High-Dimensional Forecasting in the Presence of Unit Roots and Cointegration

Abstract

We investigate how the possible presence of unit roots and cointegration affects forecasting with Big Data. As most macroeoconomic time series are very persistent and may contain unit roots, a proper handling of unit roots and cointegration is of paramount importance for macroeconomic forecasting. The high-dimensional nature of Big Data complicates the analysis of unit roots and cointegration in two ways. First, transformations to stationarity require performing many unit root tests, increasing room for errors in the classification. Second, modelling unit roots and cointegration directly is more difficult, as standard high-dimensional techniques such as factor models and penalized regression are not directly applicable to (co)integrated data and need to be adapted. We provide an overview of both issues and review methods proposed to address these issues. These methods are also illustrated with two empirical applications.