IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Vector Autoregressive Models

  • Helmut Luetkepohl

Multivariate simultaneous equations models were used extensively for macroeconometric analysis when Sims (1980) advocated vector autoregressive (VAR) models as alternatives. At that time longer and more frequently observed macroeconomic time series called for models which described the dynamic structure of the variables. VAR models lend themselves for this purpose. They typically treat all variables as a priori endogenous. Thereby they account for Sims’ critique that the exogeneity assumptions for some of the variables in simultaneous equations models are ad hoc and often not backed by fully developed theories. Restrictions, including exogeneity of some of the variables, may be imposed on VAR models based on statistical procedures. VAR models are natural tools for forecasting. Their setup is such that current values of a set of variables are partly explained by past values of the variables involved. They can also be used for economic analysis, however, because they describe the joint generation mechanism of the variables involved. Structural VAR analysis attempts to investigate structural economic hypotheses with the help of VAR models. Impulse response analysis, forecast error variance decompositions, historical decompositions and the analysis of forecast scenarios are the tools which have been proposed for disentangling the relations between the variables in a VAR model. Traditionally VAR models are designed for stationary variables without time trends. Trending behavior can be captured by including deterministic polynomial terms. In the 1980s the discovery of the importance of stochastic trends in economic variables and the development of the concept of cointegration by Granger (1981), Engle and Granger (1987), Johansen (1995) and others have shown that stochastic trends can also be captured by VAR models. If there are trends in some of the variables it may be desirable to separate the long-run relations from the short-run dynamics of the generation process of a set of variables. Vector error correction models offer a convenient framework for separating longrun and short-run components of the data generation process (DGP). In the present chapter levels VAR models are considered where cointegration relations are not modelled explicitly although they may be present. Specific issues related to trending variables will be mentioned occasionally throughout the chapter. The advantage of levels VAR models over vector error correction models is that they can also be used when the cointegration structure is unknown. Cointegration analysis and error correction models are discussed specifically in the next chapter.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://cadmus.eui.eu/bitstream/handle/1814/19354/ECO_2011_30.pdf?sequence=1
File Function: main text
Download Restriction: no

Paper provided by European University Institute in its series Economics Working Papers with number ECO2011/30.

as
in new window

Length:
Date of creation: 2011
Date of revision:
Handle: RePEc:eui:euiwps:eco2011/30
Contact details of provider: Postal: Badia Fiesolana, Via dei Roccettini, 9, 50014 San Domenico di Fiesole (FI) Italy
Phone: +39-055-4685.982
Fax: +39-055-4685.902
Web page: http://www.eui.eu/ECO/

