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The multidimensional blast furnace system is one of the most complex industrial systems and, as such, there are still many unsolved theoretical and experimental difficulties, such as silicon prediction and blast furnace automation. For this reason, this paper is concerned with developing data-driven models based on the Volterra series for this complex system. Three kinds of different low-order Volterra filters are designed to predict the hot metal silicon content collected from a pint-sized blast furnace, in which a sliding window technique is used to update the filter kernels timely. The predictive results indicate that the linear Volterra predictor can describe the evolvement of the studied silicon sequence effectively with the high percentage of hitting the target, very low root mean square error and satisfactory confidence level about the reliability of the future prediction. These advantages and the low computational complexity reveal that the sliding-window linear Volterra filter is full of potential for multidimensional blast furnace system. Also, the lack of the constructed Volterra models is analyzed and the possible direction of future investigation is pointed out.