Shrinkage Based Tests of the Martingale Difference Hypothesis

45 Pages Posted: 29 Apr 2012

See all articles by Pablo M. Pincheira

Pablo M. Pincheira

Adolfo Ibanez University - School of Business

Date Written: June 2006


In this paper we define a family of tests for the Martingale Difference Hypothesis (MDH) based upon a shrinkage principle. Tests within this family are such that rejection of the null implies that forecasts from the alternative model, adjusted by a shrinkage factor, will display lower Mean Square Prediction Error (MSPE) than forecasts from the null model. This generalizes most previous tests which compare forecast errors of one model, the null, to forecast errors of the plain alternative model, not allowing for shrinkage. We argue that tests derived from this shrinkage approach display in general better small sample properties than MSPE based tests of the MDH. This occurs because the shrinkage based tests implicitly consider the reduced variance benefits of shrinkage estimators. Finally, we illustrate the use of our tests in an empirical application within the exchange rate literature.

Keywords: forecast evaluation, hypothesis testing, martingale difference, exchange rate, mean square prediction error, shrinkage

JEL Classification: C12, C22, C32, C52, C53, F37

Suggested Citation

Pincheira, Pablo M., Shrinkage Based Tests of the Martingale Difference Hypothesis (June 2006). Available at SSRN: or

Pablo M. Pincheira (Contact Author)

Adolfo Ibanez University - School of Business ( email )

Diagonal Las Torres 2640

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