Testing serial dependence by Random-shuffle surrogates and the Wayland method

Given time series, a primary concern is existence of serial dependence and determinism. They are often tested with Random-shuffle surrogates, which totally break serial dependence, and the Wayland method. Since the statistic of the Wayland method fundamentally shows a smaller value for a more deterministic time series, for real-world data, we usually expect that the statistic for the original data is smaller than or equal to those of Random-shuffle surrogates. However, we show herewith an opposite result with wind data in high time resolution. We argue that this puzzling phenomenon can be produced by observational or dynamical noise, both of which may be produced by a low-dimensional deterministic system. Thus the one-sided test is dangerous.