Granger Centre Seminar: Ovidijus Stauskas (Lund University)

Tests of equal forecasting accuracy for nested models with estimated CCE factors (with Joakim Westerlund)

Abstract: The standard approach whenever there is uncertainty over the explanatory power of a set of regressors is to test their relevance. This is true in all fields of research, including forecasting where predictive regressions with estimated factors have recently attracted much interest. The main reason for this interest is that the factors summarize the information contained in a large panel of variables, which means that they are likely to be important for the accuracy of the forecast. They are also likely to be correlated with the predictors included in the model, which raises the issue of omitted variables bias. It is therefore important to be able to test if the factors are in fact relevant. Yet, strangely enough, there are only two tests available, and they both assume that the true number of factors is known, which is never the case in practice. Motivated by this observation, the current paper is the first to test the predictive ability of the factors when their number is unknown. The main finding is that over-specification of the number of factors is not a problem in the sense that the asymptotic distributions of the proposed test statistics only depend on the number of estimated factors, which is of course known. This result is of considerable importance in applied work, because it means that researchers are spared of the problem of having to estimate the number of factors.