2015/09/08 by Helmut Lütkepohl, Anna Staszewska‐Bystrova, Peter Winker
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #Probabilistic and Robust Engineering Design
paper · doi:10.1111/obes.12114
openalex publication_date 2015/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Abstract In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. If they are based on the joint asymptotic distribution possibly constructed with bootstrap methods in a frequentist framework, often individual confidence intervals are simply connected to obtain the bands. Such bands are known to be too narrow and have a joint coverage probability lower than the desired one. If instead the Wald statistic is used and the joint bootstrap distribution of the impulse response coefficient estimators is taken into account and mapped into the band, it is shown that such a band is typically rather conservative. It is argued that, by using the Bonferroni method, a band can often be obtained which is smaller than the Wald band.