Local Empirical Spectral Measure of Multivariate Processes with Long Range Dependence
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.Download Info
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Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2002-16.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;Other versions of this item:
- 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.
- 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
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-03-28 (All new papers)
- NEP-ECM-2004-03-28 (Econometrics)
- NEP-ETS-2004-03-28 (Econometric Time Series)
- NEP-RMG-2004-03-28 (Risk Management)
References
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- 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.
- 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.
- Siliverstovs, Boriss & Engsted, Tom & Haldrup, Niels, 2002. "Long-Run Forecasting in Multicointegrated Systems," Finance Working Papers 02-14, University of Aarhus, Aarhus School of Business, Department of Business Studies.
- 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.
- Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
- 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.
- 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.
- 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.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Zhongjun Qu, 2010.
"A Test Against Spurious Long Memory,"
Boston University - Department of Economics - Working Papers Series
WP2010-051, Boston University - Department of Economics.
- Qu, Zhongjun, 2011. "A Test Against Spurious Long Memory," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 423-438.
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