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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
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:
Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
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, 2009. "Nonlinearity and Temporal Dependence," CIRANO Working Papers 2009s-17, CIRANO.
- 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.
- 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
- 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)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Xiaohong Chen & Lars Peter Hansen & Jose Scheinkman, 2009. "Principal Components and Long Run Implications of Multivariate Diffusions," Cowles Foundation Discussion Papers 1694, Cowles Foundation for Research in Economics, Yale University.
- Xiaohong Chen & Lars Peter Hansen & Jose A. Scheinkman, 2009.
"Principal components and the long run,"
CeMMAP working papers
CWP07/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
- Bollerslev, Tim & Ole Mikkelsen, Hans, 1996.
"Modeling and pricing long memory in stock market volatility,"
Journal of Econometrics,
Elsevier, vol. 73(1), pages 151-184, July.
- Tom Doan, . "RATS program to replicate Bollerslev-Mikkelson(1996) FIEGARCH models," Statistical Software Components RTZ00173, Boston College Department of Economics.
- Granger, Clive W. J. & Terasvirta, Timo, 1999.
"A simple nonlinear time series model with misleading linear properties,"
Elsevier, vol. 62(2), pages 161-165, February.
- Granger, Clive W.J. & Teräsvirta, Timo, 1998. "A simple nonlinear time series model with misleading linear properties," Working Paper Series in Economics and Finance 237, Stockholm School of Economics.
- Lars Peter Hansen & Jose Alexandre Scheinkman, 1993.
"Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes,"
NBER Technical Working Papers
0141, National Bureau of Economic Research, Inc.
- Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
- Fabienne Comte & Eric Renault, 1998.
"Long memory in continuous-time stochastic volatility models,"
Wiley Blackwell, vol. 8(4), pages 291-323.
- Comte, F. & Renault, E., 1996. "Long Memory in Continuous Time Stochastic Volatility Models," Papers 96.406, Toulouse - GREMAQ.
- Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-77.
- Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- Hidalgo, Javier & Robinson, Peter M., 1996. "Testing for structural change in a long-memory environment," Journal of Econometrics, Elsevier, vol. 70(1), pages 159-174, January.
- Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
- Harrison, J Michael & Pitbladdo, Richard & Schaefer, Stephen M, 1984. "Continuous Price Processes in Frictionless Markets Have Infinite Variation," The Journal of Business, University of Chicago Press, vol. 57(3), pages 353-65, July.
- Darrell Duffie & Peter Glynn, 2004. "Estimation of Continuous-Time Markov Processes Sampled at Random Time Intervals," Econometrica, Econometric Society, vol. 72(6), pages 1773-1808, November.
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
- Diebold, Francis X. & Inoue, Atsushi, 2001.
"Long memory and regime switching,"
Journal of Econometrics,
Elsevier, vol. 105(1), pages 131-159, November.
- Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames).
If references are entirely missing, you can add them using this form.