HIGHER-ORDER ACCURATE, POSITIVE SEMIDEFINITE ESTIMATION OF LARGE-SAMPLE COVARIANCE AND SPECTRAL DENSITY MATRICES
A new class of large-sample covariance and spectral density matrix estimators is proposed based on the notion of flat-top kernels. The new estimators are shown to be higher-order accurate when higher-order accuracy is possible. A discussion on kernel choice is presented as well as a supporting finite-sample simulation. The problem of spectral estimation under a potential lack of finite fourth moments is also addressed. The higher-order accuracy of flat-top kernel estimators typically comes at the sacrifice of the positive semidefinite property. Nevertheless, we show how a flat-top estimator can be modified to become positive semidefinite (even strictly positive definite) while maintaining its higher-order accuracy. In addition, an easy (and consistent) procedure for optimal bandwidth choice is given; this procedure estimates the optimal bandwidth associated with each individual element of the target matrix, automatically sensing (and adapting to) the underlying correlation structure.
Year of publication: |
2011
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Authors: | Politis, Dimitris N. |
Published in: |
Econometric Theory. - Cambridge University Press. - Vol. 27.2011, 04, p. 703-744
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Publisher: |
Cambridge University Press |
Description of contents: | Abstract [journals.cambridge.org] |
Saved in:
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