A note on multiple time series model selection

Abstract

In this paper we suggest a graphical tool for multiple time series modelling with an application in macroeconomics. The asymptotic distribution of the adjusted residual traces introduced in \cite[Velilla and Nguyen]{Santiago2019} is examined and further developed. We propose critical bands of the adjusted residual traces as a useful tool in model selection. An advantage of the method is that visual displays of the critical bands and plots of the adjusted residual traces can assist in selecting a proper multiple time series model. This technique is less dependent on the choice of lag. Several simulations, examples and an application with German time series are included