Determining delay times for phase space reconstruction with application to the FFDM exchange rate

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Abstract

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 FFDM exchange rate.

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  • Cited by (0)

    1

    Preliminary versions of this work were presented at the Bureau of Labor Statistics and the 1994 Society for Nonlinear Dynamics and Econometrics Meetings in Boston, MA. I would like to thank Dominique Guillaume, Ted Jaditz, two anonymous referees, and the editor, Richard Day, for helpful comments. Craig Hiemstra generously provided the code for the dimension estimates.

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