Limiting distribution of the least squaresestimates in polynomial regression with longmemory noises
AbstractWe give the limiting distribution of the least squares estimator in the polynomial regression model driven by some long memory processes. We prove that with an appropriate normalization, the estimation error converges, in distribution, to a random vector which components are a mixture of stochastic integrals. These integrals are with respect to a Lebesgue measure, and can be computed recursively where the seed is a random variable which depends on the assumptions made on the noise process. The limiting distribution can be Gaussian or non Gaussian.
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 HAL in its series Working Papers with number halshs-00409571.
Date of creation: 01 Jan 2006
Date of revision:
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00409571/en/
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
Fractional Brownian motion ; Long memory ; Multiple Wiener-Itô integral ; Polynomial regression ; Stochastic integral;
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.:
- Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
- Marmol, Francesc & Velasco, Carlos, 2002. "Trend stationarity versus long-range dependence in time series analysis," Journal of Econometrics, Elsevier, vol. 108(1), pages 25-42, May.
- Davidson, James & de Jong, Robert M., 2000.
"The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii,"
Cambridge University Press, vol. 16(05), pages 643-666, October.
- de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October.
- Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
- Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
- Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 37-45, January.
- Zivot, Eric & Andrews, Donald W K, 1992.
"Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 10(3), pages 251-70, July.
- Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
- Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
- Tom Doan, . "ZIVOT: RATS procedure to perform Zivot-Andrews Unit Root Test," Statistical Software Components RTS00236, Boston College Department of Economics.
- Perron, P, 1988.
"The Great Crash, The Oil Price Shock And The Unit Root Hypothesis,"
338, Princeton, Department of Economics - Econometric Research Program.
- Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If references are entirely missing, you can add them using this form.