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Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing

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Author Info
Jean-Marie Dufour ()
Tarek Jouini

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Abstract

Statistical tests in vector autoregressive (VAR) models are typically based on large-sample approximations, involving the use of asymptotic distributions or bootstrap techniques. After documenting that such methods can be very misleading even with fairly large samples, especially when the number of lags or the number of equations is not small, we propose a general simulation-based technique that allows one to control completely the level of tests in parametric VAR models. In particular, we show that maximized Monte Carlo tests [Dufour (2005, Journal of Econometrics)] can provide provably exact tests for such models, whether they are stationary or integrated. Applications to order selection and causality testing are considered as special cases. The technique developed is applied to quarterly and monthly VAR models of the U.S. economy, comprising income, money, interest rates and prices, over the period 1965-1996.

Les tests statistiques sur des modèles autorégressifs multivariés (VAR) sont habituellement basés sur des approximations de grands échantillons, qui utilisent une loi asymptotique ou une technique de bootstrap. Après avoir montré que ces méthodes peuvent être très peu fiables, même avec des échantillons de taille assez grande, particulièrement lorsque le nombre des retards ou le nombre d’équations augmentent, nous proposons une technique générale basée sur la simulation qui permet de contrôler parfaitement le niveau des tests dans les modèles VAR paramétriques. En particulier, nous montrons que la technique des tests de Monte Carlo maximisés [Dufour (2005, Journal of Econometrics)] fournit des tests exacts pour de tels modèles, que ceux-ci soient stationnaires ou intégrés. Sélectionner l’ordre du modèle ainsi que tester la causalité au sens de Granger sont étudiés comme problèmes particuliers dans ce cadre. La technique proposée est appliquée à des modèles VAR, trimestriels et mensuels, de l’économie américaine, comprenant le revenu, la monnaie, un taux d’intérêt et le niveau des prix, sur la période 1965-1996.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2005s-26.

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Date of creation: 01 Aug 2005
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Handle: RePEc:cir:cirwor:2005s-26

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Keywords: bootstrap exact test Granger causality inflation interest rate macroeconomics maximized Monte Carlo test money and income Monte Carlo test nonstationary model order selection VAR vector autoregression autorégression vectorielle bootstrap causalité au sens de Granger inflation macroéconomie modèle non-stationnaire monnaie et revenu sélection de l’ordre taux d’intérêt test exact test de Monte Carlo test de Monte Carlo maximisé VAR

