Statistical Tests for Multiple Forecast Comparison

16 Pages Posted: 15 Aug 2012

See all articles by Roberto S. Mariano

Roberto S. Mariano

Singapore Management University

Daniel P. A. Preve

Singapore Management University

Date Written: August 14, 2012


We consider a multivariate version of the Diebold–Mariano test for equal predictive ability of three or more forecasting models. The Wald-type test, S, which has a null distribution that is asymptotically chi-squared, is shown to be generally invariant with respect to the ordering of the models being compared. Finite-sample corrections for the test are also developed. Monte Carlo simulations indicate that S has reasonable size properties in large samples but tends to be oversized in moderate samples. The finite-sample correction succeeds in correcting for size, but only partially. For the size-adjusted tests, power increases with sample size, as expected. It is speculated that further finite-sample improvements can be achieved using Hotelling’s T-square or bootstrap critical values.

Keywords: forecast comparison, multivariate tests of equal predictive ability, Diebold–Mariano test, finite-sample correction

Suggested Citation

Mariano, Roberto S. and Preve, Daniel P. A., Statistical Tests for Multiple Forecast Comparison (August 14, 2012). Journal of Econometrics, Vol. 169, 2012, Available at SSRN:

Roberto S. Mariano

Singapore Management University ( email )

50 Stamford Rd.
Singapore 912409, 178899

Daniel P. A. Preve (Contact Author)

Singapore Management University ( email )

90 Stamford Road
Singapore, 178903

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