COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1652R Nonlinearity and Temporal Dependence Xiaohong Chen, Lars P. Hansen and Marine Carrasco May 2008 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. |
