Abstract
The study of nonlinear and possibly chaotic time-dependent systems involves long-term data acquisition or high sample rates. The resulting big data is valuable in order to provide useful insights into long-term dynamics. However, efficient and robust algorithms are required that can analyze long time series without decomposing the data into smaller series. Here symbolic-based analysis techniques that regard the dependence of data points are of some special interest. Such techniques are often prone to capacity or, on the contrary, to undersampling problems if the chosen parameters are too large. In this paper we present and apply algorithms of the relatively new ordinal symbolic approach. These algorithms use overlapping information and binary number representation, whilst being fast in the sense of algorithmic complexity, and allow, to the best of our knowledge, larger parameters than comparable methods currently used. We exploit the achieved large parameter range to investigate the limits of entropy measures based on ordinal symbolics. Moreover, we discuss data simulations from this viewpoint.
Highlights
Symbolic-based analysis techniques are efficient and robust research tools in the study of non-linear and possibly chaotic time-dependent systems
An experimental time series x0, x1, . . . , x N with N in the natural numbers N is decoded into a sequence of symbols and, if needed, successive symbols are conflated into symbol words of length m ∈ N. These symbol sequences or symbol word sequences are analyzed mainly by considering symbol distributions or quantifiers based on the distributions, such as entropies
As a result of long-term data acquisition and high sample rates, the study of long-time series is becoming increasingly important in order to provide useful insights into long-term dynamics [1]
Summary
Symbolic-based analysis techniques are efficient and robust research tools in the study of non-linear and possibly chaotic time-dependent systems. The algorithms use overlapping information and binary representations of ordinal patterns and realize an efficient determination of different entropy measures including and generalizing permutation entropies [2]. To the best of our knowledge, our algorithm allows larger parameters N, d and m than methods presently used and compute a whole series of entropies based on ordinal words of different length and pattern order. We discuss limits of estimating the complexity of finite time series and underlying systems on the base of ordinal patterns and words. In this context, aspects of data simulation are touched.
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