Detecting dynamical nonstationarity in time series data

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Abstract
Nonlinear time series analysis is becoming an ever more powerful tool to explore complex phenomena and uncover underlying patterns from irregular data recorded from experiments. However, the existence of dynamical nonstationarity in time series data causes many results of such analysis to be questionable and inconclusive. It is increasingly recognized that detecting dynamical nonstationarity is a crucial precursor to data analysis. In this paper, we present a test procedure to detect dynamical nonstationarity by directly inspecting the dependence of nonlinear statistical distributions on absolute time along a trajectory in phase space. We test this method using a broad range of data, chaotic, stochastic and power-law noise, both computer-generated and observed, and show that it provides a reliable test method in analyzing experimental data.