ESTIMATING TIME-SERIES MODELS USING THE RELEVANT COST FUNCTION

In many forecasting problems, the forecast cost function is used only in evaluating the forecasts; a second cost function is used in estimat ing the parameters in the model. In this paper, I explore some of the ways in which the forecast cost function can be used in estimating the parameters and, more generally, in producing the forecasts. I define the optimal forecast and note that it may depend on the entire conditi onal distribution of the data, which is typically unknown. I then cons ider three of the steps involved in forming the forecast: approximatin g the optimal forecast, selecting the model, and estimating any unknow n parameters. The forecast cost function forms the basis of the approx imation, selection, and estimation. The methods are illustrated using time series models applied to 15 US macroeconomic series and in a smal l Monte Carlo experiment.