Phase Randomisation: Numerical Study of Higher Cumulants Behaviour

For the purpose of testing for stationarity in a time series, a phase randomisation procedure is reviewed and modified, and applied to a wide range of time-series models. These include linear stationary, linear non-stationary, non-linear stationary and non-linear non-stationary processes. Surrogate series are simulated using Standard and Rescaling methods. For all processes, the higher-order central moments of the original series are preserved in the surrogate series using the Rescaling method whereas under the Standard approach only the even central moments are preserved. The density of higher order cumulant estimates obtained under the Rescaling method exhibits unimodality when the process is stationary and multimodality otherwise. The primary aim is to develop a suite of diagnostic tests in order to assess the convergence of Markov Chain Monte Carlo algorithms. Applications of the method as a convergence diagnostic test of Markov Chain Monte Carlo are also discussed.