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Nonlinearity and Temporal Dependence

Xiaohong Chen (), Lars Hansen and Marine Carrasco ()

No 1652, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 C50 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
Date: 2008-05
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Related works:
Journal Article: Nonlinearity and temporal dependence (2010) Downloads
Working Paper: Nonlinearity and Temporal Dependence (2009) Downloads
Working Paper: Nonlinearity and Temporal Dependence (2009) Downloads
Working Paper: Nonlinearity and Temporal Dependence (2008) Downloads
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