Weak convergence to the matrix stochastic integral [integral operator]01 B dB'

Peter Phillips

Journal of Multivariate Analysis, 1988, vol. 24, issue 2, 252-264

Abstract: The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form [integral operator]01 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 [integral operator]01 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 [integral operator]01 B dB' under quite general conditions. The theory is applied to vector autoregressions with integrated processes.

Keywords: integrated; process; invariance; principle; near; integrated; time; series; stochastic; integral; vector; autoregression; weak; convergence (search for similar items in EconPapers)
Date: 1988
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Citations: View citations in EconPapers (7)

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