Quantifying Time-Varying Forecast Uncertainty and Risk for the Real Price of Oil

We propose a novel and numerically efficient quantification approach to forecast uncertainty of the real price of oil using a combination of probabilistic individual model forecasts. Our combination method extends earlier approaches that have been applied to oil price forecasting, by allowing for sequentially updating of time-varying combination weights, estimation of time-varying forecast biases and facets of miscalibration of individual forecast densities and time-varying inter-dependencies among models. To illustrate the usefulness of the method, we present an extensive set of empirical results about time-varying forecast uncertainty and risk for the real price of oil over the period 1974–2018. We show that the combination approach systematically outperforms commonly used benchmark models and combination approaches, both in terms of point and density forecasts. The dynamic patterns of the estimated individual model weights are highly time-varying, reflecting a large time variation in the relative performance of the various individual models. The combination approach has built-in diagnostic information measures about forecast inaccuracy and/or model set incompleteness, which provide clear signals of model incompleteness during three crisis periods. To highlight that our approach also can be useful for policy analysis, we present a basic analysis of profit-loss and hedging against price risk.

本研究提出一种新颖且数值高效的量化方法，通过融合概率个体模型预测（probabilistic individual model forecasts），对实际油价（real price of oil）的预测不确定性开展量化分析。相较于此前应用于油价预测（oil price forecasting）的各类既有方法，本文所提出的融合方法具备多项拓展性改进：支持对时变组合权重（time-varying combination weights）进行序贯更新，可估计时变预测偏差（time-varying forecast biases）、个体预测密度的校准失当（miscalibration of individual forecast densities）维度，以及模型间的时变相互依赖性（time-varying inter-dependencies among models）。为验证该方法的应用价值，本文针对1974年至2018年期间的实际油价，围绕时变预测不确定性与风险主题，呈现了一系列丰富的实证结果。研究表明，无论在点预测（point forecast）还是密度预测（density forecast）维度，该融合方法均系统性优于主流基准模型（benchmark models）与传统融合方法。估计得到的个体模型权重呈现高度时变的动态特征，反映出各类个体模型的相对表现随时间发生大幅波动。该融合方法内置了针对预测偏差与/或模型集合不完备性（model set incompleteness）的诊断指标，可在三次危机时段中清晰发出模型不完备的预警信号。为进一步凸显本方法在政策分析领域的应用潜力，本文还开展了针对损益核算与价格风险对冲（hedging against price risk）的基础分析。