() and Pentti Saikkonen
Mika Meitz: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, SE-113 83 Stockholm, Sweden
Pentti Saikkonen: Dept. of Mathematics and Statistics, University of Helsinki, Postal: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FIN-00014 University of Helsinki, Finland
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.
23 pages, June 1, 2006
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