COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1652 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
scalar diffusion models. We study this link using two notions of temporal dependence: beta-mixing
and rho-mixing. We show that beta-mixing and rho-mixing with
exponential decay are essentially equivalent concepts for scalar diffusions. For
stationary diffusions that fail to be rho-mixing, we show that they are still beta-mixing
except that the decay rates are slower than exponential. For such processes we find
transformations of the Markov states that have finite variances but infinite spectral
densities at frequency zero. Some have spectral densities that diverge at frequency zero
in a manner similar to that of stochastic processes with long memory. Finally we show how
nonlinear, state-dependent, Poisson sampling alters the unconditional distribution as well
as the temporal dependence. |
