Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 15, Iss. 3, July, 2011, pp. 407-418 @2011 Society for Chaos Theory in Psychology & Life Sciences Testing for Nonlinear Dependence in Financial Markets 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 |