CFDP 1652R

Nonlinearity and Temporal Dependence


Publication Date: May 2008

Revision Date: October 2009

Pages: 40


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.


Diffusion, Strong dependence, Long memory, Poisson sampling, Quadratic forms

JEL Classification Codes:  C12, C13, C22, C50

See CFP: 1298