Bootstrapping impulse responses of structural vector autoregressive models identified through GARCH

Abstract

Different bootstrap methods and estimation techniques for inference for structural vector autoregressive (SVAR) models identified by generalized autoregressive conditional heteroskedasticity (GARCH) are reviewed and compared in a Monte Carlo study. The bootstrap methods considered are a wild bootstrap, a moving blocks bootstrap and a GARCH residual based bootstrap. Estimation is done by Gaussian maximum likelihood, a simplified procedure based on univariate GARCH estimations and a method that does not re-estimate the GARCH parameters in each bootstrap replication. The latter method is computationally more efficient than the other methods and it is competitive with the other methods and often leads to the smallest confidence sets without sacrificing coverage precision. An empirical model for assessing monetary policy in the U.S. is considered as an example. It is found that the different inference methods for impulse responses lead to qualitatively very similar results.

Cryptocurrency shocks

“…Andersen et al. (2007), Lutkepohl and Schlaak (2019) and Bertsche and Braun (2020). However, as demonstrated in Rigobon and Sack (2003), the estimates are consistent even under some misspecification of the heteroskedasticity.…”

“…It is possible that the time-varying conditional second moment and the specification in Equation (2) may not fully capture the long memory dependence-see, e.g. Andersen et al (2007), Lutkepohl and Schlaak (2019) and Bertsche and Braun (2020). However, as demonstrated in Rigobon and Sack (2003), the estimates are consistent even under some misspecification of the heteroskedasticity.…”

An Alternative Bootstrap for Proxy Vector Autoregressions

“…It can cope, for example, with conditional heteroskedastic (ARCH) VAR errors which is an advantage in many applied studies where financial data are of interest. On the other hand, Lütkepohl and Schlaak (2019) demonstrate by simulations that the MBB can result in confidence intervals with low coverage rates in small samples.…”

svars: An R Package for Data-Driven Identification in Multivariate Time Series Analysis

“…As described in Section 3.6 there is no consensus in the literature about the optimal block length in finite samples. In applied work, however, a typical block length is about 10% of the sample size (see, e.g., Brüggemann et al 2016;Lütkepohl and Schlaak 2019). The wild bootstrap method is implemented as wild.boot(x, design = "fixed", distr = "rademacher", n.ahead = 20, nboot = 500, nc = 1, dd = NULL, signrest = NULL, itermax = 300, steptol = 200, iter2 = 50)…”