This paper presents and assesses a procedure to estimate conventional parameters characterizing fluctuations at the business cycle frequency, when the economic agents' information set is superior to the econometrician's one. Specifically, we first generalize the conditions under which the econometrician can estimate these `cyclical fluctuation' parameters from augmented laws of motion for forcing variables that fully recover the agents' superior information. Second, we document the econometric properties of the estimates when the augmented laws of motion are possibly misspecified. Third, we assess the ability of certain information criteria to detect the presence of superior information.