Periodic Long-Memory GARCH Models

Abstract

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.

Keywords:

• GARCH models
• Intra-day volatility
• Long-memory
• Periodicity

JEL Classification:

• C22
• C5

ACKNOWLEDGMENTS

The authors wish to thank Estela Bee Dagum for her valuable help and encouragement throughout all the research project. They also thank two anonymous referees for their helpful and constructive comments and suggestions. Financial support from the Italian MIUR is gratefully acknowledged.