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Volatility Regressions with Fat Tails

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  • Kim, Jihyun
  • Meddahi, Nour

Abstract

Nowadays, a common method to forecast integrated variance is to use the fitted value of a simple OLS autoregression of the realized variance. However, non-parametric estimates of the tail index of this realized variance process reveal that its second moment is possibly unbounded. In this case, the behavior of the OLS estimators and the corresponding statistics are unclear. We prove that when the second moment of the spot variance is unbounded, the slope of the spot variance’s autoregression converges to a random variable as the sample size diverges. The same result holds when one uses the integrated or realized variance instead of the spot variance. We then consider the class of diffusion variance models with an affine drift, a class which includes GARCH and CEV processes, and we prove that IV estimation with adequate instruments provide consistent estimators of the drift parameters as long as the variance process has a finite first moment regardless of the existence of the second moment. In particular, for the GARCH diffusion model with fat tails, an IV estimation where the instrument equals the sign of the centered lagged value of the variable of interest provides consistent estimators. Simulation results corroborate the theoretical findings of the paper.

Suggested Citation

  • Kim, Jihyun & Meddahi, Nour, 2020. "Volatility Regressions with Fat Tails," TSE Working Papers 20-1097, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:124237
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    References listed on IDEAS

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    3. MEDDAHI, Nour, 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Universite de Montreal, Departement de sciences economiques.
    4. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
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    7. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
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    10. So, Beong Soo & Shin, Dong Wan, 1999. "Cauchy Estimators For Autoregressive Processes With Applications To Unit Root Tests And Confidence Intervals," Econometric Theory, Cambridge University Press, vol. 15(2), pages 165-176, April.
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    Cited by:

    1. Rustam Ibragimov & Jihyun Kim & Anton Skrobotov, 2020. "New robust inference for predictive regressions," Papers 2006.01191, arXiv.org, revised Aug 2020.
    2. Neil Shephard, 2020. "An estimator for predictive regression: reliable inference for financial economics," Papers 2008.06130, arXiv.org.

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    Keywords

    volatility; autoregression; fat tails; random limits.;

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