TITLE:
An Independence Test Based on Joint Recurrences
AUTHORS:
Teresa Aparicio, Eduardo F. Pozo, Dulce Saura
KEYWORDS:
Independence Test, Joint Recurrence Plot, Recurrence Quantification Analysis, Dynamical Systems
JOURNAL NAME:
Modern Economy,
Vol.6 No.8,
August
19,
2015
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.