Periodic Long Memory GARCH models

A distinguishing feature of the intra-day 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 longmemory 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 the volatility of financial time series. Periodic long memory versions of EGARCH (PLM-EGARCH) models are also considered. Some properties and characteristics of the models are given and an estimation procedure based on quasi maximum likelihood is established. Further possible extensions of the model to take into account multiple sources of periodic long-memory behaviour are suggested. Some empirical applications on intra-day financial time series are also provided.