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Infinite-Order Cointegrated Vector Autoregressive Processes

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  • Saikkonen, Pentti
  • Lütkepohl, HELMUT

Abstract

Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992, Econometric Theory 8, 1-27). The asymptotic properties of the estimated coefficients of the autoregressive error correction model (ECM) and the pure vector autoregressive (VAR) representations are derived under the assumption that the autoregressive order goes to infinity with the sample size. These coefficients are often used for analyzing the relationships between the variables; therefore, they are important for applied work. Tests for linear restrictions on the coefficients of both the ECM and the pure VAR representation are considered under the present assumptions. It is found that they have limiting x 2 distributions. Tests are also derived under the assumption that the number of restrictions goes to infinity with the sample size.

Suggested Citation

  • Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
  • Handle: RePEc:cup:etheor:v:12:y:1996:i:05:p:814-844_00
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    Citations

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    Cited by:

    1. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
    2. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
    3. Tommaso Proietti & Alessandro Giovannelli, 1705. "A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices," CREATES Research Papers 2017-20, Department of Economics and Business Economics, Aarhus University.
    4. Ghysels, Eric & Hill, Jonathan B. & Motegi, Kaiji, 2016. "Testing for Granger causality with mixed frequency data," Journal of Econometrics, Elsevier, vol. 192(1), pages 207-230.
    5. Johansen, Søren & Juselius, Katarina, 2014. "An asymptotic invariance property of the common trends under linear transformations of the data," Journal of Econometrics, Elsevier, vol. 178(P2), pages 310-315.
    6. Zernov, Serguei & Zinde-Walsh, Victoria & Galbraith, John W., 2009. "Asymptotics for estimation of quantile regressions with truncated infinite-dimensional processes," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 497-508, March.
    7. Maynard, Alex & Shimotsu, Katsumi, 2009. "Covariance-Based Orthogonality Tests For Regressors With Unknown Persistence," Econometric Theory, Cambridge University Press, vol. 25(01), pages 63-116, February.
    8. Bauer, Dietmar & Maynard, Alex, 2012. "Persistence-robust surplus-lag Granger causality testing," Journal of Econometrics, Elsevier, vol. 169(2), pages 293-300.
    9. Lutkepohl, Helmut & Saikkonen, Pentti, 1999. "A lag augmentation test for the cointegrating rank of a VAR process," Economics Letters, Elsevier, vol. 63(1), pages 23-27, April.
    10. Qu, Zhongjun & Perron, Pierre, 2007. "A Modified Information Criterion For Cointegration Tests Based On A Var Approximation," Econometric Theory, Cambridge University Press, vol. 23(04), pages 638-685, August.
    11. Onatski, Alexei & Uhlig, Harald, 2012. "Unit Roots In White Noise," Econometric Theory, Cambridge University Press, vol. 28(03), pages 485-508, June.
    12. Marais, E. & Bates, S., 2006. "An empirical study to identify shift contagion during the Asian crisis," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 16(5), pages 468-479, December.
    13. Demetrescu Matei, 2009. "Panel Unit Root Testing with Nonlinear Instruments for Infinite-Order Autoregressive Processes," Journal of Time Series Econometrics, De Gruyter, vol. 1(2), pages 1-30, December.
    14. Hafner, C. M. & Linton, O., 2016. "Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case," Cambridge Working Papers in Economics 1664, Faculty of Economics, University of Cambridge.
    15. Dietmar Bauer & Alex Maynard, 2010. "Persistence-robust Granger causality testing," Working Papers 1011, University of Guelph, Department of Economics and Finance.
    16. Helmut Lütkepohl, 2013. "Vector autoregressive models," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 6, pages 139-164 Edward Elgar Publishing.
    17. Judith A. Clarke & Sadaf Mirza, 2003. "Some Finite Sample Results On Testing For Granger Noncausality," Econometrics Working Papers 0305, Department of Economics, University of Victoria.
    18. Serguei Zernov & Victoria Zindle-Walsh & John Galbraith, 2006. "Asymptotics For Estimation Of Truncated Infinite-Dimensional Quantile Regressions," Departmental Working Papers 2006-16, McGill University, Department of Economics.
    19. repec:gam:jecnmx:v:5:y:2017:i:3:p:36-:d:109242 is not listed on IDEAS
    20. Lutkepohl, Helmut & Saikkonen, Pentti, 1997. "Impulse response analysis in infinite order cointegrated vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 127-157, November.

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