Common learning with intertemporal dependence

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. Will the agents commonly learn the value of the parameter, i.e., will the true value of the parameter become approximate common-knowledge? If the signals are independent and identically distributed across time (but not necessarily across agents), the answer is yes (Cripps et al., Econometrica, 76(4):909–933, 2008). This paper explores the implications of allowing the signals to be dependent over time. We present a counterexample showing that even extremely simple time dependence can preclude common learning, and present sufficient conditions for common learning.