This paper analyses the predictability of a hypothetical market with freely negotiated prices on which exists a censoring of one-period returns which are in excess of an arbitrary level (‘floor’ and ‘ceiling’). It is shown that the expected value of returns (adjusted for drift) conditional on last period information regarding the censoring are equal to zero (and therefore the market is not predictable in mean) if there is no intertemporal spillover on the market. A simple simulation model is proposed and applied for the analysis of the effects of intertemporal and cross-spillovers resulting from quantity constraints. Statistical predictability tests are proposed, based on the corrected student-t statistic of a regression of returns of some information concerning the previous censoring. An illustrative empirical analysis of six main time series of returns on the warsaw stock exchange confirms their ex-ante, but not ex-post, predictability.