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The geometric ergodicity and existence of moments for a class of non-linear time series model

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  • An, Hongzhi
  • Chen, Min
  • Huang, Fuchun

Abstract

In this paper we consider the non-linear time series model xt=[var epsilon]t([alpha]0+[alpha]1xt-1r[beta]+...+[alpha]pxt-pr[beta])1/r. When r = 2 it is called the [beta]-ARCH(p) model. We examine the geometric ergodicity and the existence of higher-order moments for this model.

Suggested Citation

  • An, Hongzhi & Chen, Min & Huang, Fuchun, 1997. "The geometric ergodicity and existence of moments for a class of non-linear time series model," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 213-224, January.
    • Handle: RePEc:eee:stapro:v:31:y:1997:i:3:p:213-224
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    2. Paul D. Feigin & Richard L. Tweedie, 1985. "Random Coefficient Autoregressive Processes:A Markov Chain Analysis Of Stationarity And Finiteness Of Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 1-14, January.
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    1. Laïb, Naâmane & Lounis, Tewfik, 2021. "Asymptotically optimal tests for non-linear autoregressive model with β-ARCH errors," Statistics & Probability Letters, Elsevier, vol. 178(C).
    2. Frédérique Bec & Anders Rahbek, 2004. "Vector equilibrium correction models with non-linear discontinuous adjustments," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 628-651, December.
    3. Janusz Kawczak & Reg Kulperger & Hao Yu, 2005. "The empirical distribution function and partial sum process of residuals from a stationary arch with drift process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 747-765, December.
    4. Hwang, S. Y. & Woo, Mi-Ja, 2001. "Threshold ARCH(1) processes: asymptotic inference," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 11-20, May.
    5. Hwang, S. Y. & Kim, Tae Yoon, 2004. "Power transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 295-314, April.
    6. Carvalho, Alexandre & Skoulakis, Georgios, 2005. "Ergodicity and existence of moments for local mixtures of linear autoregressions," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 313-322, March.

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