Semiparametric Estimation for Stationary Processes whose Spectra have an Unknown Pole
AbstractWe consider the estimation of the location of the pole and memory parameter, ?0 and a respectively, of covariance stationary linear processes whose spectral density function f(?) satisfies f(?) ~ C|? - ?0|-a in a neighbourhood of ?0. We define a consistent estimator of ?0 and derive its limit distribution Z?0 . As in related optimization problems, when the true parameter value can lie on the boundary of the parameter space, we show that Z?0 is distributed as a normal random variable when ?0 ? (0, p), whereas for ?0 = 0 or p, Z?0 is a mixture of discrete and continuous random variables with weights equal to 1/2. More specifically, when ?0 = 0, Z?0 is distributed as a normal random variable truncated at zero. Moreover, we describe and examine a two-step estimator of the memory parameter a, showing that neither its limit distribution nor its rate of convergence is affected by the estimation of ?0. Thus, we reinforce and extend previous results with respect to the estimation of a when ?0 is assumed to be known a priori. A small Monte Carlo study is included to illustrate the finite sample performance of our estimators.
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 Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2005/481.
Date of creation: Jan 2005
Date of revision:
Contact details of provider:
Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp
spectral density estimation; long memory processes; Gaussian processes;
Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-02-26 (All new papers)
- NEP-ECM-2006-02-26 (Econometrics)
- NEP-ETS-2006-02-26 (Econometric Time Series)
- NEP-FIN-2006-02-26 (Finance)
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.:
- Josu Artech & Peter M Robinson, 1998. "Semiparametric Inference in Seasonal and Cyclical Long Memory Processes - (Now published in Journal of Time Series Analysis, 21 (2000), pp.1-25.)," STICERD - Econometrics Paper Series /1998/359, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Liudas Giraitis & Javier Hidalgo & Peter M Robinson, 2001. "Gaussian Estimation of Parametric Spectral Density with Unknown Pole," STICERD - Econometrics Paper Series /2001/424, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution Free Goodness-of-Fit Tests for Linear Processes," STICERD - Econometrics Paper Series /2005/482, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Liudas Giraitis & Peter M Robinson & Alexander Samarov, 1997. "Rate Optimal Semiparametric Estimation of the Memory Parameter of the Gaussian Time Serieswith Long-Range Dependence - (Now published in 'Journal of Time Series Analysis', 18 (1997), pp.49-60.)," STICERD - Econometrics Paper Series /1997/323, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Luis A. Gil-Alana & Juncal Cuñado & Guglielmo Maria Caporale, 2012.
"Modelling Long Run Trends and Cycles in Financial Time Series Data,"
Faculty Working Papers
13/12, School of Economics and Business Administration, University of Navarra.
- Guglielmo Maria Caporale & Juncal Cuñado & Luis A. Gil-Alana, 2013. "Modelling long-run trends and cycles in financial time series data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 405-421, 05.
- Guglielmo Maria Caporale & Juncal Cunado & Luis A. Gil-Alana, 2008. "Modelling Long-Run Trends and Cycles in Financial Time Series Data," CESifo Working Paper Series 2330, CESifo Group Munich.
- Buchmann, Boris & Chan, Ngai Hang, 2013. "Unified asymptotic theory for nearly unstable AR(p) processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 952-985.
- Abadir, Karim M. & Caggiano, Giovanni & Talmain, Gabriel, 2013.
"Nelson–Plosser revisited: The ACF approach,"
Journal of Econometrics,
Elsevier, vol. 175(1), pages 22-34.
- Karim M. Abadir & Gabriel Talmain & Giovanni Caggiano, 2008. "Nelson-Plosser revisited: the ACF approach," Working Paper Series 18-08, The Rimini Centre for Economic Analysis, revised Jan 2008.
- Karim Abadir & Giovanni Caggiano & Gabriel Talmain, 2005. "Nelson-Plosser Revisited: the ACF Approach," Working Papers 2005_7, Business School - Economics, University of Glasgow.
- Hassler, Uwe, 2011.
"Estimation of fractional integration under temporal aggregation,"
Journal of Econometrics,
Elsevier, vol. 162(2), pages 240-247, June.
- Uwe Hassler, 2011. "Estimation of fractional integration under temporal aggregation," Post-Print peer-00815563, HAL.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().
If references are entirely missing, you can add them using this form.