exchange volatility: why is implied volatility biased and inefficient? and does it matter?," Working Papers 2002-017, Federal Reserve Bank of St. Louis.
  4. Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004. "Estimating Long Memory in Volatility," Econometrics 0412006, EconWPA.
  5. Zaffaroni, Paolo & d'Italia, Banca, 2003. "Gaussian inference on certain long-range dependent volatility models," Journal of Econometrics, Elsevier, vol. 115(2), pages 199-258, August.
  6. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.

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