Perplexity about periodicity repeats perpetually: A response to Brookshire

Brookshire (2022) claims that previous analyses of periodicity in detection performance after a reset event suffer from extreme false-positive rates. Here we show that this conclusion is based on an incorrect implemention of a null-hypothesis of aperiodicity, and that a correct implementation confirms low false-positive rates. Furthermore, we clarify that the previously used method of shuffling-in-time, and thereby shuffling-in-phase, cleanly implements the null hypothesis of no temporal structure after the reset, and thereby of no phase locking to the reset. Moving from a corresponding phase-locking spectrum to an inference on the periodicity of the underlying process can be accomplished by parameterizing the spectrum. This can separate periodic from non-periodic components, and quantify the strength of periodicity.