Bootstrap multi-step forecasts of non-Gaussian VAR models

Abstract

a b s t r a c tIn this paper, we establish the asymptotic validity and analyse the finite sample performance of a simple bootstrap procedure for constructing multi-step multivariate forecast densities in the context of non-Gaussian unrestricted VAR models. This bootstrap procedure avoids the backward representation, and, as a consequence, can be used to obtain multivariate forecast densities in, for example, VARMA or VAR-GARCH models. In the context of bivariate stationary VAR(p) models, we show that its finite sample properties are comparable to those of alternatives based on the backward representation. The bootstrap procedure is also implemented in a VAR-DCC model which lacks a backward representation. Finally, joint forecast densities of US quarterly inflation, unemployment and GDP growth are obtained.

Calculating joint confidence bands for impulse response functions using highest density regions

“…Obviously, an operationalization of this concept is not straightforward in higher dimensions. In Fresoli et al (2015), the authors use highest density regions to illustrate the joint predictive distribution for two variables. The method has been proposed by Hyndman (1996).…”

Calculating Joint Confidence Bands for Impulse Response Functions Using Highest Density Regions

“…In Fresoli et al (2015), the authors use highest density regions to illustrate the joint predictive distribution for two variables. The method has been proposed by Hyndman (1996).…”

“…In this paper, we use the highest density region (HDR) approach proposed by Hyndman (1995Hyndman ( , 1996 and also discussed in the context of VAR analysis in Fresoli et al (2015). In contrast to the Wald approach, for this non-parametric method, the scaling of the variables or error terms, respectively, might influence the outcome.…”

Comparing Several Methods to Compute Joint Prediction Regions for Path Forecasts Generated by Vector Autoregressions

“…. , y * T +H , used for the methods of Staszewska-Bystrova (2011) and Wolf and Wunderli (2015), are generated by the following four-step bootstrap procedure of Fresoli et al (2015) Step 1: Givenβ BC LS , {y t } T t=1 and the corresponding series of centered and rescaled 9 residuals {ˆ t } T t=p+1 , generate a bootstrap sample {y * 1 , . .…”

“…The bootstrap procedure of Fresoli et al (2015) is asymptotically valid under some regularity conditions, that is, the difference betweenŶ * T,H,i and Y T,H,i converges in distribution to 0 as T → ∞, for the proof see Fresoli et al (2015, p.839).…”