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

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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.

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