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The Economic Research Institute, Stockholm School of Economics SSE/EFI Working Paper Series in Economics and Finance

No 632:
Stability of nonlinear AR-GARCH models

Mika Meitz () and Pentti Saikkonen ()

Abstract: This paper studies the stability of nonlinear autoregressive models with conditionally 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 beta-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.

Keywords: -; (follow links to similar papers)

JEL-Codes: C22; (follow links to similar papers)

23 pages, June 1, 2006

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This paper is published as:
Meitz, Mika and Pentti Saikkonen, (2008), 'Stability of nonlinear AR-GARCH models', Journal of Time Series Analysis, Vol. 29, pages 453-475



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