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Vector autoregressive analysis

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  • Lütkepohl, Helmut

Abstract

An introduction to vector autoregressive (VAR) analysis is given with special emphasis on cointegration. The models, estimating their parameters and specifying the autoregressive order, the cointegrating rank and other restrictions are discussed. Possibilities for model validation are also considered, Causality tests, impulse responses and forecast error variance decompositions are presented as tools for analyzing VAR models.

Suggested Citation

  • Lütkepohl, Helmut, 1999. "Vector autoregressive analysis," SFB 373 Discussion Papers 1999,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:199931
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    1. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    2. Peter C. B. Phillips & Mico Loretan, 1991. "Estimating Long-run Economic Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 407-436.
    3. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    4. 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.
    5. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
    6. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(1), pages 95-131, April.
    7. Holger Bartel & Helmut Lutkepohl, 1998. "Estimating the Kronecker indices of cointegrated echelon-form VARMA models," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 76-99.
    8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    9. 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.
    10. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    11. Lutkepohl, Helmut & Reimers, Hans-Eggert, 1992. "Impulse response analysis of cointegrated systems," Journal of Economic Dynamics and Control, Elsevier, vol. 16(1), pages 53-78, January.
    12. 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.
    13. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    14. Poskitt, D. & Lütkepohl, H., 1995. "Consistent Specification of Cointegrated Autoregressive Moving-Average Systems," SFB 373 Discussion Papers 1995,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    15. Banerjee, Anindya & Dolado, Juan J. & Galbraith, John W. & Hendry, David, 1993. "Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data," OUP Catalogue, Oxford University Press, number 9780198288107.
    16. Lütkepohl, Helmut & POSKITT, D.S., 1996. "Testing for Causation Using Infinite Order Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(1), pages 61-87, March.
    17. Jostein Paulsen, 1984. "Order Determination Of Multivariate Autoregressive Time Series With Unit Roots," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(2), pages 115-127, March.
    18. Hendry, David F., 1995. "Dynamic Econometrics," OUP Catalogue, Oxford University Press, number 9780198283164.
    19. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    20. 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.
    21. Lutkepohl, Helmut & Poskitt, D S, 1996. "Specification of Echelon-Form VARMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 69-79, January.
    22. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    23. Lutkepohl, Helmut & Burda, Maike M., 1997. "Modified Wald tests under nonregular conditions," Journal of Econometrics, Elsevier, vol. 78(2), pages 315-332, June.
    24. Lütkepohl, H. & Poskitt, D. S., 1996. "Consistent Estimation of the Number of Cointegration Relations in a Vector Autoregressive Model," SFB 373 Discussion Papers 1996,74, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    25. Johansen, Soren, 1992. "Determination of Cointegration Rank in the Presence of a Linear Trend," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 383-397, August.
    26. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    27. 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.
    28. Wolfgang Härdle & Helmut Lütkepohl & Rong Chen, 1997. "A Review of Nonparametric Time Series Analysis," International Statistical Review, International Statistical Institute, vol. 65(1), pages 49-72, April.
    29. Mosconi, Rocco & Giannini, Carlo, 1992. "Non-causality in Cointegrated Systems: Representation Estimation and Testing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 399-417, August.
    30. 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.
    31. Hatanaka, Michio, 1996. "Time-Series-Based Econometrics: Unit Roots and Co-integrations," OUP Catalogue, Oxford University Press, number 9780198773535.
    32. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    33. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(3), pages 468-497, December.
    34. 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 113-144, January.
    35. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-1369, November.
    36. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    37. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
    38. Perron, Pierre & Campbell, John Y, 1993. "A Note on Johansen's Cointegration Procedure When Trends Are Present," Empirical Economics, Springer, vol. 18(4), pages 777-789.
    39. Benkwitz, Alexander & Lütkepohl, Helmut & Neumann, Michael H., 1997. "Problems related to bootstrapping impulse responses of autoregressive processes," SFB 373 Discussion Papers 1997,85, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    More about this item

    Keywords

    Cointegration; forecasting; dynamic econometric models; impulse responses;
    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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