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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
DUFOUR, Jean-Marie
JOUINI, Tarek

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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 (2002)] 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.

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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2005-12.

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Length: 36 pages
Date of creation: 2005
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Handle: RePEc:mtl:montde:2005-12

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Related research
Keywords: Vector autoregression VAR exact test Monte Carlo test maximized Monte Carlo test bootstra Granger causality order selection nonstationary model macroeconomics money and income interest rate inflation

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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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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.:
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  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)
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  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)
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  24. 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)
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  27. repec:cup:etheor:v:9:y:1993:i:2:p:263-82 is not listed on IDEAS
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  29. 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.
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  33. 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:
(explanations, 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.)

  1. 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!]
  2. Jonathan B. Hill, 2007. "Efficient tests of long-run causation in trivariate VAR processes with a rolling window study of the money-income relationship," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 747-765. [Downloadable!]
    Other versions:
  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. DUFOUR, Jean-Marie, 2005. "Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics," Cahiers de recherche 2005-03, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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