Generalized Forecast Error Variance Decomposition for Linear and Nonlinear Multivariate Models
| Author | Henri Nyberg,Markku Lanne |
| Date | 01 August 2016 |
| Published date | 01 August 2016 |
| DOI | http://doi.org/10.1111/obes.12125 |
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©2016 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 78, 4 (2016) 0305–9049
doi: 10.1111/obes.12125
Generalized Forecast ErrorVariance Decomposition
for Linear and Nonlinear Multivariate Models*
Markku Lanne†,‡ and Henri Nyberg†,§
†Department of Political and Economic Studies, and HECER, University of Helsinki,
Helsinki, Finland
‡CREATES, Aarhus University, Aarhus, Denmark (e-mail: markku.lanne@helsinki.fi)
§Department of Mathematics and Statistics, University of Turku, Turku, Finland
(e-mail: henri.nyberg@utu.fi)
Abstract
We propose a new generalized forecast error variance decomposition with the attractive
property that the proportions of the impact accounted for by innovations in each variable
sum to unity. Our decomposition is based on the generalized impulse response function,
and it can easily be obtained by simulation. The new decomposition is illustrated in an
empirical application to US output growth and interest rate spread data.
I. Introduction
Impulse response and forecast error variance decomposition analyses are the prominent
tools in interpreting estimated linear and nonlinear multivariate time series models. These
methods call for the identification of the structural shocks by imposing a sufficient number
of identification restrictions on a reduced-form linear vector autoregressive (VAR) model.
However, in many cases it is difficult to come up with adequate credible identification
restrictions. In these cases as well as in nonlinear models, the generalized impulse response
functions (GIRF) and generalized forecast error variance decompositions (GFEVD) offer
alternative means of structural analysis.
The main difference between the impulse response function (IRF) and forecast error
variance decomposition (FEVD) and their generalized counterparts is the interpretation of
the shocks: in the former, they are uncorrelated and carry an economic meaning, while in the
latter, each of them is just a shock to a given equation of the model. Moreover, because
the latter shocks are not necessarily uncorrelated, the interpretation of the GFEVD as the
JEL Classification numbers: C13, C32, C53.
*Wewould like to thank the Editor Anindya Banerjee, two anonymousreferees, Pentti Saikkonen, Timo Ter¨asvirta
and the participants in the 8th International Conference on Computational and Financial Econometrics in Pisa (2014)
for useful comments. Financial support from theAcademy of Finland is gratefully acknowledged. The first author also
acknowledges financial support from CREATES (DNRF78) funded by the Danish National Research Foundation,
while the second author is grateful for financial support from the OP-Pohjola Group Research Foundation and the
Research Funds of the University of Helsinki.
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