Multiple testing correction for mean tests in time series rolling window analysis with an application of GWAS methods

Rolling window analysis is a popular tool in time series research. However, conducting hypothesis tests on all rolling windows simultaneously introduces a multiple testing problem. In the literature, bootstrapping the maximum of all statistics from rolling windows is the most commonly used, if not the only, method to address this issue. This paper seeks to provide a simpler and faster alternative to bootstrap methods by adapting p-value combination techniques that are popular in genome-wide association studies to the context of mean tests in a time series rolling window analysis. Some p-value combination methods in genetics require knowledge of the correlation structure of test statistics, which can typically be obtained from external sources. However, such information is often unavailable for time series datasets. To address this challenge, we employ the autoregressive sieve approach, which allows for the computation of correlation structures based on estimated autoregressive coefficients. We present finite sample simulations to illustrate the performance of p-value combination methods in a rolling window setting and offer recommendations for practitioners and future researchers in this area.