Shelf-estuarine exchange along the Louisiana coast is known to be dominated by barotropic, tidal and sub-tidal exchanges. Simple regression of the estuarine salinities against Mississippi River discharge and cross-spectrum analysis do not produce a successful hindcast of the observations. Parsimonious auto-regressive, moving-average predictive models of the weekly-averaged salinity data are quite skillful in hindcasting the measurements. These models are generally consistent with a conceptual model in which Mississippi River discharge alters coastal salinities and this salinity signal propagates downcoast and then up-estuary.