Seasonality on non-linear price effects in scanner-data based market-response models

Scanner data for fast moving consumer goods typically amount to panels of time series where both N and T are large. To reduce the number of parameters and to shrink parameters towards plausible and interpretable values, multi-level models turn out to be useful. Such models contain in the second level a stochastic model to describe the parameters in the first level. In this paper we propose such a model for weekly scanner data where we explicitly address (i) weekly seasonality in a limited number of yearly data and (ii) non-linear price effects due to historic reference prices. We discuss representation and inference and we propose an estimation method using Bayesian techniques. An illustration to a market-response model for 96 brands for about 8 years of weekly data shows the merits of our approach.