Assessing serial dependence in ordinal patterns processes using chi-squared tests with application to EEG data analysis

We extend Elsinger's work on chi-squared tests for independence using ordinal patterns and investigate the general class of m-dependent ordinal patterns processes, to which belong ordinal patterns processes derived from random walk, white noise, and moving average processes. We describe chi-squared asymptotically distributed statistics for such processes that take into account necessary constraints on ordinal patterns probabilities and propose a test for m-dependence, with which we are able to quantify the range of serial dependence in a process. We apply the test to epilepsy electroencephalography time series data and observe shorter m-dependence associated with seizures, suggesting that the range of serial dependence decreases during those events. Published under an exclusive license by AIP Publishing.

Automated summary

We extended Elsinger's work on chi-squared tests for independence using ordinal patterns and investigated a general class of m-dependent ordinal patterns processes. We proposed a test method to quantify the range of serial dependence in a process, and applied it to epilepsy electroencephalography time series data.