A threshold AR(1) model
- 1 June 1984
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 21 (2) , 270-286
- https://doi.org/10.2307/3213639
Abstract
We consider the modelwhereφ1,φ2are real coefficients, not necessarily equal, and theat,'s are a sequence of i.i.d. random variables with mean 0. Necessary and sufficient conditions on theφ's are given for stationarity of the process. Least squares estimators of theφ's are derived and, under mild regularity conditions, are shown to be consistent and asymptotically normal. An hypothesis test is given to differentiate between an AR(1) (the caseφ1=φ2) and this threshold model. The asymptotic behavior of the test statistic is derived. Small-sample behavior of the estimators and the hypothesis test are studied via simulated data.Keywords
This publication has 7 references indexed in Scilit:
- Threshold Autoregression, Limit Cycles and Cyclical DataJournal of the Royal Statistical Society Series B: Statistical Methodology, 1980
- STATE‐DEPENDENT MODELS: A GENERAL APPROACH TO NON‐LINEAR TIME SERIES ANALYSISJournal of Time Series Analysis, 1980
- On Conditional Least Squares Estimation for Stochastic ProcessesThe Annals of Statistics, 1978
- Nonlinear autoregressive processesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978
- Sufficient conditions for ergodicity and recurrence of Markov chains on a general state spaceStochastic Processes and their Applications, 1975
- $R$-Theory for Markov Chains on a General State Space I: Solidarity Properties and $R$-Recurrent ChainsThe Annals of Probability, 1974
- Multiple Time SeriesWiley Series in Probability and Statistics, 1970