Abstract

This paper proposes a new asymptotically valid stationary bootstrap procedure to obtain multivariate forecast densities in unrestricted vector autoregressive models. The proposed method is not based on either backward or forward representations, so it can be used for both Gaussian and non-Gaussian models. Also, it is computationally more efficient compared to the available resampling methods. The finite sample performance of the proposed method is illustrated by extensive Monte Carlo studies as well as a real-data example. Our records reveal that the proposed method is a good competitor or even better than the existing methods based on backward and/or forward representations.

Highlights

  • Since the seminal paper of Sims (1980) vector autoregressive (VAR) models have received much attention in econometrics to analyze multivariate time series data

  • We conduct a simulation study to investigate the finite sample performance of our proposed stationary bootstrap (SB) forecast regions, and compare our results with the method proposed by Fresoli et al (2015)

  • We calculate the squared errors between the Bonferroni cubes obtained by the bootstrap methods and empirical Bonferroni cube to find out which bootstrap method has the best matched forecast region with the empirical one

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Summary

Introduction

Since the seminal paper of Sims (1980) vector autoregressive (VAR) models have received much attention in econometrics to analyze multivariate time series data. They provide a flexible framework for the analysis of complex dynamics, policy analysis, structural inference and forecasting. For the financial applications of VAR model please see Lütkepohl (1991), Campbell et al (1997), Culbertson (1996), Mills (1999), and Tsay (2001). We restricted our focus to the forecasting ability of VAR models. For example, Batchelor et al (2007), Gupta et al (2011), Baumeister and Kilian (2012), D’Agostino et al (2013), Kilian and Vigfusson (2013), and Hassani et al (2015) for recent studies on VAR model in econometric applications

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