OPTIMALITY OF GLS FOR ONE-STEP-AHEAD FORECASTING WITH REGARIMA AND RELATED MODELS WHEN THE REGRESSION IS MISSPECIFIED
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回归误设时GLS在RegARIMA及相关模型一步预测中的最优性
- 研究问题
- 当时间序列的回归成分设定不足、扰动ARMA或ARIMA模型也可能错误时，GLS与OLS的一步预测表现如何比较？
- 方法与思路
- 作者在回归变量和扰动满足样本二阶矩相关条件的框架下，分析OLS与GLS均值估计的渐近偏差及其一步预测表现。
- 材料陈述的贡献
- 摘要称获得GLS相对OLS的一步预测最优性性质，并以回归估计的渐近偏差解释预测差异，为迟报数据插补提供理论支持。
- 阅读关注点
- 应核对最优性所采用的预测损失、GLS权重构造、二阶矩条件及差分处理，并检查理论与经济调查插补程序的对应关系。
- 阅读边界
- 仅依据所给出版社摘要；最优性的精确定义和完整条件未说明，不能将结论扩展到任意误设模型或多步预测。
原文摘要
We consider the modeling of a time series described by a linear regression component whose regressor sequence satisfies the generalized asymptotic sample second moment stationarity conditions of Grenander (1954, Annals of Mathematical Statistics 25, 252–272). The associated disturbance process is only assumed to have sample second moments that converge with increasing series length, perhaps after a differencing operation. The model's regression component, which can be stochastic, is taken to be underspecified, perhaps as a result of simplifications, approximations, or parsimony. Also, the autoregressive moving average (ARMA) or autoregressive integrated moving average (ARIMA) model used for the disturbances need not be correct. Both ordinary least squares (OLS) and generalized least squares (GLS) estimates of the mean function are considered. An optimality property of GLS relative to OLS is obtained for one-step-ahead forecasting. Asymptotic bias characteristics of the regression estimates are shown to distinguish the forecasting performance. The results provide theoretical support for a procedure used by Statistics Netherlands to impute the values of late reporters in some economic surveys.The author thanks two referees and the co-editor for comments and suggestions that led to substantial improvements in the exposition and also thanks John Aston and Tucker McElroy for helpful comments on an earlier draft. Any views expressed are the author's and not necessarily those of the U.S. Census Bureau.