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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 9, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:20009
    Note: 241047
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    References listed on IDEAS

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    1. 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.
    2. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    3. 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.
    4. 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.
    5. Bennett T. McCallum, 2001. "Analysis of the Monetary Transmission Mechanism: Methodological Issues," Palgrave Macmillan Books, in: Deutsche Bundesbank (ed.), The Monetary Transmission Process, chapter 1, pages 11-59, Palgrave Macmillan.
    6. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    7. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
    8. 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.
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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. Wieland, Volker & Coenen, Günter, 2002. "Inflation dynamics and international linkages: a model of the United States, the euro area and Japan," Working Paper Series 181, European Central Bank.
    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. 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.
    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. repec:bla:jcmkts:v:47:y:2009:i::p:579-599 is not listed on IDEAS
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Fabio Milani, 2009. "Adaptive Learning and Macroeconomic Inertia in the Euro Area," Journal of Common Market Studies, Wiley Blackwell, vol. 47(3), pages 579-599, June.
    12. 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.
    13. 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.

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    More about this item

    Keywords

    autocovariances and autocorrelations; bootstrap method; confidence bands; euro area; Phillips curve; vector autoregressions; yield curve;
    All these keywords.

    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
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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