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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.

Suggested Citation

  • Ørregaard Nielsen, Morten, 2004. "Local empirical spectral measure of multivariate processes with long range dependence," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 145-166, January.
  • Handle: RePEc:eee:spapps:v:109:y:2004:i:1:p:145-166
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    References listed on IDEAS

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    1. 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, March.
    2. Anna Christina D'Addio & Michael Rosholm, "undated". "Labour Market Transitions of French Youth," Economics Working Papers 2002-14, Department of Economics and Business Economics, Aarhus University.
    3. Marinucci, D & Robinson, Peter M., 1998. "Semiparametric frequency domain analysis of fractional cointegration," LSE Research Online Documents on Economics 2258, London School of Economics and Political Science, LSE Library.
    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. 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. Tom Engsted & Niels Haldrup & Boriss Siliverstovs, 2004. "Long-run forecasting in multicointegrated systems," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(5), pages 315-335.
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    Cited by:

    1. Zhongjun Qu, 2011. "A Test Against Spurious Long Memory," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 423-438, July.

    More about this item

    Keywords

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

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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