Non-linear time series and Markov chains
- 1 March 1990
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 22 (03) , 587-611
- https://doi.org/10.1017/s0001867800019893
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
This publication has 16 references indexed in Scilit:
- Existence of moments in a stationary stochastic difference equationAdvances in Applied Probability, 1990
- Ergodicity and central limit theorems for a class of Markov processesJournal of Multivariate Analysis, 1988
- Bilinear markovian representation and bilinear modelsStochastic Processes and their Applications, 1985
- On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equationsAdvances in Applied Probability, 1985
- A multiple-threshold AR(1) modelJournal of Applied Probability, 1985
- RANDOM COEFFICIENT AUTOREGRESSIVE PROCESSES:A MARKOV CHAIN ANALYSIS OF STATIONARITY AND FINITENESS OF MOMENTSJournal of Time Series Analysis, 1985
- A threshold AR(1) modelJournal of Applied Probability, 1984
- ON THE EXISTENCE OF SOME BILINEAR TIME SERIES MODELSJournal of Time Series Analysis, 1983
- Nonlinear autoregressive processesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978
- Criteria for classifying general Markov chainsAdvances in Applied Probability, 1976