A test for the absence of aliasing or white noise in locally stationary wavelet time series

Aliasing is often overlooked in time series analysis but can seriously distort the spectrum, autocovariance and their estimates. We show that dyadic subsampling of a locally stationary wavelet process, which can cause aliasing, results in a process that is the sum of asymptotic white noise and another locally stationary wavelet process with a modified spectrum. We develop a test for the absence of aliasing in a locally stationary wavelet series at a fixed location, and illustrate it on simulated data and a wind energy time series. A useful by-product is a new test for local white noise. The tests are robust to model misspecification in that it is unnecessary for the analysis and synthesis wavelets to be identical. Hence, in principle, the tests work irrespective of which wavelet is used to analyze the time series, though in practice there is a tradeoff between increasing statistical power and time localization of the test