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Threshold model with a time‐varying threshold based on Fourier approximation.

Authors :
Yang, Lixiong
Lee, Chingnun
Chen, I‐Po
Source :
Journal of Time Series Analysis; Jul2021, Vol. 42 Issue 4, p406-430, 25p
Publication Year :
2021

Abstract

Classical threshold models assume that threshold values are constant and stable, which appears overly restrictive and unrealistic. In this article, we extend Hansen's (2000) constant threshold regression model by allowing for a time‐varying threshold which is approximated by a Fourier function. Least‐square estimation of regression slopes and the time‐varying threshold is proposed, and test statistics for the existence of threshold effect and threshold constancy are constructed. We also develop the asymptotic distribution theory for the time‐varying threshold estimator. Through Monte Carlo simulations, we show that the proposed estimation and testing procedures work reasonably well in finite samples, and there is little efficiency loss by the allowance for Fourier approximation in the estimation procedure even when there is no time‐varying feature in the threshold. On the contrary, the slope estimates are seriously biased when the threshold is time‐varying but being treated as a constant. The model is illustrated with an empirical application to a nonlinear Taylor rule for the United States. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
01439782
Volume :
42
Issue :
4
Database :
Complementary Index
Journal :
Journal of Time Series Analysis
Publication Type :
Academic Journal
Accession number :
150718873
Full Text :
https://doi.org/10.1111/jtsa.12574