Estimating time series models using the relevant cost function
探讨在时间序列预测中，如何将预测成本函数用于参数估计、模型选择和预测生成，并通过美国宏观经济数据和蒙特卡洛实验展示方法。
In many forecasting problems, the forecast cost function is used only in evaluating the forecasts; a second cost function is used in estimating 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 conditional distribution of the data, which is typically unknown. I then consider three of the steps involved in forming the forecast: approximating the optimal forecast, selecting the model, and estimating any unknown parameters. The forecast cost function forms the basis of the approximation, selection, and estimation. The methods are illustrated using time series models applied to 15 US macroeconomic series and in a small Monte Carlo experiment.