Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2018 020

A Regime Shift Model with Nonparametric Switching Mechanism

Haiqiang Chen
Yingxing Li
Ming Lin
Yanli Zhu

In this paper, we propose a new class of regime shift models with exible switching
mechanism that relies on a nonparametric probability function of the observed thresh-
old variables. The proposed models generally embrace traditional threshold models
with contaminated threshold variables or heterogeneous threshold values, thus gaining
more power in handling complicated data structure. We solve the identification issue by
imposing either global shape restriction or boundary condition on the nonparametric
probability function. We utilize the natural connection between penalized splines and
hierarchical Bayes to conduct smoothing. By adopting dierent priors, our procedure
could work well for estimations of smooth curve as well as discontinuous curves with
occasionally structural breaks. Bayesian tests for the existence of threshold eects are
also conducted based on the posterior samples from Markov chain Monte Carlo (M-
CMC) methods. Both simulation studies and an empirical application in predicting
the U.S. stock market returns demonstrate the validity of our methods.

Threshold Model, Nonparametric, Markov Chain Monte Carlo, Bayesian Inference, Spline.

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