Forecasting multivariate time series under present-value model short- and long-run co-movement restrictions

Using a sequence of VAR-based nested multivariate models, we discuss the different layers of restrictions that are imposed on the VAR in levels by present-value models (PVM hereafter) for series that are subject to present-value restrictions. Our focus is novel: we are interested in the short-run restrictions entailed by PVMs (Vahid and Engle, 1993 and Vahid and Engle, 1997) and their implications for forecasting.

Using a well-known database, maintained by Robert Shiller, we implement a forecasting competition that imposes different layers of PVM restrictions. Our exhaustive investigation of several different multivariate models reveals that better forecasts can be achieved when restrictions are applied to the unrestricted VAR. Moreover, imposing short-run restrictions produces forecast winners 70% of the time for the target variables of PVMs and 63.33% of the time when all variables in the system are considered.