This paper develops a new approach to forecasting a highly persistent time series that employs feasible generalized least squares (FGLS) estimation of the deterministic components in conjunction with Mallows model averaging. Within a local-to-unity asymptotic framework, we derive analytical expressions for the asymptotic mean squared error and one-step-ahead mean squared forecast risk of the proposed estimator and show that the optimal FGLS weights are different from their ordinary least squares (OLS) counterparts. We also provide theoretical justification for a generalized Mallows averaging estimator that incorporates lag order uncertainty in the construction of the forecast. Monte Carlo simulations demonstrate that the proposed procedure yields a considerably lower finite-sample forecast risk relative to OLS averaging. An application to U.S. macroeconomic time series illustrates the efficacy of the advocated method in practice and finds that both persistence and lag order uncertainty have important implications for the accuracy of forecasts.

中文翻译：

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单位根近似的自回归的广义预测平均

本文开发了一种新的方法来预测高度持久的时间序列，该方法采用对确定性成分的可行广义最小二乘（FGLS）估计与Mallows模型平均相结合的方法。在局部到整体渐近框架内，我们推导了拟议估计量的渐进均方误差和一步一步均方预测风险的解析表达式，并表明最佳FGLS权重不同于其普通最小二乘（OLS ）同行。我们还为广义的Mallows平均估计器提供了理论依据，该估计器在预测的构建中纳入了滞后阶不确定性。蒙特卡洛模拟表明，相对于OLS平均而言，所提出的程序所产生的有限样本预测风险要低得多。到美国的申请