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Local empirical spectral measure of multivariate processes with long range dependence

  • Ørregaard Nielsen, Morten

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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  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. 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. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
  5. 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.
  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, 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.
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