Asymptotics for Duration-Driven Long Range Dependent Processes
AbstractWe consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration- driven long range dependence (DDLRD), as opposed to the more widely studied linear long range dependence based on fractional differencing of an $iid$ process. We consider in detail two specific processes having DDLRD, originally presented in Taqqu and Levy (1986), and Parke (1999). For these processes, we obtain the limiting distribution of suitably standardized discrete Fourier transforms (DFTs) and sample autocovariances. At low frequencies, the standardized DFTs converge to a stable law, as do the standardized autocovariances at fixed lags. Finite collections of standardized autocovariances at a fixed set of lags converge to a degenerate distribution. The standardized DFTs at high frequencies converge to a Gaussian law. Our asymptotic results are strikingly similar for the two DDLRD processes studied. We calibrate our asymptotic results with a simulation study which also investigates the properties of the semiparametric log periodogram regression estimator of the memory parameter.
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 EconWPA in its series Econometrics with number 0412009.
Length: 40 pages
Date of creation: 15 Dec 2004
Date of revision:
Note: Type of Document - pdf; pages: 40
Contact details of provider:
Web page: http://126.96.36.199
Long Memory; Structural Change;
Other versions of this item:
- Hsieh, Meng-Chen & Hurvich, Clifford M. & Soulier, Philippe, 2007. "Asymptotics for duration-driven long range dependent processes," Journal of Econometrics, Elsevier, vol. 141(2), pages 913-949, December.
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
- C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
- C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
- C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
- C5 - Mathematical and Quantitative Methods - - Econometric Modeling
- C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-12-20 (All new papers)
- NEP-ECM-2004-12-20 (Econometrics)
- NEP-ETS-2004-12-20 (Econometric Time Series)
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.:
- Rohit Deo & Meng-Chen Hsieh & Clifford M. Hurvich & Philippe Soulier, 2007. "Long Memory in Nonlinear Processes," Papers 0706.1836, arXiv.org.
- GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995.
CORE Discussion Papers
1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
- Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Tieslau, Margie A. & Schmidt, Peter & Baillie, Richard T., 1996. "A minimum distance estimator for long-memory processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 249-264.
- Chen, Willa W. & Hurvich, Clifford M., 2003. "Estimating fractional cointegration in the presence of polynomial trends," Journal of Econometrics, Elsevier, vol. 117(1), pages 95-121, November.
- Hurvich, Clifford M. & Soulier, Philippe, 2002. "Testing For Long Memory In Volatility," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1291-1308, December.
- William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
- Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February.
- Liu, Ming, 2000. "Modeling long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 99(1), pages 139-171, November.
- Terrin, Norma & Hurvich, Clifford M., 1994. "An asymptotic Wiener-Itô representation for the low frequency ordinates of the periodogram of a long memory time series," Stochastic Processes and their Applications, Elsevier, vol. 54(2), pages 297-307, December.
- Chung, Ching-Fan, 2002. "Sample Means, Sample Autocovariances, And Linear Regression Of Stationary Multivariate Long Memory Processes," Econometric Theory, Cambridge University Press, vol. 18(01), pages 51-78, February.
- Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
- Chen, Willa W. & Hurvich, Clifford M., 2003. "Semiparametric Estimation of Multivariate Fractional Cointegration," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 629-642, January.
- Hurvich, Clifford M. & Moulines, Eric & Soulier, Philippe, 2002. "The FEXP estimator for potentially non-stationary linear time series," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 307-340, February.
- Davidson, James & Sibbertsen, Philipp, 2009.
"Tests of bias in log-periodogram regression,"
Elsevier, vol. 102(2), pages 83-86, February.
- James Davidson & Philipp Sibbertsen, 2008. "Tests of Bias in Log-Periodogram Regression," Discussion Papers 0805, Exeter University, Department of Economics.
- Davidson, James & Sibbertsen, Philipp, 2005. "Tests of Bias in Log-Periodogram Regression," Hannover Economic Papers (HEP) dp-317, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
- Leipus, Remigijus & Paulauskas, Vygantas & Surgailis, Donatas, 2005. "Renewal regime switching and stable limit laws," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 299-327.
- Wen Cao & Clifford Hurvich & Philippe Soulier, 2012. "Drift in transcation-level asset price models," Working Papers hal-00756372, HAL.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).
If references are entirely missing, you can add them using this form.