LAUSR

Abstract Distinguishing linear series from nonlinear ones is of great importance, for not only understanding the processes generating these series but also their modeling and prediction. There are many methods and their nonlinear quantifiers to reach this goal, but no one is powerful enough to deal with any given series. In this study, the artificially generating series with given tailored phase correlation strength is applied to test the performance of some widely used methods and their nonlinear quantifiers given in the previous studies, both advantages and shortcomings are shown for these methods and their nonlinear metrics. Especially, spurious results from these methods and their nonlinear metrics can be found for some cases (much weak or strong phase correlations). In order to avoid these spurious results, modified phase correlation quantifiers are proposed. At the same time, multiple stripes found in the phase map can be explained from the view point of enhanced nonlinear strength.