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Non-linear time series and Markov chains

Published online by Cambridge University Press:  01 July 2016

Dag Tjøstheim
Dag Tjøstheim*
Affiliation:
University of Bergen
*
∗Postal address: Department of Mathematics, University of Bergen, 5007 Bergen, Norway.
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Abstract

It is shown how Markov chain theory can be exploited to study non-linear time series, the emphasis being on the classification into stationary and non-stationary models. A generalized h-step version of the Tweedie (1975), (1976) criteria is formulated, and applications are given to a number of non-linear models. New results are obtained, and known results are shown to emerge as special cases in both the scalar and vector case. A connection to stability theory is briefly discussed, and it is indicated how the Markov property can be utilized for estimation purposes.

Keywords

GEOMETRIC ERGODICITYPOSITIVE RECURRENCETRANSIENCEASTYMPTOTICS
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 3 , September 1990 , pp. 587 - 611
Copyright
Copyright © Applied Probability Trust 1990 

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