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On probabilistic properties of nonlinear ARMA(p,q) models

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  • Lee, Oesook

Abstract

We consider a general nonlinear ARMA(p,q) model Xn+1=h(en-q+1,...,en,Xn-p+1,...,Xn)+en+1, where h : Rp+q-->R is a measurable function and {en: n[greater-or-equal, slanted]1} is an i.i.d. sequence of random variables. Sufficient conditions for stationarity and geometric ergodicity of {Xn} are obtained by considering the asymptotic behaviours of the associated Markov chain.

Suggested Citation

  • Lee, Oesook, 2000. "On probabilistic properties of nonlinear ARMA(p,q) models," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 121-131, January.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:2:p:121-131
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    References listed on IDEAS

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    1. M. B. Priestley, 1980. "State‐Dependent Models: A General Approach To Non‐Linear Time Series Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 47-71, January.
    2. Bhattacharya, Rabi & Lee, Chanho, 1995. "On geometric ergodicity of nonlinear autoregressive models," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 311-315, March.
    3. An, H. Z. & Chen, S. G., 1997. "A note on the ergodicity of non-linear autoregressive model," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 365-372, June.
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    Cited by:

    1. Lee, Oesook & Shin, Dong Wan, 2000. "On geometric ergodicity of the MTAR process," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 229-237, July.

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