Simultaneous Inference Bands for the PIT Histogram

In the absence of systematic errors in forecast distributions, their Probability Integral Transforms (PITs) follow a uniform distribution over the interval [0, 1]. To assess the flatness of the empirical PIT histogram, we use simultaneous inference bands, namely Bonferroni bands and the sup-t bands of Montiel Olea and Plagborg-Møller (2019). For the case of serially independent PITs, this can be done exactly; if the PITs are serially correlated, we construct asymptotic versions for both types of bands by bootstrapping the PITs. We find that Bonferroni bands with small-sample adjustments have good size and power properties, despite their expected conservativeness. We use Bonferroni bands to evaluate the Bank of England’s inflation forecasts. pdf