The Annals of Statistics

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

K. S. Chan

Full-text: Open access

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.

Article information

Source
Ann. Statist. Volume 21, Number 1 (1993), 520-533.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176349040

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176349040

Mathematical Reviews number (MathSciNet)
MR1212191

Zentralblatt MATH identifier
0786.62089

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62J05: Linear regression

Keywords
Compound Poisson process consistency ergodicity least squares estimation limiting distribution threshold autoregressive models

Citation

Chan, K. S. Consistency and Limiting Distribution of the Least Squares Estimator of a Threshold Autoregressive Model. Ann. Statist. 21 (1993), no. 1, 520--533. doi:10.1214/aos/1176349040. http://projecteuclid.org/euclid.aos/1176349040.


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