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Title: Volatility regression with fat tails Authors:  Jihyun Kim - Toulouse School of Economics (France) [presenting]
Nour Meddahi - 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, nonparametric 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 also characterize the connection between these slopes whether the second moment of the spot variance is finite or not. Our theory also allows for a nonstationary spot variance process. We derive the results for the case of several lags in the autoregressions and multifactor volatility process. A simulation study corroborates our theoretical findings.