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Local empirical spectral measure of multivariate processes with long range dependence

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  • Ørregaard Nielsen, Morten

Abstract

We derive a functional central limit theorem for the empirical spectral measure or discretely averaged (integrated) periodogram of a multivariate long range dependent stochastic process in a degenerating neighborhood of the origin. We show that, under certain restrictions on the memory parameters, this local empirical spectral measure converges weakly to a Gaussian process with independent increments. Applications to narrow-band frequency domain estimation in time series regression with long range dependence, and to local (to the origin) goodness-of-fit testing are offered.

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Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 109 (2004)
Issue (Month): 1 (January)
Pages: 145-166

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Handle: RePEc:eee:spapps:v:109:y:2004:i:1:p:145-166

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Keywords: Brownian motion Fractional ARIMA Functional central limit theorem Goodness-of-fit test Integrated periodogram Long memory Narrow-band frequency domain least squares;

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  1. D Marinucci & Peter M. Robinson, 1998. "Semiparametric frequency domain analysis of fractional cointegration," LSE Research Online Documents on Economics 2258, London School of Economics and Political Science, LSE Library.
  2. Anna Christina D'Addio & Michael Rosholm, . "Labour Market Transitions of French Youth," Economics Working Papers 2002-14, School of Economics and Management, University of Aarhus.
  3. Morten Orregaard Nielsen, 2005. "Semiparametric Estimation in Time-Series Regression with Long-Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 279-304, 03.
  4. Boriss Siliverstovs & Tom Engsted & Niels Haldrup, 2003. "Long-Run Forecasting in Multicointegrated Systems," Discussion Papers of DIW Berlin 381, DIW Berlin, German Institute for Economic Research.
  5. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May.
  6. Kokoszka, P. & Mikosch, T., 1997. "The integrated periodogram for long-memory processes with finite or infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 55-78, February.
  7. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
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Cited by:
  1. Zhongjun Qu, 2010. "A Test Against Spurious Long Memory," Boston University - Department of Economics - Working Papers Series WP2010-051, Boston University - Department of Economics.

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