E.Rossi D.Fantazzini
Long memory and Periodicity in Intraday
Volatilities of Stock Index Futures
Quaderni
di Dipartimento #210 (12-08)
Dipartimento di economia politica e metodi quantitativi
Università degli studi di Pavia
Abstract
This paper investigates the intraday
volatility pattern of the E-mini SP500, quoted at the Chicago Mercantile Exchange,
one of the most traded American Stock Index futures. The data set consists of
round-the-clock hourly returns. The squared (and absolute) returns are
characterized by long memory and periodicity. In order to jointly model the
long memory and the periodic components in the returns volatility we introduce
two new parameterizations. The Fractionally Integrated Periodic EGARCH
(FI-PEGARCH) and the Seasonal Fractional Integrated Periodic EGARCH
(SFI-PEGARCH). For both models we compute the population kurtosis and the
autocorrelation function of power transformations of absolute returns. We find
that during the Asian and European trading time the volatility is lower than
during the American trading time when we observe a sharp increase. The results
seem to confirm the fact that hourly returns sampled over the 24 hours across
different markets are characterized by a strong seasonal pattern with a
statistically significant persistence. Finally we present the in-sample and
out-of-sample forecasts results of unrestricted and restricted long memory
periodic volatility models.