Small-shuffle surrogate data: Testing for dynamics in fluctuating data with trends

Abstract

We describe a method for identifying dynamics in irregular time series (short term variability). The method we propose focuses attention on the flow of information in the data. We can apply the method even for irregular fluctuations which exhibit long term trends (periodicities): situations in which previously proposed surrogate methods would give erroneous results. The null hypothesis addressed by our algorithm is that irregular fluctuations are independently distributed random variables (in other words, there is no short term dynamics). The method is demonstrated for numerical data generated by known systems, and applied to several actual time series.