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

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  • Coenen, Günter

Abstract

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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Bibliographic Info

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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Keywords: -method; autocovariances and autocorrelations; bootstrap method; confidence bands; euro area; Phillips curve; vector autoregressions; yield curve;

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References

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  1. Coenen, Guenter & Wieland, Volker, 2003. "A Small Estimated Euro Area Model with Rational Expectations and Nominal Rigidities," CFS Working Paper Series 2003/08, Center for Financial Studies (CFS).
  2. 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.
  3. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  4. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 1997. "Monetary policy shocks: what have we learned and to what end?," Working Paper Series, Macroeconomic Issues WP-97-18, Federal Reserve Bank of Chicago.
  5. 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.
  6. Ben S. Bernanke & Ilian Mihov, 1998. "Measuring Monetary Policy," The Quarterly Journal of Economics, MIT Press, vol. 113(3), pages 869-902, August.
  7. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
  8. Bennett T. McCallum, 1999. "Analysis of the Monetary Transmission Mechanism: Methodological Issues," NBER Working Papers 7395, National Bureau of Economic Research, Inc.
  9. Dufour, Jean-Marie & Roy, Roch, 1985. "Some robust exact results on sample autocorrelations and tests of randomness," Journal of Econometrics, Elsevier, vol. 29(3), pages 257-273, September.
  10. 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.
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Citations

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Cited by:
  1. Coenen, Günter & Orphanides, Athanasios & Wieland, Volker, 2003. "Price stability and monetary policy effectiveness when nominal interest rates are bounded at zero," Working Paper Series 0231, European Central Bank.
  2. 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.
  3. Gunter Coenen & Volker Wieland, 2002. "Inflation dynamics and international linkages: a model of the United States, the euro area, and Japan," International Finance Discussion Papers 745, Board of Governors of the Federal Reserve System (U.S.).
  4. Jang, Tae-Seok, 2012. "Structural estimation of the New-Keynesian Model: a formal test of backward- and forward-looking expectations," MPRA Paper 39669, University Library of Munich, Germany.
  5. Jang, Tae-Seok, 2012. "Structural estimation of the New-Keynesian model: A formal test of backward- and forward-looking behavior," Economics Working Papers 2012-07, Christian-Albrechts-University of Kiel, Department of Economics.
  6. Jang, Tae-Seok, 2012. "Structural estimation of the New-Keynesian Model: a formal test of backward- and forward-looking expectations," MPRA Paper 40278, University Library of Munich, Germany.
  7. Andrew Levin & Günter Coenen, 2005. "Identifying the Influences of Nominal and Real Rigidities in Aggregate Price-Setting Behavior," Computing in Economics and Finance 2005 66, Society for Computational Economics.
  8. Gunter Coenen & Volker Wieland, 2000. "A Simple Estimated Euro Area Model With Rational Expectations And Nominal Rigidities," Computing in Economics and Finance 2000 187, Society for Computational Economics.

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