The Effect of Aggregation on Prediction in the Autoregressive Model

Abstract

Abstract The article shows that if the original variable follows a pth order autoregressive system then the non-overlapping moving sum follows a pth order autoregression with at most a pth order moving-average of an independent sequence regardless of the length of the summation. From such an aggregate model we derive the optimal predictor of the aggregate variable and show that it performs remarkably well compared to the optimal disaggregate predictor. The article contains both theoretical and numerical analysis.