On the least squares estimation of multiple-threshold-variable autoregressive models

Zhang, Xinyu, Li, Dong and Tong, Howell (2023) On the least squares estimation of multiple-threshold-variable autoregressive models. Journal of Business and Economic Statistics. ISSN 0735-0015

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Abstract

Most threshold models to-date contain a single threshold variable. However, in many empirical applications, models with multiple threshold variables may be needed and are the focus of this article. For the sake of readability, we start with the Two-Threshold-Variable Autoregressive (2-TAR) model and study its Least Squares Estimation (LSE). Among others, we show that the respective estimated thresholds are asymptotically independent. We propose a new method, namely the weighted Nadaraya-Watson method, to construct confidence intervals for the threshold parameters, that turns out to be, as far as we know, the only method to-date that enjoys good probability coverage, regardless of whether the threshold variables are endogenous or exogenous. Finally, we describe in some detail how our results can be extended to the K-Threshold-Variable Autoregressive (K-TAR) model, K > 2. We assess the finite-sample performance of the LSE by simulation and present two real examples to illustrate the efficacy of our modeling.

Item Type:	Article
Official URL:	https://www.tandfonline.com/journals/ubes20
Additional Information:	© 2023 American Statistical Association.
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	10 Mar 2023 12:45
Last Modified:	15 Apr 2024 16:24
URI:	http://eprints.lse.ac.uk/id/eprint/118377

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