Weak Convergence of Sample Covariance Matrices to Stochastic Integrals via Martingale Approximations

Peter Phillips

No 846, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: Under general conditions the sample covariance matrix of a vector martingale and its differences converges weakly to the matrix stochastic integral from zero to one of BdB; where B is vector Brownian motion. For strictly stationary and ergodic sequences, rather than martingale differences, a similar result obtains. In this case, the limit is the same with a constant matrix, 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.

Keywords: Martingale approximations; stochastic integrals; weak convergence (search for similar items in EconPapers)
Pages: 9 pages
Date: 1987-07
Note: CFP 716.
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Citations: View citations in EconPapers (3)

Published in Econometric Theory (1988), 4: 528-533

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