Long memory and Periodicity in Intraday Volatility

Intraday return volatilities are characterized by the contemporaneous presence of periodicity and long memory. This paper proposes two new parameterizations of the intraday volatility: the Fractionally Integrated Periodic EGARCH and the Seasonal Fractional Integrated Periodic EGARCH, which provide the required flexibility to account for both features. The periodic kurtosis and periodic autocorrelations of power transformations of the absolute returns are computed for both models. The empirical application shows that volatility of the hourly Emini S&P 500 futures returns are characterized by a periodic leverage effect coupled with a statistically significant long-range dependence. An out-of-sample forecasting comparison with alternative models shows that a constrained version of the FI-PEGARCH provides superior forecasts. A simulation experiment is carried out to investigate the effects that sample frequency has on the fractional differencing parameter estimate.