Recurrence analysis: Method and applications

Abstract

The awareness that phenomena (social, natural) are for the most part complex and consequently require more realistic models has led to the development of powerful new concepts and tools to detect, analyse, and understand non-stationarity and apparently random behaviour. Almost all existing linear and nonlinear techniques used for the study of time series presume some kind of stationarity, but the application of such tools to non-stationarity and apparently random time series produces misleading results. Recurrence analysis is an advanced technique for nonlinear data analysis used to identify the general structure, non-stationarity, and hidden recurring elements in a time series. Differently from traditional time series techniques that previously assume the nature of the series, the recurrence analysis can be conceived as a diagnostic tool which provides an exploratory analysis identifying the structure of the series. After a general overview of the epistemological and technical underpinnings for the emergent concepts of complexity and nonlinearity, this paper examines the main features of the technique through theoretical examples and a significant review of the main applications.