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Local Empirical Spectral Measure of Multivariate Processes with Long Range Dependence

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  • Nielsen, Morten Oe.

    ()
    (Department of Economics, University of Aarhus, Denmark)

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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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2002-16.

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Length: 18
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Handle: RePEc:aah:aarhec:2002-16

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Web page: http://www.econ.au.dk/afn/

Related research

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. Boris Siliverstovs & Tom Engsted & Niels Haldrup, . "Long-run forecasting in multicointegrated systems," Economics Working Papers 2002-15, School of Economics and Management, University of Aarhus.
  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. 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.
  4. 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.
  5. Nielsen, Morten Oe., . "Semiparametric Estimation in Time Series Regression with Long Range Dependence," Economics Working Papers 2002-17, School of Economics and Management, University of Aarhus.
  6. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
  7. 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.
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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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