This paper is concerned with the case of an exogenous system in which a model is required to forecast a periodic output time series using a causal input. A novel approach is developed in which the wavelet packet transform is taken of both the dependent time series and causal input. This results in two sets of basis dictionaries and requires two bases to be chosen. It is proposed that the best bases to choose are those which maximize the mutual information. Input selection is then implemented by eliminating those coefficients of the selected input basis with low mutual information. As an example, a model is constructed to forecast short-term electrical demand.