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Residual Autocorrelation Testing for Vector Error Correction Models

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Listed:
  • Ralf BRUEGGEMANN
  • Helmut LUETKEPOHL
  • Pentti SAIKKONEN

Abstract

In applied time series analysis, checking for autocorrelation in a fitted model is a routine diagnostic tool. Therefore it is useful to know the asymptotic and small sample properties of the standard tests for the case when some of the variables are cointegrated. The properties of residual autocorrelations of vector error correction models (VECMs) and tests for residual autocorrelation are derived. In particular, the asymptotic distributions of Lagrange multiplier (LM) and portmanteau tests are given. Monte Carlo simulations show that the LM tests have advantages if autocorrelation of small order is tested whereas portmanteau tests are preferable for higher order residual autocorrelation. Their critical values have to be adjusted for the cointegration rank of the system, however.

Suggested Citation

  • Ralf BRUEGGEMANN & Helmut LUETKEPOHL & Pentti SAIKKONEN, 2004. "Residual Autocorrelation Testing for Vector Error Correction Models," Economics Working Papers ECO2004/08, European University Institute.
  • Handle: RePEc:eui:euiwps:eco2004/08
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    1. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    2. Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, vol. 127(1), pages 69-81, July.
    3. Ralf Brüggemann & Helmut Lütkepohl, 2005. "Practical Problems with Reduced‐rank ML Estimators for Cointegration Parameters and a Simple Alternative," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(5), pages 673-690, October.
    4. Gonzalo, Jesus & Ng, Serena, 2001. "A systematic framework for analyzing the dynamic effects of permanent and transitory shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1527-1546, October.
    5. Grayham E. Mizon & David F. Hendry, 1980. "An Empirical Application and Monte Carlo Analysis of Tests of Dynamic Specification," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 21-45.
    6. Saikkonen, Pentti, 2001. "Statistical Inference In Cointegrated Vector Autoregressive Models With Nonlinear Time Trends In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 17(2), pages 327-356, April.
    7. Saikkonen, Pentti, 2001. "Consistent Estimation In Cointegrated Vector Autoregressive Models With Nonlinear Time Trends In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 17(2), pages 296-326, April.
    8. Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, vol. 8(1), pages 1-27, March.
    9. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-840, September.
    10. Hatemi-J, Abdulnasser, 2004. "Multivariate tests for autocorrelation in the stable and unstable VAR models," Economic Modelling, Elsevier, vol. 21(4), pages 661-683, July.
    11. David Edgerton & Ghazi Shukur, 1999. "Testing autocorrelation in a system perspective testing autocorrelation," Econometric Reviews, Taylor & Francis Journals, vol. 18(4), pages 343-386.
    12. Gregory C. Reinsel & Sung K. Ahn, 1992. "Vector Autoregressive Models With Unit Roots And Reduced Rank Structure:Estimation. Likelihood Ratio Test, And Forecasting," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(4), pages 353-375, July.
    13. Pierre Duchesne, 2005. "Testing for serial correlation of unknown form in cointegrated time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 575-595, September.
    14. Benkwitz, Alexander & Lütkepohl, Helmut & Wolters, Jürgen, 2001. "Comparison Of Bootstrap Confidence Intervals For Impulse Responses Of German Monetary Systems," Macroeconomic Dynamics, Cambridge University Press, vol. 5(1), pages 81-100, February.
    15. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521839198, January.
    16. Vlaar, Peter J.G., 2004. "On The Asymptotic Distribution Of Impulse Response Functions With Long-Run Restrictions," Econometric Theory, Cambridge University Press, vol. 20(5), pages 891-903, October.
    17. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    18. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, January.
    19. Efstathios Paparoditis, 2005. "Testing the Fit of a Vector Autoregressive Moving Average Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 543-568, July.
    20. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    21. Fisher, Lance A. & Huh, Hyeon-seung, 1999. "Weak exogeneity and long-run and contemporaneous identifying restrictions in VEC models," Economics Letters, Elsevier, vol. 63(2), pages 159-165, May.
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    More about this item

    Keywords

    cointegration; dynamic econometric models; vector autoregressions; vector error correction models; residual autocorrelation;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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