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Semiparametric Estimation for Stationary Processes whose Spectra have an Unknown Pole

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  • Javier Hidalgo
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    Abstract

    We 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.

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    Bibliographic Info

    Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2005/481.

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    Date of creation: Jan 2005
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    Handle: RePEc:cep:stiecm:/2005/481

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    Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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    Keywords: spectral density estimation; long memory processes; Gaussian processes;

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    1. Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution Free Goodness-of-Fit Tests for Linear Processes," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2005/482, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. 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, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /1998/359, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. 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, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /1997/323, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Liudas Giraitis & Javier Hidalgo & Peter M Robinson, 2001. "Gaussian Estimation of Parametric Spectral Density with Unknown Pole," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2001/424, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. L Giraitis & J Hidalgo & Peter M. Robinson, 2001. "Gaussian estimation of parametric spectral density with unknown pole," LSE Research Online Documents on Economics 297, London School of Economics and Political Science, LSE Library.
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    Cited by:
    1. Karim Abadir & Giovanni Caggiano & Gabriel Talmain, 2005. "Nelson-Plosser Revisited: the ACF Approach," Working Papers, Business School - Economics, University of Glasgow 2005_7, Business School - Economics, University of Glasgow.
    2. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, Elsevier, vol. 162(2), pages 240-247, June.
    3. Buchmann, Boris & Chan, Ngai Hang, 2013. "Unified asymptotic theory for nearly unstable AR(p) processes," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 123(3), pages 952-985.
    4. 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.

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