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Log-Periodogram Estimation Of Long Memory Volatility Dependencies With Conditionally Heavy Tailed Returns

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  • Jonathan 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 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 United States 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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  • Jonathan Wright, 2002. "Log-Periodogram Estimation Of Long Memory Volatility Dependencies With Conditionally Heavy Tailed Returns," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 397-417.
  • Handle: RePEc:taf:emetrv:v:21:y:2002:i:4:p:397-417
    DOI: 10.1081/ETC-120015382
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    6. 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.
    7. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    8. Neely, Christopher J., 2009. "Forecasting foreign exchange volatility: Why is implied volatility biased and inefficient? And does it matter?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(1), pages 188-205, February.
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    12. 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.
    13. Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005. "Estimating Long Memory in Volatility," Econometrica, Econometric Society, vol. 73(4), pages 1283-1328, July.
    14. Geoffrey Ngene & Kenneth A. Tah & Ali F. Darrat, 2017. "Long memory or structural breaks: Some evidence for African stock markets," Review of Financial Economics, John Wiley & Sons, vol. 34(1), pages 61-73, September.
    15. Dalla, Violetta, 2015. "Power transformations of absolute returns and long memory estimation," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 1-18.
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