Periodic Long-Memory GARCH models

A distinguishing feature of the intraday time-varying volatility of financial time series is given by the presence of long-range dependence of periodic type, due mainly to time-of-the-day phenomena. In this work, we introduce a model able to describe the empirical evidence given by this periodic long-memory behaviour. The model, named PLM-GARCH (Periodic Long-Memory GARCH), represents a natural extension of the FIGARCH model proposed for modelling long-range persistence of volatility. Periodic long memory versions of EGARCH (PLM-EGARCH) and of Log-GARCH (PLM-LGARCH) models are also examined. Some properties and characteristics of the models are given and finite sample performance of quasi-maximum likelihood estimation are studied with Monte Carlo simulations. Further possible extensions of the model to take into account multiple sources of periodic long-memory behaviour are proposed. Two empirical applications on intra-day financial time series are also provided.