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This paper proposes a modified version of support vector machines (SVMs), called ϵ-descending support vector machines (ϵ-DSVMs), to model non-stationary financial time series. The ϵ-DSVMs are obtained by incorporating the problem domain knowledge – non-stationarity of financial time series into SVMs. Unlike the standard SVMs which use a constant tube in all the training data points, the ϵ-DSVMs use an adaptive tube to deal with the structure changes in the data. The experiment shows that the ϵ-DSVMs generalize better than the standard SVMs in forecasting non-stationary financial time series. Another advantage of this modification is that the ϵ-DSVMs converge to fewer support vectors, resulting in a sparser representation of the solution.