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

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  • Phillips, P. C. B.

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.

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, arXiv.org, revised Aug 2020.
    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. Smith, James, 2008. "That elusive elasticity and the ubiquitous bias: Is panel data a panacea?," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 760-779, June.
    4. Herwartz, Helmut & Neumann, Michael H., 2005. "Bootstrap inference in systems of single equation error correction models," Journal of Econometrics, Elsevier, vol. 128(1), pages 165-193, September.
    5. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2010. "A Sieve Bootstrap Test For Cointegration In A Conditional Error Correction Model," Econometric Theory, Cambridge University Press, vol. 26(3), pages 647-681, June.
      • Arnold Zellner & Franz C. Palm, 2000. "Correction," Econometrica, Econometric Society, vol. 68(5), pages 1293-1294, September.
    6. 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.
    7. del Barrio Castro, Tomas, 2006. "On the performance of the DHF tests against nonstationary alternatives," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 291-297, February.

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