Linear prediction of temporal aggregates under model misspecification

This paper aims to demonstrate a possible aggregation gain in predicting future aggregates under a practical assumption of model misspecification. Empirical analysis of a number of economic time series suggests that the use of the disaggregate model is not always preferred over the aggregate model in predicting future aggregates, in terms of an out-of-sample prediction root-mean-square error criterion. One possible justification of this interesting phenomena is model misspecification. In particular, if the model fitted to the disaggregate series is misspecified (i.e., not the true data generating mechanism), then the forecast made by a misspecified model is not always the most efficient. This opens up an opportunity for the aggregate model to perform better. It will be of interest to find out when the aggregate model helps. In this paper, we study a framework where the underlying disaggregate series has a periodic structure. We derive and compare the efficiency loss in linear prediction of future aggregates using the adapted disaggregate model and aggregate model. Some scenarios for aggregation gain to occur are identified. Numerical results show that the aggregate model helps over a fairly large region in the parameter space of the periodic model that we studied.