Modelling multiple REIT indices using TAR models based on aggregation functions

The aim of this paper is to compare descriptive and predictive qualities of multivariate TAR models with threshold variables obtained via aggregation functions versus one-dimensional TAR models with endogenous as well as exogenous threshold variables. Time series of REIT indexes of 5 selected G7 countries (USA, Japan, Great Britain, France, Canada) were modelled. They manifest similar behaviour in the considered time period, January 1, 2000-May 8, 2012, divided into 3 sub-periods determined by the recent global financial markets crisis (July 1, 2008-April 30, 2009). The multivariate TAR models with threshold variables constructed via aggregation functions have in all cases better descriptive properties and in most cases they also show better prediction properties. A new subclass of those models, based on the OMA type of aggregation functions, exhibit promising properties both with respect to their descriptive and predictive performance.