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Asymptotic confidence bands for the estimated autocovariance and autocorrelation functions of vector autoregressive models

  • Coenen, Günter

This paper provides closed-form formulae for computing the asymptotic standard errors of the estimated autocovariance and autocorrelation functions for stable VAR models by means of the d-method. These standard errors can be used to construct asymptotic confidence bands for the estimated autocovariance and autocorrelation functions in order to assess the underlying estimation uncertainty. A Monte Carlo experiment gives evidence on the small-sample performance of these asymptotic confidence bands compared with that obtained using bootstrap methods. The usefulness of the asymptotic confidence bands for empirical work is illustrated by two applications to euro area data on inflation, output and interest rates. JEL Classification: C13, C32, E31, E43

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Paper provided by European Central Bank in its series Working Paper Series with number 0009.

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Date of creation: Jan 2000
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Handle: RePEc:ecb:ecbwps:20000009
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  1. Coenen, Günter & Wieland, Volker, 2002. "A Small Estimated Euro Area Model with Rational Expectations and Nominal Rigidities," CEPR Discussion Papers 3574, C.E.P.R. Discussion Papers.
  2. Bennett T. McCallum, 1999. "Analysis of the Monetary Transmission Mechanism: Methodological Issues," NBER Working Papers 7395, National Bureau of Economic Research, Inc.
  3. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148 Elsevier.
  4. 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.
  5. Dufour, J.M. & Roy, R., 1984. "Some Robust Exact Results on Sample Autocorrelations and Tests of Randomness," Cahiers de recherche 8412, Universite de Montreal, Departement de sciences economiques.
  6. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  7. Ben S. Bernanke & Ilian Mihov, 1995. "Measuring Monetary Policy," NBER Working Papers 5145, National Bureau of Economic Research, Inc.
  8. Fagan, Gabriel & Henry, Jerome & Mestre, Ricardo, 2005. "An area-wide model for the euro area," Economic Modelling, Elsevier, vol. 22(1), pages 39-59, January.
  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. Russell Davidson & James G. MacKinnon, 1994. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," Working Papers 903, Queen's University, Department of Economics.
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