Despite an extraordinary level of debate about the concept of `causality' and establishing causal links, Granger (1969)  proposed an approach based on the arrow of time and the eects of eliminating the history of some variables from the joint distribution of all variables.
There was no Granger causality from the eliminated variables if the conditional and marginal distributions of the remaining variables were the same. In practice, the non-operational nature of his denition was nessed by testing whether dropping a subset of variables from a larger set aected the goodness of t of models of the remaining variables. This paper notes the drawbacks that arise from such a route to making his concept of causality operational, but also emphasises its pervasive role in econometric modelling of time series.
Hendry, D. F. (2017). ‘Granger Causality’. European Journal of Pure and Applied Mathematics, 10, 12-29.