White noise testing for functional time series

Abstract

We review white noise tests in the context of functional time series, and compare many of them using a custom developed R package wwntests. The tests are categorized based on whether they are conducted in the time domain or spectral domain, and whether they are valid for i.i.d. or general uncorrelated noise. We also review and extend several residual-based goodness-of-fit tests of popular models used in functional data analysis. Through numerous simulation experiments and a data application, we demonstrate the use of these tests, and are able to provide practical guidance on their implementation, benefits, and drawbacks.