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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

Suggested Citation

  • Coenen, Günter, 2000. "Asymptotic confidence bands for the estimated autocovariance and autocorrelation functions of vector autoregressive models," Working Paper Series 0009, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:20000009
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    References listed on IDEAS

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    1. Ben S. Bernanke & Ilian Mihov, 1998. "Measuring Monetary Policy," The Quarterly Journal of Economics, Oxford University Press, vol. 113(3), pages 869-902.
    2. 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.
    3. G. Coenen & J.-L. Vega, 2001. "The demand for M3 in the euro area," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 727-748.
    4. 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.
    5. 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.
    6. Coenen, Gunter & Wieland, Volker, 2005. "A small estimated euro area model with rational expectations and nominal rigidities," European Economic Review, Elsevier, vol. 49(5), pages 1081-1104, July.
    7. 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.
    8. 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.
    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. Bennett T. McCallum, 1999. "Analysis of the Monetary Transmission Mechanism: Methodological Issues," NBER Working Papers 7395, National Bureau of Economic Research, Inc.
    11. 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, 2004. "Price Stability and Monetary Policy Effectiveness when Nominal Interest Rates are Bounded at Zero," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-25, February.
    2. 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.
    3. Coenen, Gunter & Wieland, Volker, 2005. "A small estimated euro area model with rational expectations and nominal rigidities," European Economic Review, Elsevier, vol. 49(5), pages 1081-1104, July.
    4. Günter Coenen & Volker Wieland, 2002. "Inflation Dynamics and International Linkages: A Model of the United States, the Euro Area and Japan," Computing in Economics and Finance 2002 240, Society for Computational Economics.
    5. Coenen, Gunter & Levin, Andrew T. & Christoffel, Kai, 2007. "Identifying the influences of nominal and real rigidities in aggregate price-setting behavior," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2439-2466, November.
    6. 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.
    7. 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.
    8. 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.
    9. Fabio Milani, 2009. "Adaptive Learning and Macroeconomic Inertia in the Euro Area," Journal of Common Market Studies, Wiley Blackwell, vol. 47, pages 579-599, June.
    10. Mehdiyev, Mehdi & Ahmadov, Vugar & Huseynov, Salman & Mammadov, Fuad, 2015. "Ölkə iqtisadiyyatı üzrə göstəricilərin modelləşdirilməsi və proqnozlaşdırılması: problemlər və praktiki çətinliklər
      [Modeling and forecasting of macroeconomic variables of the national economy: pro
      ," MPRA Paper 63517, University Library of Munich, Germany.

    More about this item

    Keywords

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

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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