Weak Convergence to the Matrix Stochastic Integral BdB

Peter Phillips

No 796, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form integral_{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 integral_{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 integral_{0}^{1}BdB' 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)
Pages: 18 pages
Date: 1986-07
Note: CFP 697.
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Citations: View citations in EconPapers (5)

Published in Journal of Multivariate Analysis (February 1988), 24(2): 252-264

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