Changing-regime volatility: a fractionally integrated SETAR model

Abstract

This article presents a 2-regime SETAR model with different long-memory processes in both regimes. We briefly present the memory properties of this model and propose an estimation method. Such a process is applied to the absolute and squared returns of five stock indices. A comparison to simple ARFIMA models is made using some forecastibility criteria. Our empirical results suggest that our model offers an interesting alternative competing framework to describe the persistent dynamics in modelling the returns.

Notes

¹ Although we limit our attention to the case where 0 < d < 1/2, a question is whether it would be interesting to extend the model to the case where 1/2 < d < 1. In terms of estimation, once the threshold parameter is determined, it is possible to see whether one of the two regimes is charaterized by a nonstationary fractional process using the methods suggested by Hassler and Wolters (1995), Huswitch and Ray (1995), Velasco (1999), Lobato and Velasco (2000) and Gil Alana (2001). However, as is pointed out in the recent empirical literature, the most interesting question concerning nonstationary long-memory processes is how they can be distinguished from nonlinear models such as the SETAR models or the Markov switching models. The question is of importance in regard to the puzzle of the usual inability to reject the null of fractional nonstationarity when nonlinearities are present in the series.

² In his article, Tsay (1989) used a recursive-based regression, which was adapted to standard short-memory SETAR models. Because of the presence of a long-memory regime, the method used here to locate the threshold parameter is different and is explained in the following paragraphs.