This paper presents a weighted optimization framework that unifies the binary, multivalued, and continuous treatment—as well as mixture of discrete and continuous treatment—under a unconfounded treatment assignment. With a general loss function, the framework includes the average, quantile,...

It is well known that temporal aggregation has adverse effects on Granger causality tests. Time series are often sampled at different frequencies. This is typically ignored, and data are merely aggregated to the common lowest frequency. We develop a set of Granger causality tests that explicitly...