IDEAS home Printed from https://ideas.repec.org/p/ecb/ecbwps/20009.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.ecb.europa.eu//pub/pdf/scpwps/ecbwp009.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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, September.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Luca Brugnolini, 2018. "About Local Projection Impulse Response Function Reliability," CEIS Research Paper 440, Tor Vergata University, CEIS, revised 09 Jun 2018.
    4. 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.
    5. Brüggemann, Ralf & Jentsch, Carsten & Trenkler, Carsten, 2016. "Inference in VARs with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 191(1), pages 69-85.
    6. Dufour, Jean-Marie & Pelletier, Denis & Renault, Eric, 2006. "Short run and long run causality in time series: inference," Journal of Econometrics, Elsevier, vol. 132(2), pages 337-362, June.
    7. 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.
    8. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, October.
    9. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    10. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 2005-12, Universite de Montreal, Departement de sciences economiques.
    11. Nicoletta Batini & Edward Nelson, 2001. "The Lag from Monetary Policy Actions to Inflation: Friedman Revisited," International Finance, Wiley Blackwell, vol. 4(3), pages 381-400.
    12. Hanson, Michael S., 2006. "Varying monetary policy regimes: A vector autoregressive investigation," Journal of Economics and Business, Elsevier, vol. 58(5-6), pages 407-427.
    13. Òscar Jordà & Alan M. Taylor, 2024. "Local Projections," NBER Working Papers 32822, National Bureau of Economic Research, Inc.
    14. Dufour, Jean-Marie & Jouini, Tarek, 2006. "Finite-sample simulation-based inference in VAR models with application to Granger causality testing," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 229-254.
    15. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    16. Leon Berkelmans, 2005. "Credit and Monetary Policy: An Australian SVAR," RBA Research Discussion Papers rdp2005-06, Reserve Bank of Australia.
    17. Kilian, Lutz & Kim, Yun Jung, 2009. "Do Local Projections Solve the Bias Problem in Impulse Response Inference?," CEPR Discussion Papers 7266, C.E.P.R. Discussion Papers.
    18. Vitek, Francis, 2006. "Measuring the Stance of Monetary Policy in a Small Open Economy: A Dynamic Stochastic General Equilibrium Approach," MPRA Paper 802, University Library of Munich, Germany.
    19. Matteo Barigozzi & Antonio M. Conti & Matteo Luciani, 2014. "Do Euro Area Countries Respond Asymmetrically to the Common Monetary Policy?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(5), pages 693-714, October.
    20. Michael W. McCracken & Michael T. Owyang & Tatevik Sekhposyan, 2021. "Real-Time Forecasting and Scenario Analysis Using a Large Mixed-Frequency Bayesian VAR," International Journal of Central Banking, International Journal of Central Banking, vol. 17(71), pages 1-41, December.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecb:ecbwps:20009. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Official Publications (email available below). General contact details of provider: https://edirc.repec.org/data/emieude.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.