Partial Structural Break Identification

Published date01 April 2017
DOIhttp://doi.org/10.1111/obes.12153
Date01 April 2017
145
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 79, 2 (2017) 0305–9049
doi: 10.1111/obes.12153
Partial Structural Break Identification*
Chulwoo Han† and Abderrahim Taamouti
Durham University Business School, Mill Hill LaneDurham, DH1 3LB, UK
(e-mail: chulwoo.han@durham.ac.uk, abderrahim.taamouti@durham.ac.uk)
Abstract
We propose an extension of the existing information criterion-based structural break iden-
tification approaches. The extended approach helps identify both pure structural change
(break) and partial structural change (break). A pure structural change refers to the case
when breaks occur simultaneously in all parameters of regression equation, whereas a par-
tial structural change happens when breaks occur in some parameters only. Our approach
consistently outperforms other well-known approaches. We also extend the simulation
studies of Bai and Perron (2006) and Hall, Osborn and Sakkas (2013) by including more
general cases. This provides more comprehensive results and reveals the cases where the
existing identification approaches lose power,which should be kept in mind when applying
them.
I. Introduction
Structural breaks have been observed in many economic and financial time series, see
Stock and Watson(1996) among others. It is well established that ignoring these breaks has
undesirable consequences on time series analysis. In particular, authors such as Clements
and Hendry (1998, 1999) consider the ignorance of structural breaks as a main reason
of forecast failure. Hence, the importance of providing robust statistical procedure for
detecting and estimating the number of breaks cannot be overemphasized.
Several approaches have been proposed to detect structural breaks in economic and
financial time series. Andrews (1993) and Bai and Perron (1998) introduced statistical
testing procedures to investigate the presence and timing of change when one or more
breaks occur within the available time series data. Perron and Qu (2006) extended these
results to the case where arbitrary linear restrictions on the coefficients are available a
priori. Another class of approaches are based on information criteria. Yao (1988), Liu,
Wu and Zidek (1997), and Zhang and Siegmund (2007) considered Bayesian information
criterion (BIC) of Schwarz (1978), whereas Ninomiya (2005) used Akaike’s information
criterion (AIC) of Akaike (1973). In addition, Bai (2000) established conditions under
which an information criterion is consistent for estimation of the number of breaks in vector
JEL Classification numbers: C01, C1, C51, C52.
*The authors thank the anonymous referee and the Editor Prof. Anindya Banerjee for severaluseful comments.
146 Bulletin
autoregressions with martingale difference sequence errors. Finally, recentlyChen, Gerlach
and Liu (2011) have used a Bayesian computational method to identify the locations of
structural breaks in the context of time-varying regression model and in the presence of
heteroscedasticity and autocorrelation.
In this paper, we extend the existing information criterion-based approaches to identify
both pure and partial structural changes. A pure structural change refers to the case when
breaks occur simultaneously in all parameters of regression equation, whereas a partial
structural change refers to the case when breaks occur in some parameters only. One
drawback of the existing approaches is that they assume pure (simultaneous) structural
breaks only, although this may not be the case in reality. For example, if a monetary
policy measure is included as one of the regressors and one wants to examine the effect
of changes in this measure on a dependent macro variable, there is no reason to assume
that other regressors will also experience a structural break at the same time. If breaks
occur only in some of the regressors, as explained in section III, the existing information
criterion-based approaches will underestimate the number of breaks. Our extension aims
to address this problem of the existing approaches and detect partial structural breaks as
well as pure structural breaks.
Another contribution of this paper is that we provide a Monte Carlo simulation study
which compares the performance of our approach with the existing ones for a large set
of data-generating processes that represent different contexts encountered in practice. We
extend the simulation studies of Bai and Perron (2006) and Hall et al. (2013) by including
more general cases, especially the cases where break detection becomes difficult. This
provides more comprehensive results and reveals the potential areas where the existing
methods lose their power. Simulation results show that our approach consistently outper-
forms other well-known approaches such as the ones introduced by Yao (1988) and Bai
and Perron (1998).
The rest of the paper is organized as follows. The framework that defines the regres-
sion model with multiple breaks and a general procedure that identifies these breaks is
introduced in section II. Section III provides a brief summary of the existing information
criterion-based approaches and discusses our approach for detecting partial breaks. In sec-
tion IV, we use Monte Carlo simulations to investigate the performance of our approach
by comparing it with the existing ones. Section V concludes.
II. Framework
We consider the following N-variable linear system with Kbreaks
yt=Xtk+et, for k1tk, with k=1,,K+1, (1)
where Xt=[1 x1t··· xNt] is a vector of covariates, k=[0k··· Nk]is a vector of
parameters of interest that are subject to multiple structural breaks, and etis an error term.
Kbreaks means that we are in presence of K+1 regimes that are defined by the time set
{0=1,…, K+1=T}within the whole sample of size T. The problem now is to identify
the number (K) and timing (k) of the breaks. A general procedure for this consists of the
following two steps.
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd

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