IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/796.html
   My bibliography  Save this paper

Weak Convergence to the Matrix Stochastic Integral BdB

Author

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.

Suggested Citation

  • 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.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d07/d0796.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Muhammad Shahbaz & Pervaz Azim & Khalil Ahmad, 2011. "Exports-Led Growth Hypothesis in Pakistan: Further Evidence," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 1(3), pages 182-197.
    2. Ventosa-Santaulària Daniel & Gómez-Zaldívar Manuel, 2011. "Testing for a Deterministic Trend When There is Evidence of Unit Root," Journal of Time Series Econometrics, De Gruyter, vol. 2(2), pages 1-26, January.
    3. Shiqing Ling & W. K. Li & Michael McAleer, 2003. "Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence," Econometric Reviews, Taylor & Francis Journals, vol. 22(2), pages 179-202.
    4. Li, Dao & He, Changli, 2012. "Testing for Linear Cointegration Against Smooth-Transition Cointegration," Working Papers 2012:6, Örebro University, School of Business.
    5. Peter C. B. Phillips, 2023. "Discrete Fourier Transforms of Fractional Processes with Econometric Applications," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Theory, volume 45, pages 3-71, Emerald Group Publishing Limited.
    6. Christis Katsouris, 2023. "Predictability Tests Robust against Parameter Instability," Papers 2307.15151, arXiv.org.
    7. Robert Amano & Tony S. Wirjanto, "undated". "A Further Analysis of Exchange Rate Targeting in Canada," Staff Working Papers 94-2, Bank of Canada.
    8. Uwe Hassler, 2006. "A note on Phillips-Perron-type statistics for cointegration testing," Economics Bulletin, AccessEcon, vol. 3(17), pages 1-7.
    9. Choi, In & Chul Ahn, Byung, 1998. "Testing the null of stationarity for multiple time series," Journal of Econometrics, Elsevier, vol. 88(1), pages 41-77, November.
    10. Suzanne McCoskey & Chihwa Kao, 1998. "A residual-based test of the null of cointegration in panel data," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 57-84.
    11. Philip Bodman, 1997. "The Australian Trade Balance and Current Account: a Time Series Perspective," International Economic Journal, Taylor & Francis Journals, vol. 11(2), pages 39-57.
    12. Trapani, Lorenzo, 2021. "Inferential theory for heterogeneity and cointegration in large panels," Journal of Econometrics, Elsevier, vol. 220(2), pages 474-503.
    13. Ericsson, Neil R. & Campos, Julia & Tran, Hong-Anh, 1990. "Pc-Give and David Hendry'S Econometric Methodology," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 10(1), April.
    14. Dong Wan Shin & Oesook Lee, 2004. "M‐Estimation for regressions with integrated regressors and arma errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 283-299, March.
    15. Gregory, Allan W. & Hansen, Bruce E., 1996. "Residual-based tests for cointegration in models with regime shifts," Journal of Econometrics, Elsevier, vol. 70(1), pages 99-126, January.
    16. Yikang, Li, 1998. "Low-pass filtered least squares estimators of cointegrating vectors," Journal of Econometrics, Elsevier, vol. 85(2), pages 289-316, August.
    17. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2022. "Moment tests of independent components," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 13(1), pages 429-474, May.
    18. Haldrup, Niels & Montanes, Antonio & Sanso, Andreu, 2005. "Measurement errors and outliers in seasonal unit root testing," Journal of Econometrics, Elsevier, vol. 127(1), pages 103-128, July.
    19. 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.
    20. Ling, Shiqing & McAleer, Michael, 2004. "Regression quantiles for unstable autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 304-328, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:796. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.