Cross-temporal probabilistic forecast reconciliation: Methodological and practical issues
横截面与时间联合概率预测协调：方法与实践问题AI 解读 ↓
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横截面与时间联合概率预测协调：方法与实践问题
- 研究问题
- 对于同时受到横截面加总和时间聚合约束的多元序列，如何把不一致的概率预测转为一致预测，并处理高维预测误差协方差？
- 方法与思路
- 作者扩展概率预测协调框架，使用高斯参数法和自助法抽样，并提出多步残差、重叠残差及四种协方差构造方案。
- 材料陈述的贡献
- 摘要称，模拟及澳大利亚GDP、旅游需求实验展示方法表现；两项应用中，最优协调方案在两种概率评分上优于基础预测。
- 阅读关注点
- 应核对协调变换如何保证联合约束、协方差方案的适用条件，以及多步残差的构造和评分比较是否采用一致的预测评估设计。
- 阅读边界
- 这是arXiv预印本，同行评审或接收状态未核实；摘要未提供评分改善幅度、显著性检验细节或普遍优势条件，结论限于所述实验。
原文摘要
Forecast reconciliation is a post-forecasting process that involves transforming a set of incoherent forecasts into coherent forecasts which satisfy a given set of linear constraints for a multivariate time series. In this paper we extend the current state-of-the-art cross-sectional probabilistic forecast reconciliation approach to encompass a cross-temporal framework, where temporal constraints are also applied. Our proposed methodology employs both parametric Gaussian and non-parametric bootstrap approaches to draw samples from an incoherent cross-temporal distribution. To improve the estimation of the forecast error covariance matrix, we propose using multi-step residuals, especially in the time dimension where the usual one-step residuals fail. To address high-dimensionality issues, we present four alternatives for the covariance matrix, where we exploit the two-fold nature (cross-sectional and temporal) of the cross-temporal structure, and introduce the idea of overlapping residuals. We assess the effectiveness of the proposed cross-temporal reconciliation approaches through a simulation study that investigates their theoretical and empirical properties and two forecasting experiments, using the Australian GDP and the Australian Tourism Demand datasets. For both applications, the optimal cross-temporal reconciliation approaches significantly outperform the incoherent base forecasts in terms of the Continuous Ranked Probability Score and the Energy Score. Overall, the results highlight the potential of the proposed methods to improve the accuracy of probabilistic forecasts and to address the challenge of integrating disparate scenarios while coherently taking into account short-term operational, medium-term tactical, and long-term strategic planning.