This paper puts forth a concept of Adptivety Rational Equilibrium (A.R.E) where agents base decisions upon predictions of future values of endogenous variables whose actual values are determined by equilibrium equations.

The simulation result of Nunes, Kuan, and Newbold suggests that it is possible to estimate a spurious break for a regression model with I(1) disturbances. In this note, we provide a rigorous proof for this phenomenon.