Nonlinearity and Temporal Dependence

32 Pages Posted: 21 May 2008

See all articles by Xiaohong Chen

Xiaohong Chen

Yale University - Cowles Foundation

Lars Peter Hansen

University of Chicago - Department of Economics; National Bureau of Economic Research (NBER)

Marine Carrasco

University of Montreal - Departement de Ciences Economiques

Date Written: 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.

Keywords: Mixing, Diffusion, Strong dependence, Long memory, Poisson sampling

JEL Classification: C12, C13, C22, C50

Suggested Citation

Chen, Xiaohong and Hansen, Lars Peter and Carrasco, Marine, Nonlinearity and Temporal Dependence (May 2008). Cowles Foundation Discussion Paper No. 1652, Yale Economics Department Working Paper No. 48, Available at SSRN:

Xiaohong Chen (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Lars Peter Hansen

University of Chicago - Department of Economics ( email )

1101 E 58th ST
Chicago, IL 60637
United States
773-702-8170 (Phone)
773-702-8490 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Marine Carrasco

University of Montreal - Departement de Ciences Economiques ( email )

C.P. 6128, succursale Centre-Ville
Montreal, Quebec H3C 3J7
(514) 343-2394 (Phone)


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