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Consistency and Limiting Distribution of the Least Squares Estimator of a Threshold Autoregressive Model

The Annals of Statistics · 1993 · Vol. 21(1)

Abstract

It is shown that, under some regularity conditions, the least squares estimator of a stationary ergodic threshold autoregressive model is strongly consistent. The limiting distribution of the least squares estimator is derived. It is shown that the estimator of the threshold parameter is N consistent and its limiting distribution is related to a compound Poisson Process.

Statistical Methods and Inference Stochastic processes and financial applicationsMathematicsAutoregressive modelAsymptotic distributionEstimatorSTAR modelStatisticsApplied mathematicsStrong consistencyConsistency (knowledge bases)Least-squares function approximation

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