Recurrence Plot Representation for Multivariate Time-Series Analysis

Abstract

The analysis of time-series is a productive field, which is applied in different areas such as finance, bio-medicine, neurology, among others. However, one of the main challenges is the identification of non-linear patterns. Thus, the apparent chaotic behavior of a time-series can mean the manifestation of a dynamic system. Often, these phenomena are recurrent, meaning that certain regions of their available state space are frequently visited along of time. For this reason, the use of recurrence plots (RPs) and Recurrent Quantification Analysis (RQA) are used to extract features of time series that allow their better understanding and facilitate prediction tasks (classification, regression and novelty detection). However, to successfully apply this transformation in the aforementioned tasks, it is necessary to obtain the best combination of three parameters: time lag ($\tau$), embedding dimension (m) and recurrence rate (RR). In other studies to find these parameters it is necessary to apply the prediction process for each possible combination, which represents a high computational cost. We propose to use a measure that seeks to maximize the entropy with the lowest possible randomness to calculate $RP_{[\tau ,m,RR]}$ before the application of the prediction. In this way, reduce the computational complexity, where we initially validate these claims using Bitcoin’s multidimensional time-series, with results that surpass the accuracy of previous studies.

This work has been supported/funded by KPiQa and Xertica companies.