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.