An Overview of FIGARCH and Related Time Series Models

Abstract

This paper reviews the theory and applications related to fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) models, mainly for describing the observed persistence in the volatility of a time series. The long memory nature of FIGARCH models allows to be a better candidate than other conditional heteroscedastic models for modeling volatility in exchange rates, option prices, stock market returns and inflation rates. We discuss some of the important properties of FIGARCH models inthis review. We also compare the FIGARCH with the autoregressive fractionally integrated moving average (ARFIMA) model. Problems related to parameter estimation and forecasting using a FIGARCH model are presented. The application of a FIGARCH model to exchange rate data is discussed. We briefly introduce some other models, that are closely related to FIGARCH models. The paper ends with some concluding remarks and future directions of research.