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Multivariate Subset Autoregressive Modelling with Zero Constraints for Detecting 'Overall Causality' - Financial and Economic Forecasting (Chapter 4)

The necessary and sufficient condition to test for 'overall causality', i.e., the presence of Granger-causality and instantaneous causal relations, in a bivariate and trivariate autoregressive model with recursive form is discussed. It is argued that the conventional AR model (the reduced form AR) is a more straightforward and effective means of testing for 'overall causality'. To detect instantaneous causality it is proposed to select the best subset system in a residual regression system in conjunction with model selection criteria. The Canadian money-income-bank rate system is re-examined in this way and by using a previously proposed algorithm we identify the optimum multivariate subset AR with constraints to detect whether there is 'overall causality' in that system.