There are two gaps in the literature: (1) there has been no effort yet considering the black-box productive process, through which financial ratio-inputs are turned into financial ratio-outputs; (2) the previous studies have not yet considered the underlying temporal dependence embedded in the input/output set. Filling in the first gap would contribute to the literature from the methodological perspective, while addressing the second issue is supposed to provide more robust efficiency results. In correspondence to these two gaps, we propose an innovative DEA-Ratio model for undesirable financial output ratios considering weak disposability. In addition, we employ the generalized Auto-Regressive Moving Average model to analyze temporal dependence in the input/output set, which allows us to project the efficiency levels five year ahead. We apply our proposed method to a sample of 124 OECD banks over a twelve-year time window.