Ordinal patterns-based methodologies for distinguishing chaos from noise in discrete time series

Abstract One of the most important aspects time series is their degree stochasticity vs. chaoticity. Since discovery chaotic maps, many algorithms have been proposed to discriminate between these two alternatives and assess prevalence in real-world series. Approaches based on combination “permutation patterns” with different metrics provide a more complete picture series’ nature, are especially useful tackle pathological maps. Here, we review such approaches, theoretical foundations, application discrete problems. We compare performance using set representative noisy evaluate applicability through respective computational cost, discuss limitations.