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Activity Number:
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88
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Type:
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Contributed
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Date/Time:
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Monday, August 4, 2003 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #302024 |
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Title:
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Multivariate Time-Dependent Spectral Analysis Using Cholesky Decomposition
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Author(s):
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Wensheng Guo*+ and Ming Dai
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Companies:
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University of Pennsylvania and University of Pennsylvania
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Address:
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CCEB Division of Biostatics, Philadelphia, PA, 19104,
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Keywords:
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bootstrap ; Cholesky decomposition ; locally stationary time series ; smoothing spline ; spectral analysis
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Abstract:
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We propose a nonparametric method to estimate the spectrum of a multivariate locally stationary process, which is assumed to be smooth in both time and frequency. In order to ensure that the final estimate of the multivariate spectrum is positive definite while allowing enough flexibility in estimating each of its elements, we propose to smooth the Cholesky decomposition of an initial spectral estimate and the final spectral estimate is reconstructed from the smoothed Cholesky elements. We propose a two-stage estimation procedure. The final estimate is a smooth function in time and frequency, has a global interpretation, and is consistent and positive definite. We show that the Cholesky decomposition of a time-varying spectrum can be used as a transfer function to generate a locally stationary time series with the designed spectrum. This not only provides us much flexibility in simulations, but also allows us to construct bootstrap confidence intervals on the time varying multivariate spectrum. A numerical example and an application to an EEG data set recorded during an epileptic seizure are used as illustrations.
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