Comparison of Methods for Constructing Joint Confidence Bands for Impulse Response Functions

Abstract

Abstract. In vector autoregressive analysis confidence intervals for individual impulse responses are typically reported to indicate the sampling uncertainty in the estimation results. A range of methods are reviewed and a new proposal is made for constructing joint confidence bands, given a prespecified coverage level, for the impulse responses at all horizons considered simultaneously. The methods are compared in a simulation experiment and recommendations for empirical work are provided.

Skewness-adjusted bootstrap confidence intervals and confidence bands for impulse response functions

“…The bootstrap algorithm given below includes optional steps for conducting a bias correction or a skewness adjustment or both. Aside from the mirroring steps, the bootstrap procedure described here is in large parts similar to that in Kilian (1998a,b) as well as to that in Lütkepohl et al (2015a). The bootstrap procedure is given in Algorithm 1.…”

“…Furthermore, we construct five types of joint confidence bands. The bands are constructed based on the Bonferroni adjusted (Ba) method introduced in Lütkepohl et al (2015a). Out of the different possibilities given in the literature, the Ba method is chosen here because it was shown to work well in previous studies.…”

“…The envelope of the remaining (1−a)B functions represents the Ba band. For a more detailed discussion of the Ba method see Staszewska-Bystrova and Winker (2014) and Lütkepohl et al (2015a). If the Ba bands are computed based on IRFs obtained with the bias corrected bootstrap, the bands are labelled Efron-Kilian (EK) bands.…”

Monte Carlo Analysis of Forecast Error Variance Decompositions under Alternative Model Identification Schemes

“…In the VAR context, estimation uncertainty is usually depicted using confidence intervals or bands (see e.g. Staszewska, 2007;Lütkepohl, Staszewska-Bystrova, Winker, 2015a;2015b). Larger estimation accuracy implies narrower and hence more informative confidence regions.…”

Wild bootstrap tests for autocorrelation in vector autoregressive models

“…Kilian (1998a, b), Kilian (1999), Lütkepohl (2000Lütkepohl ( , 2013, Benkwitz et al (2001), Lütkepohl et al (2015) for impulse response analysis, and for cointegration rank determination, van Giersbergen (1996), Swensen (2006Swensen ( , 2009, Ahlgren and Antell (2008), Cavaliere et al (2012). Inference based on the conventional IID bootstrap may be misleading in the presence of (conditional) heteroskedasticity.…”