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Tail behaviour of the stationary density of general non-linear autoregressive processes of order 1

Part of: Inference from stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Jean Diebolt  and
Dominique Guégan
Jean Diebolt*
Affiliation:
Université Paris VI
Dominique Guégan*
Affiliation:
Université Paris XIII
*
∗∗ Postal address: L.S.T.A. University Paris VI, 4 place Jussieu, Tour 45–55, 75252 Paris CEDEX 05, France.
∗∗∗ Postal address: Institut Galilée, Dept of Mathematics, University Paris XIII, Av. J.B. Clément, 93430 Villetaneuse, France.
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Abstract

We examine the main properties of the Markov chain Xt = T(Xt– 1) + σ(Xt– 1)ε t. Under general and tractable assumptions, we derive bounds for the tails of the stationary density of the process {Xt} in terms of the common density of the ε t's.

Keywords

MARKOV CHAINTAIL OF THE STATIONARY DENSITYNON-LINEAR TIME SERIES

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 62M10: Time series, auto-correlation, regression, etc.
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 2 , June 1993 , pp. 315 - 329
Copyright
Copyright © Applied Probability Trust 1993 

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