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On The Consistency Of Least Squares Estimators For A Threshold Ar(1) Model

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  • Joseph D. Petruccelli

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.

Suggested Citation

  • Joseph D. Petruccelli, 1986. "On The Consistency Of Least Squares Estimators For A Threshold Ar(1) Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(4), pages 269-278, July.
    • Handle: RePEc:bla:jtsera:v:7:y:1986:i:4:p:269-278
    DOI: 10.1111/j.1467-9892.1986.tb00494.x
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    Cited by:

    1. Diego Chávez & Javier E. Contreras-Reyes & Byron J. Idrovo-Aguirre, 2022. "A Threshold GARCH Model for Chilean Economic Uncertainty," JRFM, MDPI, vol. 16(1), pages 1-15, December.
    2. Grabowski Daniel & Staszewska-Bystrova Anna & Winker Peter, 2017. "Generating prediction bands for path forecasts from SETAR models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(5), pages 1-18, December.

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