Nonlinearity and Temporal Dependence
AbstractNonlinearities 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.
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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1652R.
Length: 40 pages
Date of creation: Oct 2009
Date of revision:
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
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.
- Chen, Xiaohong & Hansen, Lars Peter & Carrasco, Marine, 2008. "Nonlinearity and Temporal Dependence," Working Papers 48, Yale University, Department of Economics.
- Xiaohong Chen & Lars P. Hansen & Marine Carrasco, 2009. "Nonlinearity and Temporal Dependence," CIRANO Working Papers 2009s-17, CIRANO.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-07-24 (All new papers)
- NEP-ECM-2010-07-24 (Econometrics)
- NEP-ETS-2010-07-24 (Econometric Time Series)
- NEP-ORE-2010-07-24 (Operations Research)
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