Title: Volatility regressions with fat tails
Authors: Nour Meddahi - Toulouse School of Economics (France) [presenting]
Jihyun Kim - Toulouse School of Economics (France)
Abstract: Nowadays, a common practice to forecast integrated variance is to do simple OLS autoregressions of the observed realized variance data. 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 when the sample size diverges. Likewise, the same result holds when one consider either integrated variance's autoregression or the realized variance one. We then consider a class of variance models based on diffusion processes having an affine form of drift, where the class includes GARCH and CEV processes, and we prove that IV estimations 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 finite second moment. In particular, for the GARCH diffusion model with fat tails, an IV estimation where the instrument equals the sign of the (demeaned) lagged value of the variable of interest provides consistent estimators. Simulation results corroborate the theoretical findings.