Rational expectations must not be expected to change. Hence, a rational expectation about a future random quantity follows a pure martingale until the uncertainty is resolved. This implies that the expectation itself could be non-stationary and, in fact, is non-stationary if the increments are iid. Most asset prices are functions of expectations about future quantities, so asset prices also could be non-stationary. This has consequences for tests based on prices rather than on returns.