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Residual Autocorrelation Testing for Vector Error Correction Models

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  • 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.

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Bibliographic Info

Paper provided by European University Institute in its series Economics Working Papers with number ECO2004/08.

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Date of creation: 2004
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Handle: RePEc:eui:euiwps:eco2004/08

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Keywords: cointegration; dynamic econometric models; vector autoregressions; vector error correction models; residual autocorrelation;

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  1. David Edgerton & Ghazi Shukur, 1999. "Testing autocorrelation in a system perspective testing autocorrelation," Econometric Reviews, Taylor & Francis Journals, vol. 18(4), pages 343-386.
  2. 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, 07.
  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. Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, vol. 127(1), pages 69-81, July.
  5. Pierre Duchesne, 2005. "Testing for serial correlation of unknown form in cointegrated time series models," Annals of the Institute of Statistical Mathematics, Springer, vol. 57(3), pages 575-595, September.
  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(02), pages 327-356, April.
  7. 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.
  8. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  9. Saikkonen, Pentti, 2001. "Consistent Estimation In Cointegrated Vector Autoregressive Models With Nonlinear Time Trends In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 17(02), pages 296-326, April.
  10. Mizon, Grayham E & Hendry, David F, 1980. "An Empirical Application and Monte Carlo Analysis of Tests of Dynamic Specification," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 21-45, January.
  11. Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, vol. 8(01), pages 1-27, March.
  12. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
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Citations

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Cited by:
  1. Huang, Jikun & Yang, Jun & Rozelle, Scott, 2013. "The political economy of food pricing policy in China," Working Paper Series UNU-WIDER Research Paper , World Institute for Development Economic Research (UNU-WIDER).
  2. Ralf Brueggemann & Helmut Luetkepohl, 2004. "A Small Monetary System for the Euro Area Based on German Data," Economics Working Papers ECO2004/24, European University Institute.
  3. Mezgebo, Taddese, 2009. "A multivariate approach for identification of optimal locations with in Ethiopia’s wheat market to tackle soaring inflation on food price (Extended version)," MPRA Paper 17960, University Library of Munich, Germany.
  4. Patilea, V. & Raïssi, H., 2013. "Corrected portmanteau tests for VAR models with time-varying variance," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 190-207.
  5. Mezgebo, Taddese, 2009. "A multivariate approach for identification of optimal locations with in Ethiopia’s wheat market to tackle soaring inflation on food price," MPRA Paper 18663, University Library of Munich, Germany.
  6. Poulin, Jennifer & Duchesne, Pierre, 2008. "On the power transformation of kernel-based tests for serial correlation in vector time series: Some finite sample results and a comparison with the bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4432-4457, May.
  7. Park, Byeong U. & Mammen, Enno & Härdle, Wolfgang & Borak, Szymon, 2009. "Time Series Modelling With Semiparametric Factor Dynamics," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 284-298.
  8. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
  9. Ida Wolden Bache, 2006. "Assessing the structural VAR approach to exchange rate pass-through," Computing in Economics and Finance 2006 309, Society for Computational Economics.
  10. Arbus, Ignacio, 2009. "Departure from normality of increasing-dimension martingales," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1304-1315, July.
  11. Helmut Luetkepohl, 2011. "Vector Autoregressive Models," Economics Working Papers ECO2011/30, European University Institute.

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