Efficient computation of hierarchical trends

To model a large database containing selling prices for houses, in which local trends, general trends, and specific characteristics play a role, we derived a new procedure to implement a state-space model for repeated measurements. The original model is decomposed into two parts, which are treated differently. The first part is ordinary least squares on data in deviation from means. This step provides a prior for coefficients to be used in the second step, which is a Kalman filter, providing estimates of the trends and the parameters. The procedure exploits and illustrates the Bayesian interpretation of a Kalman filter.