Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models

Mika Meitz (), Pentti Saikkonen and University of Helsinki

No 327, Economics Series Working Papers from University of Oxford, Department of Economics

Abstract: This paper studies a class of Markov models which consist of two components. Typically, one of the components is observable and the other is unobservable or `hidden`. Conditions under which geometric ergodicity of the unobservable component is inherited by the joint process formed of the two components are given. This implies existence of initial values such that the joint process is strictly stationary and â-mixing. In addition to this, conditions for the existence of moments are also obtained and extensions to the case of nonstationary initial values are provided. All these results are applied to a general model which includes as special cases various first order generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional duration (ACD) models with possibly complicated non-linear structures. The results only require mild moment assumptions and in some cases provide necessary and sufficient conditions for geometric ergodicity.

Keywords: Generalized Autoregressive Conditional Heteroskedasticity; Autoregressive Conditional Duration; GARCH-in-mean; Nonlinear Time Series Models; Geometric Ergodicity; Mixing; Strict Stationarity; Existence of Moments; Markov Models (search for similar items in EconPapers)
JEL-codes: C10 C22 (search for similar items in EconPapers)
Date: 2007-05-01
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ict
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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Related works:
Journal Article: ERGODICITY, MIXING, AND EXISTENCE OF MOMENTS OF A CLASS OF MARKOV MODELS WITH APPLICATIONS TO GARCH AND ACD MODELS (2008)
Working Paper: Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models (2007)
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