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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 155 (2010)
Issue (Month): 2 (April)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jeconom
Diffusion Strong dependence Long memory Poisson sampling Quadratic forms;
Other versions of this item:
- 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.
- 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.
- 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.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
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.:
- 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.
- 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.
- 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.
- Granger, Clive W. J. & Terasvirta, Timo, 1999. "A simple nonlinear time series model with misleading linear properties," Economics Letters, Elsevier, vol. 62(2), pages 161-165, February.
- 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.
- Diebold, Francis X. & Inoue, Atsushi, 2001.
"Long memory and regime switching,"
Journal of Econometrics,
Elsevier, vol. 105(1), pages 131-159, November.
- 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.
- 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.
- 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.
- Comte, F. & Renault, E., 1996.
"Long Memory in Continuous Time Stochastic Volatility Models,"
96.406, Toulouse - GREMAQ.
- Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323.
- 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.
- 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.
- 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.
- 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.
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
- 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.
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: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.