Journal of Time Series Analysis

ON THE CONSISTENCY OF LEAST SQUARES ESTIMATORS FOR A THRESHOLD AR(1) MODEL

Journal Article

Abstract. For the SETAR (2; 1,1) model

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where {at(i)} are i.i.d. random variables with mean 0 and variance σ2(i), i = 1,2, and {at(l)} is independent of {at(2)}, we consider estimators of φ1, φ2 and r which minimize weighted sums of the sum of squares functions for σ2(1) and σ2(2). These include as a special case the usual least squares estimators. It is shown that the usual least squares estimators of φ1, φ2 and r are consistent. If σ2(1) ≠σ2(2) conditions on the weights are found under which the estimators of r and φ1 or φ2 are not consistent.

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