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ASYMPTOTIC THEORY ON THE LEAST SQUARES ESTIMATION OF THRESHOLD MOVING-AVERAGE MODELS

Published online by Cambridge University Press:  12 November 2012

Dong Li ,
Shiqing Ling  and
Wai Keung Li
Dong Li
Affiliation:
Hong Kong University of Science and Technology
Shiqing Ling
Affiliation:
Hong Kong University of Science and Technology
Wai Keung Li*
Affiliation:
University of Hong Kong
*
*Address correspondence to Wai Keung Li, Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong; e-mail: [email protected].
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Abstract

This paper studies the asymptotic theory of least squares estimation in a threshold moving average model. Under some mild conditions, it is shown that the estimator of the threshold is n-consistent and its limiting distribution is related to a two-sided compound Poisson process, whereas the estimators of other coefficients are strongly consistent and asymptotically normal. This paper also provides a resampling method to tabulate the limiting distribution of the estimated threshold in practice, which is the first successful effort in this direction. This resampling method contributes to threshold literature. Simultaneously, simulation studies are carried out to assess the performance of least squares estimation in finite samples.

Type
Articles
Information
Econometric Theory , Volume 29 , Issue 3 , June 2013 , pp. 482 - 516
Copyright
Copyright © Cambridge University Press 2012 

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Footnotes

S. Ling thanks Hong Kong Research Grants Council, grants HKUST602609 and HKUST641912, for partial support. W.K. Li thanks Hong Kong Research Grants Council, grant HKU7036/06P, for partial support. The authors also thank the co-editor and two anonymous referees for their helpful comments that improved the presentation.

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