Determining delay times for phase space reconstruction with application to the FF/DM exchange rate

Economists have widely applied the correlation integral of Grassberger and Procaccia (1983) to determine the dimension of a nonlinear dynamical system. A key judgmental input into this procedure is the choice of delay time for reconstructing a possible attractor. The literature, however, lacks a rigorous procedure for choosing the delay time. In this paper, I apply a simple nonparametric test for independence developed in Mizrach (1995a) to determine the appropriate lag for reconstruction and dimension estimation. In an application to the Lorenz equations, I obtain the best estimates of the correlation dimension at the lag chosen by the test. I then use the method to uncover nonlinear structure in the FF/DM exchange rate.