  We show that the existence of a martingale approximation of a stationary
process depends on the choice of the filtration. There exists a stationary
linear process which has a martingale approximation with respect to the natural
filtration, but no approximation with respect to a larger filtration with
respect to wich it is adapted and regular. There exists a stationary process
adapted, regular, and having a martingale approximation with respect to a given
filtration but not (regular and having a martingale approximation) with respect
to the natural filtration.
