Improving the forecast accuracy of provisional data: an application of the Kalman filter to retail sales estimates

If forecasts of economic activity are to rely on preliminary data, the predictable component of the data revisions should be taken into account. This paper applies the Kalman filter to improve the forecast accuracy of published preliminary estimates of retail sales. Successive estimates of retail sales are modeled jointly as a vector autoregressive process, incorporating panel rotation and calendar effects. Estimates of retail sales based on this model are then combined with the raw Census estimates via the Kalman filter. This technique, which may be applied to other bodies of data, yields a significant improvement in the efficiency of the raw Census data, reducing the mean-squared error by about 1/3.