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 W dW, 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 B dB′, where B( r) is vector Brownian motion with a non-scalar covariance matrix. This paper studies the weak convergence of sample covariance matrices to ∫ 0 1 B dB′ under quite general conditions. The theory is applied to vector autoregressions with integrated processes.
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