Kim, Jihyun and Meddahi, Nour (2020) Volatility regressions with fat tails. Journal of Econometrics, vol. 218 (n° 2). pp. 690-713.

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Identification Number : 10.1016/j.jeconom.2020.04.034


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.

Item Type: Article
Language: English
Date: October 2020
Refereed: Yes
Uncontrolled Keywords: volatility, autoregression, fat tails, random limits
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 06 May 2020 12:33
Last Modified: 27 May 2021 10:06
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