k -Factor GARMA models for intraday volatility forecasting

Abstract

This paper studies the ability of the k -factor GARMA processes to model and forecast the volatility of an intraday financial time series. Forecasting results from the k -factor GARMA model are obtained and compared with those produced by a conventional SARIMA model.

State space modeling of Gegenbauer processes with long memory

“…The true generating process is [100,200,500,1000]. In one such experiment the estimated value and the standard error for the long memory model parameter d = 0.45 of a series with n = 1000 after 100 replications was far superior to a similar result from a 2 factor GARMA model with the same length and 1000 replications presented in Bisaglia et al (2003). Furthermore, estimates comparable with the results given by Chan and Palma (1998) for the ARFIMA model were obtained through additional Monte Carlo experiments.…”

Periodic Long-Memory GARCH Models

“…This characteristic is typical in the study of the intra-daily movements of the conditional variance. Recently some authors (see Guegan (2000) and Bisaglia et al (2003) among others) proposed the use of k−factor GARMA models (Gegenbauer ARMA), introduced by Woodward et al (1998) in order to model this feature. This class of parameterizations allows for long memory together with multiple periodicity.…”

“…This class of parameterizations allows for long memory together with multiple periodicity. More precisely Bisaglia et al (2003), in order to describe the volatility of an intra-daily financial time series, consider a proxy for the true conditional variance and use a k−factor GARMA model on this transformed series. This approach seems really promising, even though it can be ineffective when the main goal of the analysis is to forecast the original series.…”

A wavelet Whittle estimator of generalized long-memory stochastic volatility

“…Taqqu and Teverovsky 1997) In this paper, we consider an extension of the LMSV model by representing the log-volatility by a k-factor Gegenbauer autoregressive moving average (k-GARMA) process that accounts for k persistent periodicities in the volatility series. The k-GAR-MA model has been shown to represent well electricity load demand series (Soares and Souza 2006), and the volatility of an intraday financial time series (Bisaglia et al 2003). Although locations of periodicities are usually known in many financial time series, we do not make such assumption to provide generality to the proposed approach.…”

“…It is an important characteristic of intraday data (see e.g. Andersen and Bollerslev 1997;Bisaglia et al 2003). To account for this persistent cyclic dynamic, Arteche (2004) proposed an extension of the LMSV model in the form of seasonal or cyclical asymmetric long memory (SCALM) as defined in Arteche and Robinson (2000).…”