Document Type
Discussion Paper
Publication Date
5-1-2008
CFDP Number
1652R
CFDP Revision Date
2009-10-01
CFDP Pages
40
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.
Recommended Citation
Chen, Xiaohong; Hansen, Lars P.; and Carrasco, Marine, "Nonlinearity and Temporal Dependence" (2008). Cowles Foundation Discussion Papers. 1956.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/1956