Detecting dynamical nonstationarity in time series data

Nonlinear time series analysis is becoming an ever more powerful tool to ex plore complex phenomena and uncover underlying patterns from irregular data recorded from experiments. However, the existence of dynamical nonstationa rity in time series data causes many results of such analysis to be questio nable and inconclusive. It is increasingly recognized that detecting dynami cal nonstationarity is a crucial precursor to data analysis. In this paper, we present a test procedure to detect dynamical nonstationarity by directl y inspecting the dependence of nonlinear statistical distributions on absol ute time along a trajectory in phase space. We test this method using a bro ad range of data, chaotic, stochastic and power-law noise, both computer-ge nerated and observed, and show that it provides a reliable test method in a nalyzing experimental data. (C) 1999 American Institute of Physics. [S1054- 1500(99)00804-6].