# Statistical tests for multiple forecast comparison

*Roberto Mariano* () and
*Daniel Preve*

*Journal of Econometrics*, 2012, vol. 169, issue 1, 123-130

**Abstract:**
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 T2 or bootstrap critical values.

**Keywords:** Forecast comparison; Multivariate tests of equal predictive ability; Diebold–Mariano test; Finite-sample correction (search for similar items in EconPapers)

**JEL-codes:** C12 C52 (search for similar items in EconPapers)

**Date:** 2012

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:econom:v:169:y:2012:i:1:p:123-130

**DOI:** 10.1016/j.jeconom.2012.01.014

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