This paper presents a new approach to constructing multistep combination forecasts in a nonstationary framework with stochastic and deterministic trends. Existing forecast combination approaches in the stationary setup typically target the in-sample asymptotic mean squared error (AMSE), relying on its approximate equivalence with the asymptotic forecast risk (AFR). Such equivalence, however, breaks down in a nonstationary setup. This paper develops combination forecasts based on minimizing an accumulated prediction errors (APE) criterion that directly targets the AFR and remains valid whether the time series is stationary or not. We show that the performance of APE-weighted forecasts is close to that of the optimal, infeasible combination forecasts. Simulation experiments are used to demonstrate the finite sample efficacy of the proposed procedure relative to Mallows/Cross-Validation weighting that target the AMSE as well as underscore the importance of accounting for both persistence and lag order uncertainty. An application to forecasting US macroeconomic time series confirms the simulation findings and illustrates the benefits of employing the APE criterion for real as well as nominal variables at both short and long horizons. A practical implication of our analysis is that the degree of persistence can play an important role in the choice of combination weights.

中文翻译：

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随机和确定性趋势的多步预测平均


本文提出了一种在具有随机和确定性趋势的非平稳框架中构建多步组合预测的新方法。固定设置中的现有预测组合方法通常以样本内渐近均方误差 (AMSE) 为目标，依赖于其与渐近预测风险 (AFR) 的近似等价性。然而，这种等价性在非平稳设置中就会失效。本文开发了基于最小化累积预测误差 (APE) 标准的组合预测，该标准直接针对 AFR，并且无论时间序列是否平稳，都保持有效。我们表明，APE 加权预测的性能接近于最优、不可行组合预测的性能。模拟实验用于证明所提出的程序相对于针对 AMSE 的 Mallows/交叉验证权重的有限样本功效，并强调考虑持久性和滞后阶不确定性的重要性。预测美国宏观经济时间序列的应用证实了模拟结果，并说明了在短期和长期范围内对实际变量和名义变量采用 APE 标准的好处。我们分析的一个实际意义是，持久性程度可以在组合权重的选择中发挥重要作用。