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Weak Convergence to the Matrix Stochastic Integral BdB

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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.

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  • Peter C.B. Phillips, 1986. "Weak Convergence to the Matrix Stochastic Integral BdB," Cowles Foundation Discussion Papers 796, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:796
    Note: CFP 697.
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d07/d0796.pdf
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    1. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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    Cited by:

    1. Westerlund, Joakim, 2005. "Panel Cointegration Tests of the Fisher Hypothesis," Working Papers 2005:10, Lund University, Department of Economics.
    2. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    3. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    4. Peter C.B. Phillips & Sam Ouliaris, 1986. "Testing for Cointegration Using Principal Component Measures," Cowles Foundation Discussion Papers 809R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1987.
    5. Joseph Beaulieu, J. & Miron, Jeffrey A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 305-328.

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