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Calibrating Wald Tests with Newey-West Standard Errors
A Placebo Experiment and a Restricted Wild Bootstrap on Daily Electricity Data, five hypothesis tests on 2,519 day-to-day changes in Iberian grid data. The textbook p-values reject true hypotheses up to three times as often as they should. A bootstrap brings them close to the nominal rate, and the evidence for one of the conclusions drops by an order of magnitude.
Diogo Ribeiro is a mathematician, researcher and lecturer at the Faculdade de Media Artes e Design, Universidade Técnica do Porto. ORCID 0009–0001–2022–7072. GitHub diogoribeiro7. Gitlab diogoribeiro7.
A p-value is a comparison between a statistic and a reference distribution, and it is only as good as the reference. In regression on time series the default reference is an asymptotic one: a Wald statistic built with a heteroskedasticity- and autocorrelation-consistent covariance, usually Newey-West, is referred to a chi-square distribution with as many degrees of freedom as there are restrictions. That approximation holds in the limit. Whether it holds for the sample at hand is an empirical question, and it can be answered with the sample itself.
This article answers it for five tests from an analysis of the Iberian electricity system, using two tools that any…
