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


  • Phillips, P. C. B.


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.

Suggested Citation

  • Phillips, P. C. B., 1988. "Weak convergence to the matrix stochastic integral [integral operator]01 B dB'," Journal of Multivariate Analysis, Elsevier, vol. 24(2), pages 252-264, February.
  • Handle: RePEc:eee:jmvana:v:24:y:1988:i:2:p:252-264

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    Cited by:

    1. Yicong Lin & Hanno Reuvers, 2019. "Efficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve," Papers 1908.02552,
    2. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Carsten Jentsch & Dimitris N. Politis & Efstathios Paparoditis, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 416-441, May.
    3. Jentsch, Carsten & Paparoditis, Efstathios & Politis, Dimitris N., 2014. "Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes," Working Papers 14-18, University of Mannheim, Department of Economics.


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