PRACTITIONER'S CORNER*: Comparing Time‐Series and Nonlinear Model‐Based Forecasts†
| DOI | http://doi.org/10.1111/j.1468-0084.1984.mp46004007.x |
| Published date | 01 November 1984 |
| Author | Kenneth F. Wallis |
| Date | 01 November 1984 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 46, 4 (1984)
0305 -9049 S3.00
PRACTITIONER'S CORNER*
Comparing Time-Series and Nonlinear Model-Based
Forecasts t
Kenneth F. Wallis
I. INTRODUCTION
In a dynamic linear model relating a set of jointly dependent, endo-
genous variables to a set of explanatory, exogenous variables also
generated by linear processes there are two approaches to forecasting.
In the first approach, which we term 'econometric' or 'model-based',
forecasts of the exogenous variables based on their past values are
inserted into the model, which is then solved to yield forecasts of the
endogenous variables. The second approach uses only the past values of
the variables in question, and the 'time-series' forecast is obtained
purely extrapolatively. It can be seen as an application of the univariate
representation of an endogenous variable which is implied by the model
(Prothero and Wallis, 1976; Wallis, 1977; Zeilner and Palm, 1974). In
general the time-series forecast has greater mean square error than the
model-based forecast (Pierce, 1975; Wallis, 1980).
Comparisons of the two forecasts have often been used to evaluate
empirical macroeconometric models (Christ, 1975; Cooper, 1972;
Nelson, 1972; and many more recent examples). It is argued that a
model that cannot forecast better thaii the purely extrapolative forecast
should be discarded. The results of such practical comparisons are not
always favourable to the econometric model, in contrast to the
theoretical result cited above. The general issues surrounding the
relevance of this result to the practical evaluation of econometric
models are discussed by Salmon and Wallis (1982), and in this note we
further consider one specific feature, namely that while the theoretical
result refers to linear models, most practical macroeconometric models
are nonlinear in variables.
In nonlinear models, the conditional expectation of the endogenous
variables, which is the optimal forecast with respect to a quadratic loss
function, can be estimated as the mean of replicated stochastic simula-
tions. However, comparative exercises are orten based on the deter-
* The purpose of Practitioner's Corner is to publish brief methodological flotes of interest to
applied economists. The Editors welcome submissions of this Sort.
t The research assistance of Peter Burridge is gratefully acknowledged. This research was
supported by a grant from the Social Science Research Council.
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