I have linear time series regression model where the dependent variable Y is bounded between 0 and 1.
Using classical unit root tests (dickey-fuller and kpss), results would make you conclude that Y is non-stationary (cannot reject $H_0$ in dickey-fuller and kpss rejects).
However, at the same time the mean of Y cannot be infinite since it is bounded; and I assume that for the same reason neither the variance can (right?).
Recalling the definition of weak stationarity, I am probably missing something related to the autocovariances of Y as well - they should depend only on the lag, but I have no formal test for this.
Is then Y really non-stationary because of unit-root, even if it is bounded?