Ordinal Patterns-based Time Series Analysis

Abstract

Most real-world phenomena exhibit non-stationary behavior, where the statistical properties of the underlying process change over time. Most pre-existing techniques perform very well for time series realized from stationary processes, but fail for non-stationary processes. Traditional stationary techniques may not adequately capture the dynamics of the data; neglecting non-stationarity can lead to erroneous conclusions and flawed models. In this dissertation, we introduce a novel technique to generate surrogate data for time series measured from non-stationary systems. The surrogates generated are called Order Preserving surrogates and are defined in a way that preserves the ordinal patterns of the original signal up to a predefined length. Recently, there has been growing interest in studying non-stationarty time series using ordinal partition transition networks (OPTN) generated from them. Our surrogate method preserves the OPTN generated from the original signal, such that the OPTN will be the same for all the surrogates of the same signal. We have applied our novel approach for generating surrogates to two separate projects. Our first project focuses on detecting nonlinearity in possibly non-stationary signals using numerous discriminating statistics. Our second project uses the Order Preserving surrogates to detect spatial patterns between two signals evolving over time. We use the Order Preserving surrogates in combination with wavelet coherence to detect statistically significant correlation between signals