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

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  • DUFOUR, Jean-Marie
  • JOUINI, Tarek

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.

Suggested Citation

  • DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 16-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  • Handle: RePEc:mtl:montec:16-2005
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    References listed on IDEAS

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    Cited by:

    1. Majid M. Al-Sadoon, 2015. "Testing subspace Granger causality," Economics Working Papers 1495, Department of Economics and Business, Universitat Pompeu Fabra.
    2. 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.
    3. 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.
    4. 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.

    More about this item

    Keywords

    Vector autoregression; VAR; exact test; Monte Carlo test; maximized Monte Carlo test; bootstrap; Granger causality; order selection; nonstationary model; macroeconomics; money and income; interest rate; inflation;

    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
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • 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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