Using out-of-sample mean squared prediction errors to test the martingale difference hypothesis

We consider using out-of-sample mean squared prediction errors (MSPEs) to evaluate the null that a given series follows a zero mean martingale difference against the alternative that it is linearly predictable. Under the null of no predictability, the population MSPE of the null “no change” model eq...

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Bibliographic Details
Published inJournal of econometrics Vol. 135; no. 1; pp. 155 - 186
Main Authors Clark, Todd E., West, Kenneth D.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.11.2006
Elsevier
Elsevier Sequoia S.A
SeriesJournal of Econometrics
Subjects
Causality
Econometrics
Economic efficiency
Efficient markets
Error analysis
Exchange rate
Exchange rates
Forecasting
Forecasts
Market theory
Parameter estimation
Random walk
Simulation
Statistical analysis
Studies
Testing
C530
C220
Efficient markets
F370
Random walk
Causality
Exchange rate
Forecasting
Testing
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Summary:We consider using out-of-sample mean squared prediction errors (MSPEs) to evaluate the null that a given series follows a zero mean martingale difference against the alternative that it is linearly predictable. Under the null of no predictability, the population MSPE of the null “no change” model equals that of the linear alternative. We show analytically and via simulations that despite this equality, the alternative model's sample MSPE is expected to be greater than the null's. For rolling regression estimators of the alternative model's parameters, we propose and evaluate an asymptotically normal test that properly accounts for the upward shift of the sample MSPE of the alternative model. Our simulations indicate that our proposed procedure works well.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2005.07.014