Alvaro Diaz-Ruelas

Chaos 32, 123136 (2022)

The incorporation of stochastic ingredients in models describing phenomena in all disciplines is now a standard in scientific practice. White noise is one of the most important of such stochastic ingredients. Although tools for identifying white and other types of noise exist,1,2 there is a permanent demand for reliable and robust statistical methods for analyzing data in order to distinguish noise and filter it from signals in experiments. Or in hypothesis tests, for assessing the plausibility of the outcome of an experiment being the result of randomness and not a significant, controllable effect. Due to its ubiquity in experiments and its mathematical simplicity, white noise is very often the most convenient stochastic component that adds realism to a dynamic model, commonly regarded as the noise polluting observations. It can be continuous or discrete both in time and in distribution, so it can be applied to many scenarios. It is a stationary and independent and identically distributed process, all relatively simple properties for a stochastic process. Here, we present a combinatorial perspective to study white noise inspired in the concept of ordinal patterns.

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