Local Empirical Spectral Measure of Multivariate Processes with Long Range Dependence
AbstractWe 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 InfoPaper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2002-16.
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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)
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