Statistical Analysis for Long Term Correlations in the Stress Time Series of Jerky Flow

Abstract

Stress time series from the PLC effect typically exhibit stick-slips of upload and download type. These data contain strong short-term correlations of a nonlinear type. We investigate whether there are also long term correlations, i.e. the successive up-down patterns are generated by a deterministic mechanism. A statistical test is conducted for the null hypothesis that the sequence of the up-down patterns is totally random. The test is constructed by means of surrogate data, suitably generated to represent the null hypothesis. Linear and nonlinear estimates are used as test statistics, namely autocorrelation, mutual information and Lyapunov exponents, which are found to have proper performance for the test. The test is then applied to three stress time series under different experimental conditions. Rejections are obtained for one of them and not with all statistics. From the overall results we cannot conclude that the underlying mechanism to the PLC effect has long memory.