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit

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  1. 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. [Downloadable!] (restricted)
  2. Ben S. Bernanke & Ilian Mihov, 1998. "Measuring Monetary Policy," The Quarterly Journal of Economics, MIT Press, vol. 113(3), pages 869-902, August. [Downloadable!] (restricted)
    Other versions:
  3. 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. [Downloadable!] (restricted)
  4. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January. [Downloadable!] (restricted)
  5. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 2003-12, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
  6. G. S. Hongyi Li, 1996. "Bootstrapping time series models," Econometric Reviews, Taylor and Francis Journals, vol. 15(2), pages 115-158. [Downloadable!] (restricted)
  7. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-63, May. [Downloadable!] (restricted)
  8. Juan J. DOLADO & Helmut LUETKEPOHL, . "Making Wald Tests Work for Cointegrated Var Systems," Sonderforschungsbereich 373 1994-44, Humboldt Universitaet Berlin.
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  9. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-93, November. [Downloadable!] (restricted)
    Other versions:
  10. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation, Yale University, revised Feb 1987. [Downloadable!]
    Other versions:
  11. Yamada, Hiroshi & Toda, Hiro Y., 1998. "Inference in possibly integrated vector autoregressive models: some finite sample evidence," Journal of Econometrics, Elsevier, vol. 86(1), pages 55-95, June. [Downloadable!] (restricted)
  12. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August. [Downloadable!] (restricted)
    Other versions:
  13. 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. [Downloadable!] (restricted)
  14. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January. [Downloadable!] (restricted)
    Other versions:
  15. Kilian, L. & Demiroglu, U., 1997. "Residual-Based Bootstrap Tests for Normality in Autoregressions," Papers 97-14, Michigan - Center for Research on Economic & Social Theory.
  16. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99. [Downloadable!] (restricted)
  17. 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. [Downloadable!] (restricted)
  18. Inoue, Atsushi & Kilian, Lutz, 2003. "The Continuity Of The Limit Distribution In The Parameter Of Interest Is Not Essential For The Validity Of The Bootstrap," Econometric Theory, Cambridge University Press, vol. 19(06), pages 944-961, September. [Downloadable!]
  19. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
  20. Kilian, L. & Caner, M., 1999. "Size Distortions of Tests of the Null Hypothesis of Stationarity: Evidence and Implications for the PPP Debate," Papers 99-05, Michigan - Center for Research on Economic & Social Theory.
    Other versions:
  21. Alexander Benkwitz & Michael Neumann & Helmut Lütekpohl, 2000. "Problems related to confidence intervals for impulse responses of autoregressive processes," Econometric Reviews, Taylor and Francis Journals, vol. 19(1), pages 69-103. [Downloadable!] (restricted)
  22. Hiro Y. Toda & Peter C.B. Phillips, 1991. "Vector Autoregression and Causality: A Theoretical Overview and Simulation Study," Cowles Foundation Discussion Papers 1001, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  23. 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.). [Downloadable!]
    Other versions:
  24. Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May. [Downloadable!] (restricted)
  25. Blough, Stephen R, 1992. "The Relationship between Power and Level for Generic Unit Root Tests in Finite Samples," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(3), pages 295-308, July-Sept. [Downloadable!] (restricted)
  26. Benedikt M. Poetscher, 2002. "Lower Risk Bounds and Properties of Confidence Sets for Ill-Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation, Unit Roots, and Estimation of Long Memory Parame," Econometrica, Econometric Society, vol. 70(3), pages 1035-1065, May. [Downloadable!] (restricted)
    Other versions:
  27. Jon Faust, 1996. "Theoretical confidence level problems with confidence intervals for the spectrum of a time series," International Finance Discussion Papers 575, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  28. repec:cup:etheor:v:9:y:1993:i:2:p:263-82 is not listed on IDEAS
  29. Jean-Marie Dufour & Denis Pelletier & Éric Renault, 2003. "Short Run and Long Run Causality in Time Series: Inference," CIRANO Working Papers 2003s-61, CIRANO. [Downloadable!]
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  30. 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.
  31. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor and Francis Journals, vol. 17(1), pages 1-29. [Downloadable!] (restricted)
  32. Cochrane, John H., 1991. "A critique of the application of unit root tests," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 275-284, April. [Downloadable!] (restricted)
  33. 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. [Downloadable!] (restricted)
  34. Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Simulation based finite and large sample tests in multivariate regressions," Journal of Econometrics, Elsevier, vol. 111(2), pages 303-322, December. [Downloadable!] (restricted)
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Cited by:
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  1. Jonathan B. Hill, 2004. "Efficient Tests of Long-Run Causation in Trivariate VAR Processes with a Rolling Window Study of the Money-Income Relationship," Working Papers 0413, Florida International University, Department of Economics. [Downloadable!]
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  2. Jonathan B. Hill, 2005. "Causation Delays and Causal Neutralization up to Three Steps Ahead: The Money-Output Relationship Revisited," Econometrics 0503016, EconWPA, revised 23 Mar 2005. [Downloadable!]
  3. Jonathan B. Hill, 2004. "Causation Delays and Causal Neutralization: The Money-Output Relationship Revisited," Working Papers 0403, Florida International University, Department of Economics. [Downloadable!]
  4. Jean-Marie Dufour, 2005. "Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and non-standard asymptotics," CIRANO Working Papers 2005s-02, CIRANO. [Downloadable!]
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