Forecasting Vector ARMA Processes With Systematically Missing Observations
比较两种预测方法：基于完整序列建模与基于系统缺失观测序列建模，发现前者在均方误差意义上通常更优，但存在例外情况，并用经济时间序列示例说明。
Abstract The following two predictors are compared for time series with systematically missing observations: (a) A time series model is fitted to the full series Xt , and forecasts are based on this model, (b) A time series model is fitted to the series with systematically missing observations Y τ, and forecasts are based on the resulting model. If the data generation processes are known vector autoregressive moving average (ARMA) processes, the first predictor is at least as efficient as the second one in a mean squared error sense. Conditions are given for the two predictors to be identical. If only the ARMA orders of the generation processes are known and the coefficients are estimated, or if the process orders and coefficients are estimated, the first predictor is again, in general, superior. There are, however, exceptions in which the second predictor, using seemingly less information, may be better. These results are discussed, using both asymptotic theory and small sample simulations. Some economic time series are used as illustrative examples. KEY WORDS: Aggregation of stock variablesModel specificationMultiple time seriesForecast mean squared errorForecast efficiency