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A note on a simple Markov bilinear stochastic process

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

Abstract

In this paper we note that while the results of a 1981 paper of H. Tong's are generally valid and can be strengthened, there is a special case that behaves differently.

Suggested Citation

  • Cline, Daren B. H. & Pu, Huay-min H., 2002. "A note on a simple Markov bilinear stochastic process," Statistics & Probability Letters, Elsevier, vol. 56(3), pages 283-288, February.
    • Handle: RePEc:eee:stapro:v:56:y:2002:i:3:p:283-288
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    References listed on IDEAS

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    1. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
    2. 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.
    3. B. G. Quinn, 1982. "A Note On The Existence Of Strictly Stationary Solutions To Bilinear Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(4), pages 249-252, July.
    4. Tweedie, Richard L., 1975. "Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space," Stochastic Processes and their Applications, Elsevier, vol. 3(4), pages 385-403, October.
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    Cited by:

    1. Cline, Daren B.H., 2007. "Regular variation of order 1 nonlinear AR-ARCH models," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 840-861, July.
    2. Psaradakis, Zacharias, 2006. "Blockwise bootstrap testing for stationarity," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 562-570, March.
    3. Aknouche, Abdelhakim, 2015. "Unified quasi-maximum likelihood estimation theory for stable and unstable Markov bilinear processes," MPRA Paper 69572, University Library of Munich, Germany.

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