Testing for Nonlinear Dependence in Financial Markets

Mohammed Dore, Brock University, Canada
Mariano Matilla-Garcia, Universidad Nacional de Educacion a Distancia, Spain
Manuel Ruiz Marin, Universidad Politecnica de Cartagena, Spain

Abstract: This article addresses the question of improving the detection of nonlinear dependence by means of recently developed nonparametric tests. To this end a generalized version of BDS test and a new test based on symbolic dynamics are used on realizations from a well-known artificial market for which the dynamic equation governing the market is known. Comparisons with other tests for detecting nonlinearity are also provided. We show that the test based on symbolic dynamics outperforms other tests with the advantage that it depends only on one free parameter, namely the embedding dimension. This does not hold for other tests for nonlinearity.

Keywords: nonlinear dynamics, artificial financial market, DJIA, symbolic dynamics, BDS test, delay coordinates method, correlation integral, hypothesis testing, semiparametric and nonparametric methods, expectations, speculations