Confidence Bands for Impulse Responses: Bonferroni versus Wald

32 Pages Posted: 6 Mar 2014

See all articles by Helmut Luetkepohl

Helmut Luetkepohl

German Institute for Economic Research (DIW Berlin)

Anna Staszewska-Bystrova

University of Lodz, Department of Economics and Sociology

Peter Winker

University of Giessen - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: February 20, 2014

Abstract

In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. These bands may be based on frequentist or Bayesian methods. If they are based on the joint distribution in the Bayesian framework or the joint asymptotic distribution possibly constructed with bootstrap methods in the frequentist framework often individual confidence intervals or credibility sets are simply connected to obtain the bands. Such bands are known to be too narrow and have a joint confidence content lower than the desired one. If instead the joint distribution of the impulse response coefficients is taken into account and mapped into the band it is shown that such a band is typically rather conservative. It is argued that a smaller band can often be obtained by using the Bonferroni method. While these considerations are equally important for constructing forecast bands, we focus on the case of impulse responses in this study.

Keywords: impulse responses, Bayesian error bands, frequentist confidence bands, Wald statistic, vector autoregressive process

JEL Classification: C320

Suggested Citation

Luetkepohl, Helmut and Staszewska-Bystrova, Anna and Winker, Peter, Confidence Bands for Impulse Responses: Bonferroni versus Wald (February 20, 2014). CESifo Working Paper Series No. 4634. Available at SSRN: https://ssrn.com/abstract=2404896

Helmut Luetkepohl (Contact Author)

German Institute for Economic Research (DIW Berlin) ( email )

Mohrenstra├če 58
Berlin, 10117
Germany

Anna Staszewska-Bystrova

University of Lodz, Department of Economics and Sociology ( email )

Narutowicza 65 str.
PL 90-131, Lodz
Poland

Peter Winker

University of Giessen - Department of Economics ( email )

Licher Str. 62
D-35394 Giessen, DE
Germany

HOME PAGE: http://wiwi.uni-giessen.de/home/oekonometrie/

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