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Ralf BRUEGGEMANN & Helmut LUETKEPOHL & Pentti SAIKKONEN, 2004. "Residual Autocorrelation Testing for Vector Error Correction Models," Economics Working Papers ECO2004/08, European University Institute.
  2. Rossi, Barbara & Pesavento, Elena, 2003. "Small Sample Confidence Intervals for Multivariate Impulse Response Functions at Long Horizons," Working Papers 03-19, Duke University, Department of Economics.
  3. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1986. "Forecasting and conditional projection using realistic prior distribution," Staff Report 93, Federal Reserve Bank of Minneapolis.
  4. Marco Del Negro & Frank Schorfheide, 2002. "Priors from general equilibrium models for VARs," Working Paper 2002-14, Federal Reserve Bank of Atlanta.
  5. Nikolay Gospodinov, 2004. "Asymptotic confidence intervals for impulse responses of near-integrated processes," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 505-527, December.
  6. Toda, Hiro Y. & Yamamoto, Taku, 1995. "Statistical inference in vector autoregressions with possibly integrated processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 225-250.
  7. Lütkepohl, Helmut & POSKITT, D.S., 1996. "Testing for Causation Using Infinite Order Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(01), pages 61-87, March.
  8. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
  9. Burbidge, John & Harrison, Alan, 1985. "An historical decomposition of the great depression to determine the role of money," Journal of Monetary Economics, Elsevier, vol. 16(1), pages 45-54, July.
  10. Jean-Marie Dufour & Eric Renault, 1998. "Short Run and Long Run Causality in Time Series: Theory," Econometrica, Econometric Society, vol. 66(5), pages 1099-1126, September.
  11. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2012. "Prior Selection for Vector Autoregressions," NBER Working Papers 18467, National Bureau of Economic Research, Inc.
  12. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
  13. Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
  14. Granger, Clive W.J., 2001. "Overview Of Nonlinear Macroeconometric Empirical Models," Macroeconomic Dynamics, Cambridge University Press, vol. 5(04), pages 466-481, September.
  15. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
  16. Jeremy Berkowitz & Lutz Kilian, 1996. "Recent developments in bootstrapping time series," Finance and Economics Discussion Series 96-45, Board of Governors of the Federal Reserve System (U.S.).
  17. Baumeister, Christiane & Kilian, Lutz, 2011. "Real-Time Forecasts of the Real Price of Oil," CEPR Discussion Papers 8414, C.E.P.R. Discussion Papers.
  18. Christopher A. Sims & Tao Zha, 1995. "Error bands for impulse responses," Working Paper 95-6, Federal Reserve Bank of Atlanta.
  19. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  20. Atsushi Inoue & Lutz Kilian, 2000. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometric Society World Congress 2000 Contributed Papers 0401, Econometric Society.
  21. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  22. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
  23. repec:cup:cbooks:9780521565882 is not listed on IDEAS
  24. Daniel F. Waggoner & Tao Zha, 1998. "Conditional forecasts in dynamic multivariate models," Working Paper 98-22, Federal Reserve Bank of Atlanta.
  25. Kadiyala, K. Rao & Karlsson, Sune, 1994. "Numerical Aspects of Bayesian VAR-modeling," SSE/EFI Working Paper Series in Economics and Finance 12, Stockholm School of Economics.
  26. Boswijk, H. Peter, 2000. "Mixed Normality And Ancillarity In I(2) Systems," Econometric Theory, Cambridge University Press, vol. 16(06), pages 878-904, December.
  27. Ingram, Beth F. & Whiteman, Charles H., 1994. "Supplanting the 'Minnesota' prior: Forecasting macroeconomic time series using real business cycle model priors," Journal of Monetary Economics, Elsevier, vol. 34(3), pages 497-510, December.
  28. Lorenzo Pascual & Juan Romo & Esther Ruiz, 2004. "Bootstrap predictive inference for ARIMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 449-465, 07.
  29. repec:cup:cbooks:9780521562607 is not listed on IDEAS
  30. Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Multivariate GARCH models," CREATES Research Papers 2008-06, School of Economics and Management, University of Aarhus.
  31. Sims, Christopher A. & Waggoner, Daniel F. & Zha, Tao, 2008. "Methods for inference in large multiple-equation Markov-switching models," Journal of Econometrics, Elsevier, vol. 146(2), pages 255-274, October.
  32. Hiro Y. Toda & Peter C.B. Phillips, 1991. "Vector Autoregression and Causality," Cowles Foundation Discussion Papers 977, Cowles Foundation for Research in Economics, Yale University.
  33. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
  34. Hatanaka, Michio, 1996. "Time-Series-Based Econometrics: Unit Roots and Co-integrations," OUP Catalogue, Oxford University Press, number 9780198773535, March.
  35. Lutkepohl, Helmut, 2006. "Forecasting with VARMA Models," Handbook of Economic Forecasting, Elsevier.
  36. Kilian, Lutz & Chang, Pao-Li, 2000. "How accurate are confidence intervals for impulse responses in large VAR models?," Economics Letters, Elsevier, vol. 69(3), pages 299-307, December.
  37. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
  38. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  39. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  40. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
  41. H. Lütkepohl & P. Saikkonen, 1995. "Impulse Response Analysis in Infinite Order Cointegrated Vector Autoregressive Processes," SFB 373 Discussion Papers 1995,11, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  42. Grigoletto, Matteo, 1998. "Bootstrap prediction intervals for autoregressions: some alternatives," International Journal of Forecasting, Elsevier, vol. 14(4), pages 447-456, December.
  43. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155, March.
  44. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
  45. Kilian, Lutz, 2011. "Structural Vector Autoregressions," CEPR Discussion Papers 8515, C.E.P.R. Discussion Papers.
  46. Johansen, Soren, 2006. "Statistical analysis of hypotheses on the cointegrating relations in the I(2) model," Journal of Econometrics, Elsevier, vol. 132(1), pages 81-115, May.
  47. Kilian, Lutz & Demiroglu, Ufuk, 2000. "Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 40-50, January.
  48. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February.
  49. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Smooth Functions of Slope Parameters and Innovation Variances in VAR (∞) Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 309-332, May.
  50. Z. Lomnicki, 1961. "Tests for departure from normality in the case of linear stochastic processes," Metrika, Springer, vol. 4(1), pages 37-62, December.
  51. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, vol. 15(4), pages 393-403, October.
  52. Wright, Jonathan H, 2000. "Confidence Intervals for Univariate Impulse Responses with a Near Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 368-73, July.
  53. Villani, Mattias, 2005. "Bayesian Reference Analysis Of Cointegration," Econometric Theory, Cambridge University Press, vol. 21(02), pages 326-357, April.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eui:euiwps:eco2011/30. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Rhoda Lane)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.