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

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  • Günter Coenen

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Abstract

This paper provides closed-form formulae for computing the asymptotic covariance matrices of the estimated autocovariance and autocorrelation functions of stable VAR models by means of the delta method. These covariance matrices can be used to construct asymptotic confidence bands for the estimated autocovariance and autocorrelation functions to assess the underlying estimation uncertainty. The usefulness of the formulae for empirical work is illustrated by an application to inflation and output gap data for the U.S. economy indicating the existence of a significant short-run Phillips-curve tradeoff. Copyright Springer-Verlag 2005

Suggested Citation

  • Günter Coenen, 2005. "Asymptotic confidence bands for the estimated autocovariance and autocorrelation functions of vector autoregressive models," Empirical Economics, Springer, vol. 30(1), pages 65-75, January.
  • Handle: RePEc:spr:empeco:v:30:y:2005:i:1:p:65-75
    DOI: 10.1007/s00181-004-0214-8
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. 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.
    5. Ben S. Bernanke & Ilian Mihov, 1998. "Measuring Monetary Policy," The Quarterly Journal of Economics, Oxford University Press, vol. 113(3), pages 869-902.
    6. 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.
    7. Bennett T. McCallum, 1999. "Analysis of the Monetary Transmission Mechanism: Methodological Issues," NBER Working Papers 7395, National Bureau of Economic Research, Inc.
    8. 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.
    9. 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.
    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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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Coenen, Günter & Wieland, Volker, 2002. "Inflation dynamics and international linkages: a model of the United States, the euro area and Japan," Working Paper Series 0181, European Central Bank.
    6. 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.
    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. 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.

    More about this item

    Keywords

    Vector autoregressive models; autocovariance and autocorrelation functions; confidence bands; delta method; phillips curve; C13; C32; E31;

    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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