Inference About Predictive Ability When There are Many Predictors

42 Pages Posted: 25 Apr 2007 Last revised: 12 Aug 2009

Date Written: January 1, 2007


We enhance the theory of asymptotic inference about predictive ability by considering the case when a set of variables used to construct predictions is sizable. To this end, we consider an alternative asymptotic framework where the number of predictors tends to infinity with the sample size, although more slowly. Depending on the situation the asymptotic normal distribution of an average prediction criterion either gains additional variance as in the few predictors case, or gains non-zero bias which has no analogs in the few predictors case. By properly modifying conventional test statistics it is possible to remove most size distortions when there are many predictors, and improve test sizes even when there are few of them.

Keywords: Predictive ability, testing, t-statistic, asymptotic distribution, asymptotic variance, asymptotic bias, many predictors

JEL Classification: C13, C22, C52

Suggested Citation

Anatolyev, Stanislav, Inference About Predictive Ability When There are Many Predictors (January 1, 2007). Available at SSRN: or

Stanislav Anatolyev (Contact Author)

New Economic School ( email )

Skolkovskoe shosse, 45
Moscow, 121353

CERGE-EI ( email )

P.O. Box 882
7 Politickych veznu
Prague 1, 111 21
Czech Republic

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