An Independence Test Based on Joint Recurrences

Abstract

We propose in this paper a test procedure to determine whether two series proceed from independent systems or not. Our starting point is a multivariate extension of the methodology called Recurrence Quantification Analysis (RQA). We derive the test procedure from the probability distribution of the number of joint recurrences of both series under the null hypothesis of independence. The behavior of the test is evaluated by means of a large set of simulations, carried out with different types of dynamical systems: random, deterministic chaotic, deterministic non-chaotic, systems affected by noise and coupled systems. We obtain satisfactory results in all cases. Finally, the methodology is used to study two questions, on which the bulk of the existing economic literature agrees: 1) the relationship between the nominal interest rate and the inflation rate; and 2) the relationship between the gross domestic product and the employment. The results suggest that our test can be a suitable tool for detecting linear and nonlinear dependence between real series.

A combinatorial multiverse of time-loops: Probabilistic inference on time-series based on recurrence analysis with symbolic methods

“…These analyze the overall proportion of recurring states, but cannot account for their internal structure. For instance, under 9,10 procedures, two trajectories bearing a similar proportion of recurring states in their diagonals will yield indistinguishable metrics. Even if it is the case that one these trajectories present such recurrences in noticeably regular patterns.…”

“…Several approaches have been proposed to perform statistical inference on recurrence patterns. Solutions generally consider the assumption of a binomial distribution for frequencies of recurrences and non-recurrences 9,10 . These strategies analyze the overall proportion of recurring states, but cannot account for their internal structure.…”

Detecting Associations Based on the Multi-Variable Maximum Information Coefficient

“…The improved algorithm for approximation of MIC (IAMIC) [11], [12] improves the accuracy of MIC by searching more optimal partitions on the yaxis than equipartition. The most commonly used toolkit for MIC is the Maximal Information-based Nonparametric Exploration (MINE) [2] which is compatible with C++, Python, and R. There are also many data independence testing tools based on MIC, including testforDEP [13] for R, MICtools [14] for Python. RapidMic [15] is a cross-platform tool for the rapid calculation of MIC based on parallel technology.…”