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Stability of nonlinear AR-GARCH models

  • Mika Meitz
  • Pentti Saikkonen

This article 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 &bgr;-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. Copyright 2008 The Authors

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Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 29 (2008)
Issue (Month): 3 (05)
Pages: 453-475

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Handle: RePEc:bla:jtsera:v:29:y:2008:i:3:p:453-475
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  1. Lundbergh, Stefan & Terasvirta, Timo, 2002. "Evaluating GARCH models," Journal of Econometrics, Elsevier, vol. 110(2), pages 417-435, October.
  2. Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, vol. 127(1), pages 69-81, July.
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