Choosing Between Different Time‐Varying Volatility Models for Structural Vector Autoregressive Analysis
| DOI | http://doi.org/10.1111/obes.12238 |
| Published date | 01 August 2018 |
| Author | Helmut Lütkepohl,Thore Schlaak |
| Date | 01 August 2018 |
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©2018 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 80, 4 (2018) 0305–9049
doi: 10.1111/obes.12238
Choosing Between DifferentTime-Varying Volatility
Models for StructuralVector Autoregressive
Analysis*
Helmut L ¨
utkepohl† and Thore Schlaak‡
†DIW Berlin and Freie Universit ¨at Berlin, Mohrenstr. 58, 10117 Berlin, Germany
(e-mail: hluetkepohl@diw.de)
‡DIW Berlin, Mohrenstr. 58, 10117 Berlin, Germany (e-mail: tschlaak@diw.de)
Abstract
The performance of information criteria and tests for residual heteroscedasticity for choos-
ing between different models for time-varying volatility in the context of structural vector
autoregressive analysis is investigated. Although it can be difficult to find the true volatility
model with the selection criteria, using them is recommended because they can reduce the
mean squared error of impulse response estimates substantially relative to a model that
is chosen arbitrarily based on the personal preferences of a researcher. Heteroscedasticity
tests are found to be useful tools for deciding whether time-varying volatility is present
but do not discriminate well between different types of volatility changes. The selection
methods are illustrated by specifying a model for the global market for crude oil.
I. Introduction
Following the seminal publication by Engle (1982), time-varying volatility in time series
data has received increasing attention. It has been diagnosed in many time series and it is
taken into account to improve inference, for risk analysisand for economic studies not only
in univariate but also in multivariate time series models. Engle introduced ARCH (auto-
regressive conditional heteroscedasticity) processes for modelling time-varying volatility.
In the meantime, a range of alternative models for conditional as well as unconditional
heteroscedasticity have been developed to capture various volatility patterns. For applied
work, this raises the question which model is best suited for a given volatility pattern.
So far the choice of a volatility model is often not well justified. It is sometimes dic-
tated by convenience, the preferences of the analyst or it is based on ad hoc criteria with
JEL Classification numbers: C32.
*The paper was written in part while the first author was a Bundesbank Professor at the Freie Universit¨at Berlin.
Financial support was providedby the Deutsche Forschungsgemeinschaft through the SFB 649 ‘Economic Risk’. The
authors thank the high-performance computing service at Freie Universit¨at Berlin for providing the computational
resources required for this work.All calculations were conducted using the statistical software R3.3.3. The comments
of two anonymous referees are gratefully acknowledged.
716 Bulletin
unclear implications for the objective of the analysis. Hence, it is clearly desirableto better
understand the implications of choosing a specific model for time-varying volatility and
the second moment structure of a time series variable or set of variables more generally.
An improved understanding of the choice of the model for the second moment structure
of a time series is best considered in the context of a specific modelling and analysis frame-
work. A number of studies have compared the forecasting ability of univariate volatility
models (e.g. Hansen and Lunde, 2005; Becker and Clements, 2008; Caporin and McAleer,
2012). The performance of multivariate volatility models has been studied with the ob-
jective of covariance forecasting or risk assessment in mind (e.g. Caporin and McAleer,
2011; Laurent, Rombouts and Violante, 2012; Becker et al., 2015). Some of these studies
are based on specific data sets and may be difficult to generalize. Moreover, some studies
compare generalized ARCH (GARCH) type models only.
A crucial issue in comparisons of volatility models is the metric used for the comparison.
In the present study, we focus on structural vector autoregressive (SVAR) analysis. In
that framework alternative models for time-varying volatility have been used to support
the identification of structural shocks. Therefore, we focus in this study on choosing an
appropriate volatility structure for vector autoregressive (VAR) models with the specific
objective of SVAR analysis in mind. Specifically, we consider volatility models that have
been used as tools for identifying structural shocks in SVAR analysis.
The volatility models of interest in this context range from simple exogenous jumps in
the residual variance (Rigobon, 2003; Lanne and L¨utkepohl, 2008) or a smooth transition
between differentvolatility states (L ¨utkepohland Net ˇsunajev, 2017b) to more sophisticated
GARCH processes (Normandin and Phaneuf, 2004; Bouakez and Normandin, 2010) and
Markov switching mechanisms (Lanne, L¨utkepohl and Maciejowska, 2010; Herwartz and
L¨utkepohl, 2014). In some of the related literature even competing models are applied to
the same data and it is unclear which of them best describes the time-varying volatility of a
given system of variables (see, e.g., L¨utkepohl and Netˇsunajev, 2017a). In such a situation
having objective criteria that facilitate the selection of a model would be desirable. At the
same time, however, little is known about the consequences of selecting a specific volatility
model for parameter estimation and inference.
The objective of this study is to compare different procedures that discriminate between
competing volatility models and to determine which ones are most helpful in deciding on
a volatility model for SVAR analysis. We investigate how the choice of a model affects
the outcome of structural analysis and use evaluation criteria for model selection that are
based on inference for impulse response analysis, which is often the objective of SVAR
analysis.
For this purpose, we perform the following experiment. We generate time series with
different types of volatility changes and then fit a set of different models that allow for
changing volatility.These models are compared with different specification tests and model
selection criteria. The goal is to determine which tests or criteria are best suited for finding
the process that has actually generated the data and to investigate the impact of model
selection on the structural parameters of interest.
We find that tests for heteroscedasticity are useful tools for detecting time-varying
volatility but are less useful for deciding on a specific model type. We compare three
standard information criteria for selecting the specific volatility model and find that it
©2018 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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