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

Xinyu Zhang, Dong Li and Howell Tong

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: compound Poisson process; degeneracy of a spatial process; multiple threshold variables; TAR model; weighted Nadaraya-Watson method (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2023-02-23
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Journal of Business and Economic Statistics, 23, February, 2023. ISSN: 0735-0015

Downloads: (external link)
http://eprints.lse.ac.uk/118377/ Open access version. (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:118377

Access Statistics for this paper

More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC.
Bibliographic data for series maintained by LSERO Manager ().