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

Sangyeol Lee and T. N. Sriram

Stochastic Processes and their Applications, 1999, vol. 84, issue 2, 343-355

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.

Keywords: TAR; models; Ergodicity; Asymptotic; risk; efficiency; Asymptotic; efficiency; Uniform; integrability; Geometrically; [beta]-mixing; Stopping; rule (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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