In this paper we use the "Recurrence Quantification Analysis" proposed by Zbilut and Webber [Zbilut, J.P., Webber Jr., C.L., 1992. Embeddings and delays as derived from quantification of recurrence plots. Physics Letters A 171,[199][200][201][202][203] to develop three test procedures that allow us to detect general dependence and, from that, possible deterministic behavior underlying series. Based on the concept of "Percent of Determinism" we obtain three statistics that allow us to test for the null hypothesis of randomness. The results of the application of these procedures to a set of simulated and real series reveal good behavior in a wide variety of situations, including different sample sizes and series affected by noise.
These data provide epidemiological information on chronic wound infections, representing support for diagnosis, treatment and management of this pathology.
In this paper we try to bring forward evidence on the practical application of the Grassberger–Procaccia algorithm, in particular on the determination of the "delay time" parameter. For this purpose, we analyze the results obtained from applying the main methods proposed to calculate this delay time for series simulated from well-known chaotic systems. As the most relevant result we conclude that, in general, all the methods display inadequate behavior, except for that based on the previous filtering of the series according to singular value decomposition. In a second stage we apply the same study to three financial series, with the results appearing to confirm the advantage of this method.
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.
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