Long Memory and Periodicity in Intraday Volatility

Intraday return volatility is characterized by the contemporaneous presence of periodicity and long memory. This article proposes two new parameterizations of the intraday volatility process that account for both features: the Fractionally Integrated Periodic EGARCH and the Seasonal Fractional Integrated Periodic EGARCH. The analysis of hourly E-mini S&P 500 futures returns shows that the volatility is characterized by a statistically significant long-range dependence coupled with a periodic leverage effect, with negative return shocks having a larger effect on volatility during the US trading period. Long memory estimates obtained with nonperiodic long memory models are greater than those obtained with FI-PEGARCH and SFI-PEGARCH models. A simulation experiment shows that the long memory component can be strongly biased when periodic patterns are not properly modelled at the intraday level. An out-of-sample forecasting comparison with alternative models shows that a constrained version of the FI-PEGARCH provides superior forecasts.