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

Joseph D. Petruccelli

Journal of Time Series Analysis, 1986, vol. 7, issue 4, 269-278

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

Date: 1986
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