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.

Focused information criterion for locally misspecified vector autoregressive models

“…We have displayed the results for the response of variable 1 to a structural shock in the variable 1 for horizons 2 and 6. The DGP is given in Equation ( which is similar to the VAR used in Lütkepohl et al (2015) for impulse response analyses. This process has the same roots as the univariate process of Equation (3.1) but with double multiplicity.…”

“…A naive Cartesian product of the individual con dence intervals leads to severe undercoverage, whereas con dence bands based on the Bonferroni inequality have good coverage but are at the same time excessively wide. O en considered alternatives are bootstrap methods, e.g., Kilian (2001), Lütkepohl et al (2015), and Bruder and Wolf (2017).…”

Estimation of structural impulse responses: short-run versus long-run identifying restrictions

“…This type of DGP has been used in a number of other studies of estimation and inference properties of structural impulse responses (see Kilian (1998), Lütkepohl, Staszewska-Bystrova and Winker (2015a, 2015b). The parameter α 11 determines the persistence of the process.…”

Bootstrap multi-step forecasts of non-Gaussian VAR models

“…In this way, we follow Runkle (1987) when generating the bootstrap replicates used to estimate the parameters and use the forward instead of the BR. The forward algorithm for obtaining bootstrap replicates of Y T +h is a direct generalization of the algorithm proposed by Pascual et al (2004a); see Lütkepohl et al (2015), Staszewska-Bystrova and Winker (2013) and Wolf and Wunderli (2012) for implementations of the forward bootstrap for obtaining path forecasts in VAR models.…”

“…Finally, using arguments put forward by Pascual, Romo, and Ruiz (2004a) in the context of univariate ARIMA models, one can implement simple bootstrap procedures that incorporate the parameter uncertainty without requiring the BR. For example, Lütkepohl, Staszewska-Bystrova, and Winker (2015), Staszewska-Bystrova and Winker (2013) and Wolf and Wunderli (2012) implement the bootstrap procedure originally described by Pascual, Ruiz, and Fresoli (2011) 1 for constructing bands for forecast paths. It is important to note that the forward bootstrap procedure implemented in these papers is closely related to the bootstrap procedure proposed by Kilian (1998a,b,c) for the construction of confidence bands in the context of impulse response functions.…”