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Stability of nonlinear AR(1) time series with delay

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  • Cline, Daren B. H.
  • Pu, Huay-min H.

Abstract

The stability of generally defined nonlinear time series is of interest as nonparametric and other nonlinear methods are used more and more to fit time series. We provide sufficient conditions for stability or nonstability of general nonlinear AR(1) models having delay d[greater-or-equal, slanted]1. Our results include conditions for each of the following modes of the associated Markov chain: geometric ergodicity, ergodicity, null recurrence, transience and geometric transience. The conditions are sharp for threshold-like models and they characterize parametric threshold AR(1) models with delay.

Suggested Citation

  • Cline, Daren B. H. & Pu, Huay-min H., 1999. "Stability of nonlinear AR(1) time series with delay," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 307-333, August.
    • Handle: RePEc:eee:spapps:v:82:y:1999:i:2:p:307-333
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    References listed on IDEAS

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    1. K. S. Chan & H. Tong, 1986. "On Estimating Thresholds In Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 179-190, May.
    2. Lu, Zudi, 1996. "A note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 305-311, November.
    3. Cline, Daren B. H. & Pu, Huay-min H., 1998. "Verifying irreducibility and continuity of a nonlinear time series," Statistics & Probability Letters, Elsevier, vol. 40(2), pages 139-148, September.
    4. Wolfgang Härdle & Helmut Lütkepohl & Rong Chen, 1997. "A Review of Nonparametric Time Series Analysis," International Statistical Review, International Statistical Institute, vol. 65(1), pages 49-72, April.
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    Cited by:

    1. Tweedie, R. L., 2001. "Drift conditions and invariant measures for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 345-354, April.

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