Asymptotic variance of Brier (skill) score in the presence of serial correlation

We propose autocorrelation-robust asymptotic variances of the Brier score and Brier skill score, which are generally applicable in circumstances with weak serial correlation. An empirical application in macroeconomics underscores the importance of taking care of serial correlation. We find that the conventional variances are too conservative to account for the sampling variability in estimating the Brier (skill) score.