Subspace Exponent Entropy and Its Application in Nonlinearity Test

Detecting the nonlinearity of the time series is a prerequisite for time series analysis, while the selection of nonlinearity test statistics is crucial for the validity of the test results. We propose a new test statistic for nonlinearity test named subspace exponent entropy. Subspace exponent entropy divides the reconstructed state space of the time series into subspaces, and then measures the complexity of the phase point distribution in the subspaces. The nonlinearity test experiment tests the nonlinearity of five kinds of signals, including AR signal, Henon signal, Lorenz signal, ECG and SCR signal. The length of all the signals is 1000 points. In addition to subspace exponent entropy, we used other four test statistics commonly used in nonlinearity test named time reversibility, higher order autocovariance, nonlinear prediction error and approximate entropy. The experiment results show that the subspace exponent entropy can distinguish the nonlinearity of all signals, and has a high level of anti-noise performance. The subspace exponent entropy is an effective and stable test statistic for the nonlinearity test of short and noisy time series.