Tests of Equal Forecasting Accuracy for Nested Models with Estimated CCE Factors*

Abstract

In this article, we propose new tests of equal predictive ability between nested models when factor-augmented regressions are used to forecast. In contrast to the previous literature, the unknown factors are not estimated by principal components but by the common correlated effects (CCE) approach, which employs cross-sectional averages of blocks of variables. This makes for easy interpretation of the estimated factors, and the resulting tests are easy to implement and they account for the block structure of the data. Assuming that the number of averages is larger than the true number of factors, we establish the limiting distributions of the new tests as the number of time periods and the number of variables within each block jointly go to infinity. The main finding is that the limiting distributions do not depend on the number of factors but only on the number of averages, which is known. The important practical implication of this finding is that one does not need to estimate the number of factors consistently in order to apply our tests.

Keywords:

• Common correlated effects
• Common factor model
• Factor-augmented regression model
• Forecasting

Supplementary Materials

The supplement materials include proofs and additional results.

Acknowledgments

The authors thank to seminar and conference participants, and in particular Ignace De Vos, David Edgerton, Per Johansson, Rolf Larsson, Johan Lyhagen, Serena Ng, Simon Reese, Lorenzo Trapani, David Harvey, Povilas Lastauskas, Greg Franguridi, an associate editor, and two anonymous referees for many valuable comments and suggestions. Westerlund thank to the Knut and Alice Wallenberg Foundation for financial support through a Wallenberg Academy Fellowship.