Title

Weak Convergence to the Matrix Stochastic Integral BdB

Document Type

Discussion Paper

Publication Date

7-1-1986

CFDP Number

796

CFDP Pages

18

Abstract

The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form ∫ 0 1 WdW , where W ( r ) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA processes the theory involves weak convergence to matrix stochastic integrals of the form ∫ 0 1 BdB ’, where B ( r ) is vector Brownian motion with non scalar covariance matrix. This paper studies the weak convergence of sample covariance matrices to ∫ 0 1 BdB ’ under quite general conditions. The theory is applied to vector autoregressions with integrated processes.

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