Stability of nonlinear AR-GARCH models

Mika Meitz (), Pentti Saikkonen and University of Helsinki

No 328, Economics Series Working Papers from University of Oxford, Department of Economics

Abstract: This paper studies the stability of nonlinear autoregressive models with conditionality heteroskedastic errors. We consider a nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. Conditions under which the model is stable in the sense that its Markov chain representation is geometrically ergodic are provided. This implies the existence of an initial distribution such that the process is strictly stationary and β-mixing. Conditions under which the stationary distribution has finite moments are also given. The results cover several nonlinear specifications recently proposed for both the conditional mean and conditional variance, and only require mild moment conditions.

Keywords: Nonlinear Autoregression; Generalized Autoregressive Conditional Heteroskedasticity; 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 and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Related works:
Journal Article: Stability of nonlinear AR‐GARCH models (2008)
Working Paper: Stability of nonlinear AR-GARCH models (2006)
Working Paper: Stability of nonlinear AR-GARCH models (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:oxf:wpaper:328

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