A New Test for Chaos and Determinism based on Symbolic Dynamics

Mariano Matilla-García (1) , Manuel Ruiz Marín (1)

1 UPCT - Universidad Politécnica de Cartagena / Technical University of Cartagena

We propose a novel test to determine, given a time series, if the dynamics are generated by a deterministic (including low dimensional chaos), rather than a stochastic, process. In addition, we introduce a new nonparametric bootstrap test for independence which is consistent against a broad class of alternatives. The conditions under which the tests can be applied are very weak. The advantages of the presented methods are simplicity, invariance with respect to monotonic transformations and the applicability of the tests regardless of the discrete or continuous nature of the data generating process. We conduct several simulation studies to evaluate the performance of our tests on well-known dynamic processes. Finally, our tests are applied to several sets of financial returns that have been recently studied.

Mots clés: Social Sciences & Humanities

Domaines: Économie et finance quantitative [q-fin]

Mariano Matilla-García, Manuel Ruiz Marín. A New Test for Chaos and Determinism based on Symbolic Dynamics. Journal of Economic Behavior and Organization, 2010, 76 (3), pp.600. ⟨10.1016/j.jebo.2010.09.017⟩. ⟨hal-00911819⟩