Multistep ahead forecasting of vector time series
发展了向量时间序列多步超前预测的理论，适用于非平稳和协整数据，给出了半无限过去和有限样本下的预测公式，并通过欧元区宏观数据、生育率回溯、长期通胀和区域住房开工四个案例展示了其灵活性。
This article develops the theory of multistep ahead forecasting for vector time series that exhibit temporal nonstationarity and co-integration. We treat the case of a semi-infinite past by developing the forecast filters and the forecast error filters explicitly. We also provide formulas for forecasting from a finite data sample. This latter application can be accomplished by using large matrices, which remains practicable when the total sample size is moderate. Expressions for the mean square error of forecasts are also derived and can be implemented readily. The flexibility and generality of these formulas are illustrated by four diverse applications: forecasting euro area macroeconomic aggregates; backcasting fertility rates by racial category; forecasting long memory inflation data; and forecasting regional housing starts using a seasonally co-integrated model.