Received: 14 January 2016 Revised: 14 August 2017
An efficient Bayesian approach to multiple structural
change in multivariate time series
John M. Maheu
DeGroote School of Business, McMaster
University, Hamilton, Ontario, Canada
RCEA, Rimini, Italy
Department of Economics, Faculty of
Business and Economics, University of
Melbourne, Melbourne, Victoria, Australia
Yong Song, 111 Barry Street, Carlton,
Victoria, 3010, Australia.
This paper provides a feasible approach to estimation and forecasting of multi-
ple structural breaks for vector autoregressions and other multivariate models.
Owing to conjugate prior assumptions we obtain a very efficient sampler for the
regime allocation variable. A new hierarchical prior is introduced to allow for
learning over different structural breaks. The model is extended to independent
breaks in regression coefficients and the volatility parameters. Two empirical
applications show the improvements the model has over benchmarks. In a
macro application with seven variables we empirically demonstrate the benefits
from moving from a multivariate structural break model to a set of univariate
structural break models to account for heterogeneous break patterns across data
Multivariate time series data play a central role in macroeconomic analysis and prediction. Linear models such as vector
autoregressions (VARs) are standard tools to calculate the impulse response function and forecasts. Recently, many papers
have highlighted the importance of nonlinearity associated with structural instability for macroeconomic and financial
variables such as gross domestic product (GDP) growth, real interest rate, inflation and equity returns, among many
others. However, because the estimation usually involves intensive computation, most of the change-point models are
applied to univariate time series. Existing multivariate change-point models have restrictions on the number of regimes
a priori. It is either fixed at a small number (2 or 3) as in Jochmann and Koop (2011) or assumed equal to the length
of the data as in Cogley and Sargent (2005). A multivariate approach that can estimate and forecast in the presence of
an unknown number of regimes is missing in the current literature. This paper develops a new multivariate time series
model to fill the gap by exploring the full posterior distribution for the allocation of the data to their respective regimes.
The speed of estimation of the new approach is increased by using a conjugate prior for the parameters that characterize
each regime. The simulation of the regime allocation of the data from its posterior distribution is very efficient, because
the time-varying parameters for the conditional data density are integrated out. A new hierarchical structure is introduced
to exploit the information across regimes.
Accounting for structural instability in macroeconomic and financial time series modeling and forecasting is important.
Empirical applications by Clark and McCracken (2010), Giordani, Kohn, and Van Dijk (2007), Liu and Maheu (2008),
Wang and Zivot (2000), and Stock and Watson (1996), among others, demonstrate strong evidence for the existence of
nonlinearity in the form of structural changes.
The challenges of estimation and forecasting in the presence of structural breaks has been recently addressed by Koop
and Potter (2007), Maheu and Gordon (2008), and Pesaran, Pettenuzzo, and Timmermann (2006) using Bayesian methods.
These approaches provide feasible solutions for univariate time series modeling, but they are computationally intensive.
J Appl Econ. 2018;33:251–270. wileyonlinelibrary.com/journal/jae Copyright © 2017 John Wiley & Sons, Ltd. 251