Content Horizons For Forecasts Of Economic Time Series

We consider the problem of determining the horizon beyond which forecasts from time series models of stationary processes add nothing to the forecast implicit in the conditional mean. We refer to this as the content horizon for forecasts, and define a forecast content function at horizons s = 1,... S as the proportionate reduction in mean squared forecast error available from a time series forecast relative to the unconditional mean. This function depends upon parameter estimation uncertainty as well as on autocorrelation structure of the process under investigation. We give an approximate expression (to o(1/T)) for the forecast content function at s for a general autoregressive process, and show by simulation that the expression gives a good approximation even at modest sample sizes. Finally we consider parametric and non-parametric (kernel) estimators of the empirical forecast content function, and apply the results to forecast horizons for inflation and the growth rate of GDP, in U.S. and Canadian data.