Speculative trading stems from disagreements among traders. Besides the approaches based on the existence of private information (and noise traders) or the dierences of opinions, Harrison and Kreps(1978) and Morris(1996) relied on the presence of diverse beliefs to explain speculative phenomena. This paper proposes a new model of speculative trading by introducing rational beliefs of Kurz(1994) and Kurz and Wu(1996). Agents hold diverse beliefs which are rational” in the sense of being compatible with observed data. In a non-stationary environment the agents may learn only about the stationary measure of observed data. Agents’ beliefs can be non-stationary and diverse even when their stationary measures become the same as that of the data with complete learning.In a Markovian framework of dividends and beliefs, we obtainanalytical results on how the speculative premium depends on the extent of heterogeneity of beliefs. In addition, we demonstrate the possible emergence of endogenous uncertainty (as dened by Kurz and Wu(1996)) and the persistent presence of diverse beliefs and positive speculative premiums.