Detection of Determinism
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In Chap. 2 we have illustrated the applications of ordinal patterns with four examples. In this chapter we present a further application, this time to the detection of determinism in noisy time series. Following the common usage of the term in applied science, “determinism” is meant here as the opposite to statistical independence, hence it includes colored noise as well. This application hinges on two basic properties of ordinal patterns: existence of forbidden patterns in the orbits of maps (Sects. 1.2, 3.3, and 7.7) and robustness to observational noise (Sects. 3.4.3, and 9.1). We shall actually present two detection methods.
Method I is based on the number of missing ordinal patterns. It proceeds by (i) counting the number of missing ordinal patterns in sliding, overlapping windows of size L along the data sequence, (ii) randomizing the sequence, and (iii) repeating (i) with the randomized sequence. Is the result of step (iii) clearly greater than the result of step (i), so may we conclude that the original noisy sequence has a deterministic component.
KeywordsTime Series Gaussian White Noise Colored Noise Multivariate Time Series Permutation Entropy
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