A nonlinear threshold model for the dependence of extremes of stationary sequences

Abstract

We propose a TAR(3,1)-GARCH(1,1) model able to describe two different types of extreme events: a first type generated by large uncertainty regimes and a second type where extremes come from isolated dread/joy events. The novelty of this model resides on the definition of the regimes, motivated by the occurrence of extreme values, and of the threshold variable, defined by the shock affecting the process one period lagged. The model is able to uncover dependence and clustering of extremes in high and low volatility periods. A Wald type test to detect nonlinearities on the conditional mean process defined by an unobservable threshold variable is introduced. In the empirical application, we find evidence of predictability for extreme returns on SPDR S&P500 fund during the recent crisis period, July 2008 to March 2011. This finding seems to support the presence of some persistence and mean reversion in the dynamics of returns after the occurrence of extreme shocks.

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ORCID for Jose Olmo: orcid.org/0000-0002-0437-7812

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