Bootstrap prediction bands for forecast paths from vector autoregressive models

Abstract

The problem of forecasting from vector autoregressive models has attracted considerable attention in the literature. The most popular non-Bayesian approaches use either asymptotic approximations or bootstrapping to evaluate the uncertainty associated with the forecast. The practice in the empirical literature has been to assess the uncertainty of multi-step forecasts by connecting the intervals constructed for individual forecast periods. This paper proposes a bootstrap method of constructing prediction bands for forecast paths. The bands are constructed from forecast paths obtained in bootstrap replications using an optimization procedure to fi nd the envelope of the most concentrated paths. From extensive Monte Carlo study, it is found that the proposed method provides more accurate assessment of predictive uncertainty from the vector autoregressive model than its competitors.

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

“…It has been recognized that a rigorous econometric analysis often requires, besides the path forecast, a joint prediction region that contains the whole future path with a prespecified coverage probability. This paper investigates the finite-sample performance of the methods of constructing joint prediction regions of Jordà and Marcellino (2010), Staszewska-Bystrova (2011) and Wolf and Wunderli (2015) in various scenarios through a MC study. The finite-sample performance of the asymptotic method of Jordà and Marcellino (2010) is clearly inferior to the bootstrap-based methods of Staszewska-Bystrova (2011) and Wolf and Wunderli (2015).…”

“…However, the Euclidian norm seems to works better according to the simulation study in Staszewska-Bystrova (2011).…”

“…The method is on the one hand based on the assumption that the conditional distribution of the prediction errors is asymptotically normal and on the other hand on the application of results by Scheffé (1953Scheffé ( , 1959 and Bowden (1970). Staszewska-Bystrova (2011) proposes a heuristic bootstrap-based method. The joint prediction region with coverage probability (1−α) is constructed as the envelope of the remaining (1−α)% of generated conditional bootstrap paths that survived a heuristic iterative elimination procedure.…”

“…In this paper, the finite-sample performance of the methods of Jordà and Marcellino (2010), 1 The method of Staszewska-Bystrova and Winker (2013) is basically a refinement of Staszewska-Bystrova (2011). However, the computational burden is enormous and yet the performance is generally inferior to the one of Staszewska-Bystrova (2011); for details see Staszewska-Bystrova and Winker (2013, Section 4).…”

“…However, the computational burden is enormous and yet the performance is generally inferior to the one of Staszewska-Bystrova (2011); for details see Staszewska-Bystrova and Winker (2013, Section 4). Thus, the method of Staszewska-Bystrova and Winker (2013) is omitted from our following performance analysis.…”