This paper investigates selection and averaging of linear
regressions with a possible structural break. Our main contribution is the
construction of a Mallows criterion for the structural break model. We show
that the correct penalty term is non-standard and depends on unknown
parameters, but it can be approximated by an average of limiting cases to yield
a feasible penalty with good performance. Following Hansen (2007) we recommend
averaging the structural break estimates with the no-break estimates where the
weight is selected to minimize the Mallows criterion. This estimator is simple
to compute, as the weights are a simple function of the ratio of the penalty to
the Andrews SupF test statistic.
To assess performance we focus on asymptotic mean-squared error (AMSE) in a
local asymptotic framework. We show that the AMSE of the estimators depends
exclusively on the parameter variation function. Numerical comparisons show
that the unrestricted least-squares and pretest estimators have very large AMSE
for certain regions of the parameter space, while our averaging estimator has
AMSE close to the infeasible optimum..
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Some
of the above material is based upon work supported by the National Science
Foundation under Grants No. SES-9022176, SES-9120576,
SBR-9412339, and SBR-9807111. Any opinions, findings, and conclusions,
or recommendations expressed in this material are those of the author(s), and
do not necessarily reflect the views of the NSF.