A new surrogate data method for nonstationary time series

Hypothesis testing based on surrogate data has emerged as a popular way to test the null hypothesis that a signal is a realization of a linear stochastic process. Typically, this is done by generating surrogates which are made to conform to autocorrelation (power spectra) and amplitude distribution of the data (this is not necessary if data are Gaussian). Recently, a new algorithm was proposed, the null hypothesis addressed by this algorithm is that data are a realization of a non stationary linear stochastic process, surrogates generated by this algorithm preserve the autocorrelation and local mean and variance of data. Unfortunately, the assumption of Gaussian amplitude distribution is not always valid. Here we propose a new algorithm; the hypothesis addressed by our algorithm is that data are a realization of a nonlinear static transformation of a non stationary linear stochastic process. Surrogates generated by our algorithm preserve the autocorrelation, amplitude distribution and local mean and variance of data. We present some numerical examples where the previously proposed surrogate data methods fail, but our algorithm is able to discriminate between linear and nonlinear data, whether they are stationary or not. Using our algorithm we also confirm the presence of nonlinearity in the monthly global average temperature and in a small segment of a signal from a Micro Electrode Recording.