Statistical test of quasiperiodicity in the presence of dynamical noise

Abstract

We propose a statistical method to test whether time series data are quasiperiodic or periodic. A time series is defined to be quasiperiodic if its generating map is topologically conjugate to an irrational rotation. We present an algorithm to estimate the conjugacy map from time series data. We also show that a noisy irrational rotation is equivalent to a random walk model. Since there are general tests for a random walk, we can statistically evaluate quasiperiodicity of a time series by using the estimated conjugacy map. The proposed method is validated by asymmetric chaotic neural networks controlled to be quasiperiodic.