A Stochastic Recurrence Equation Approach to Stationarity and phi-Mixing of a Class of Nonlinear ARCH Models

Francisco Blasques () and Marc Nientker ()
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Marc Nientker: VU Amsterdam, The Netherlands

No 17-072/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This article generalises the results of Saidi and Zakoian (2006) to a considerably larger class of nonlinear ARCH models with discontinuities, leverage effects and robust news impact curves. We propose a new method of proof for the existence of a strictly stationary and phi-mixing solution. Moreover, we show that any path converges to this solution. The proof relies on stochastic recurrence equation theory and builds on the work of Bougerol (1993) and Straumann (2005). The assumptions that we need for this approach are less restrictive than those imposed in Saidi and Zakoian (2006) and typically found in Markov chain theory, as they require very little from the distribution of the underlying process. Furthermore, they can be stated in a general setting for random functions on a separable Banach space as is done in Straumann and Mikosch (2006). Finally, we state sufficient conditions for the existence of moments.

Keywords: Ergodicity; GARCH-type models; mixing; nonlinear time series; stationarity; stochastic recurrence equations; threshold models (search for similar items in EconPapers)
JEL-codes: C50 C51 C58 (search for similar items in EconPapers)
Date: 2017-08-02
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Citations: View citations in EconPapers (2)

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