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CPS1158 Varun A. et al.

Bayesian inference of multiple structural breaks
in multiple regimes threshold
autoregressive model

Varun Agiwal, Jitendra Kumar
Central University of Rajasthan

Abstract
This paper provides a Bayesian setup of multiple regimes threshold
autoregressive model with possible break points. A full conditional posterior
distribution is obtained for all model parameters using the suitable prior
information’s, including threshold and break point variables that are not attain
standard form distributions. In order to compute posterior distributions, we
applied Gibbs sampler with Metropolis-Hastings algorithm. A variety of loss
function is considered for optimizing the risk associated with each parameter.
For empirical evidence, simulation study and real data illustration are carried
out.

Keywords
Threshold autoregressive model; Prior & Posterior Distribution; MCMC
method; Structural Break

1. Introduction
Linear time series model are very popular for investigation of dynamic
structure of a series over time. There are several linear time series model which
adequately explore the characteristics such as stationarity, unit root, de-
trending, co-integration and so on to recognize the process efficiency and
improving the prediction (Dickey and Fuller(1979), Nelson & Plosser (1982),
Watson (1986)). However, series is non-linear in nature due to non-stationarity
or non-Gaussian of the stochastic trend. This possibility often arises during the
permanent change (structural break), temporary effect (outlier) or varying
structure relationship. For that reasons, a range of non linear time series model
was introduced and used for better analysis. The concept of break point(s) in
time series addressed by Albert and Chib (1993), Wang and Zivot (2000),
Meligkotsidou et al. (2011) in various univariate and multivariate AR model for
detection, estimation and testing purpose. All are considering structural
breaks in the time horizon. Although, series generation framework may
change during own past realizations. First, Tong (1983) introduced a standard
non linear time series model known as threshold autoregressive model (TAR)
and Chan (1993) derived the limiting distribution of the least square estimator.
Gonzalo and Wolf (2005) proposed a subsampling methodology to obtain the
consistent confidence interval of threshold and regression parameter when

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