Nonlinearity and Temporal Dependence
AbstractNonlinearities 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.
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Bibliographic InfoPaper provided by Yale University, Department of Economics in its series Working Papers with number 48.
Date of creation: May 2008
Date of revision:
Other versions of this item:
- Xiaohong Chen & Lars P. Hansen & Marine Carrasco, 2008. "Nonlinearity and Temporal Dependence," Cowles Foundation Discussion Papers 1652, Cowles Foundation for Research in Economics, Yale University.
- Xiaohong Chen & Lars P. Hansen & Marine Carrasco, 2009. "Nonlinearity and Temporal Dependence," CIRANO Working Papers 2009s-17, CIRANO.
- Xiaohong Chen & Lars P. Hansen & Marine Carrasco, 2009. "Nonlinearity and Temporal Dependence," Cowles Foundation Discussion Papers 1652R, Cowles Foundation for Research in Economics, Yale University.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-02-07 (All new papers)
- NEP-ECM-2009-02-07 (Econometrics)
- NEP-ORE-2009-02-07 (Operations Research)
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