Weak Convergence of Sample Covariance Matrices to Stochastic Integrals Via Martingale Approximations
Under general conditions the sample covariance matrix of a vector martingale and its differences converges weakly to the matrix stochastic integral ∫<sub>0</sub><sup>1</sup> <italic>BdB′</italic>, where <italic>B</italic> is vector Brownian motion. For strictly stationary and ergodic sequences, rather than martingale differences, a similar result obtains. In this case, the limit is ∫<sub>0</sub><sup>1</sup> <italic>BdB′</italic> + Λ and involves a constant matrix Λ of bias terms whose magnitude depends on the serial correlation properties of the sequence. This note gives a simple proof of the result using martingale approximations.
Year of publication: |
1988
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Authors: | Phillips, P.C.B. |
Published in: |
Econometric Theory. - Cambridge University Press. - Vol. 4.1988, 03, p. 528-533
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Publisher: |
Cambridge University Press |
Description of contents: | Abstract [journals.cambridge.org] |
Saved in:
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