Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2017-08-02
Number: 17-072/III
Author-Name: Francisco (F.) Blasques
Author-Email: f.blasques@vu.nl
Author-Workplace-Name: VU Amsterdam, The Netherlands; Tinbergen Institute, The Netherlands
Author-Name: Marc Nientker
Author-Email: m.h.c.nientker@vu.nl
Author-Workplace-Name: VU Amsterdam, The Netherlands
Title: A Stochastic Recurrence Equation Approach to Stationarity and phi-Mixing of a Class of Nonlinear ARCH Models
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.
Classification-JEL: C50, C51, C58
Keywords: Ergodicity, GARCH-type models, mixing, nonlinear time series, stationarity,stochastic recurrence equations, threshold models
File-Url: https://papers.tinbergen.nl/17072.pdf
File-Format: application/pdf
File-Size: 321817 bytes
Handle: RePEc:tin:wpaper:20170072