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Nonlinearity and Temporal Dependence

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Abstract

Nonlinearities in the drift and diffusion coefficients influence temporal dependence in diffusion models. We study this link using three measures of temporal dependence: rho-mixing, beta-mixing and alpha-mixing. Stationary diffusions that are rho-mixing have mixing coefficients that decay exponentially to zero. When they fail to be rho-mixing, they are still beta-mixing and alpha-mixing; but coefficient decay is slower than exponential. For such processes we find transformations of the Markov states that have finite variances but infinite spectral densities at frequency zero. The resulting spectral densities behave like those of stochastic processes with long memory. Finally we show how state-dependent, Poisson sampling alters the temporal dependence.

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File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1652-r.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1652R.

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Length: 40 pages
Date of creation: Oct 2009
Date of revision:
Handle: RePEc:cwl:cwldpp:1652r

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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Diffusion; Strong dependence; Long memory; Poisson sampling; Quadratic forms;

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