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Sequential point estimation of parameters in a threshold AR(1) model

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  • Lee, Sangyeol
  • Sriram, T. N.

Abstract

We show that if an appropriate stopping rule is used to determine the sample size when estimating the parameters in a stationary and ergodic threshold AR(1) model, then the sequential least-squares estimator is asymptotically risk efficient. The stopping rule is also shown to be asymptotically efficient. Furthermore, non-linear renewal theory is used to obtain the limit distribution of appropriately normalized stopping rule and a second-order expansion for the expected sample size. A central result here is the rate of decay of lower-tail probability of average of stationary, geometrically [beta]-mixing sequences.

Suggested Citation

  • Lee, Sangyeol & Sriram, T. N., 1999. "Sequential point estimation of parameters in a threshold AR(1) model," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 343-355, December.
    • Handle: RePEc:eee:spapps:v:84:y:1999:i:2:p:343-355
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    References listed on IDEAS

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    1. Fakhrezakeri, I. & Lee, S. Y., 1993. "Sequential Estimation of the Mean Vector of a Multivariate Linear Process," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 196-209, November.
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    Cited by:

    1. Lee, Sangyeol, 2003. "The sequential estimation in stochastic regression model with random coefficients," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 71-81, January.

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