Forecasting brand sales with wavelet decompositions of related causal series

We consider methods for forecasting brand sales utilising wavelet decompositions of related causal series. Wavelet decompositions can uncover the hidden periodicities inherent in marketing time series like pricing and can therefore provide superior information in causal sales forecasting methods. We specifically address the problem of multicollinearity since the proposed wavelet packet transformation of a time series of length T, generates 2T – 2 correlated vectors of coefficients, each of length T. We find that partial least-squares provide the most accurate forecasting method which at the same time achieves the desired dimension reduction in the estimation problem.