The Gibbons, Ross, and Shanken (1989) F-test of mean-variance efficiency of asset returns is stated incorrectly for the multi-factor case. We first derive the correct formula for the test statistic for the general case of K factors and N test assets, then highlight the impact of the error in...

We clear up an ambiguity in Gibbons, Ross and Shanken (1989, GRS hereafter) by providing the correct formula of the GRS test statistic for the multiple factor case and proving its exact F distribution, issues unaddressed in GRS (1989). We theoretically and empirically illustrate the consequences...

This paper proposes a test for the conditional superior predictive ability (CSPA) of a family of forecast methods with respect to a benchmark. The test is functional in nature: Under the null hypothesis, the benchmark's conditional expected loss is no more than those of the competitors,...

This paper concerns the uniform inference for nonparametric series estimators in time-series applications. We develop a strong approximation theory of sample averages of serially dependent random vectors with dimensions growing with the sample size. The strong approximation is first proved for...