Constructing Joint Confidence Bands for Impulse Response Functions of VAR Models: A Review

Abstract

Methods for constructing joint confidence bands for impulse response functions which are commonly used in vector autoregressive analysis are reviewed. While considering separate intervals for each horizon individually still seems to be the most common approach, a substantial number of methods have been proposed for making joint inferences about the complete impulse response paths up to a given horizon. A structured presentation of these methods is provided. Furthermore, existing evidence on the small-sample performance of the methods is gathered. The collected information can help practitioners to decide on a suitable confidence band for a structural VAR analysis.

Bootstrap VAR forecasts: The effect of model uncertainties

“…In this paper, instead of pursuing a comparison across different forecast regions, we aim to assess how different sources of uncertainty affect the empirical coverages of the Bonferroni forecast cubes. It is also worth mentioning the growing literature that analyzes methods to construct confidence paths, either for impulse response coefficients or out‐of‐sample forecasts; see, for example, Lütkepohl et al (2015), Bruder and Wolf (2018) and Lütkepohl et al (2020). Identifying and assessing the different sources of uncertainty are critical to the construction of forecast regions or paths with a certain nominal coverage.…”