Point and probabilistic forecast reconciliation for general linearly constrained multiple time series
一般线性约束多元时间序列的点预测与概率预测协调AI 解读 ↓
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一般线性约束多元时间序列的点预测与概率预测协调
- 研究问题
- 当多元时间序列受一般线性约束、不能直接区分上下层级时，如何统一表达预测协调，并使点预测和概率预测满足约束？
- 方法与思路
- 作者以自由变量和受约束变量替代传统层级划分，推导类似结构式的协调表达，建立概率预测框架并用于多口径 GDP 数据。
- 材料陈述的贡献
- 摘要称一般线性约束下仍可获得类似结构式的协调公式，并将框架用于澳大利亚及欧元区多口径、多国家 GDP 预测协调。
- 阅读关注点
- 应核对自由变量选取与约束矩阵条件、结构式和投影式的等价关系，以及概率预测协调的定义、分布处理与评价方法。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审及接收状态未核验；摘要未给预测精度或概率校准结果，满足约束本身不能证明预测更准。
原文摘要
Forecast reconciliation is the post-forecasting process aimed to revise a set of incoherent base forecasts into coherent forecasts in line with given data structures. Most of the point and probabilistic regression-based forecast reconciliation results ground on the so called "structural representation" and on the related unconstrained generalized least squares reconciliation formula. However, the structural representation naturally applies to genuine hierarchical/grouped time series, where the top- and bottom-level variables are uniquely identified. When a general linearly constrained multiple time series is considered, the forecast reconciliation is naturally expressed according to a projection approach. While it is well known that the classic structural reconciliation formula is equivalent to its projection approach counterpart, so far it is not completely understood if and how a structural-like reconciliation formula may be derived for a general linearly constrained multiple time series. Such an expression would permit to extend reconciliation definitions, theorems and results in a straightforward manner. In this paper, we show that for general linearly constrained multiple time series it is possible to express the reconciliation formula according to a "structural-like" approach that keeps distinct free and constrained, instead of bottom and upper (aggregated), variables, establish the probabilistic forecast reconciliation framework, and apply these findings to obtain fully reconciled point and probabilistic forecasts for the aggregates of the Australian GDP from income and expenditure sides, and for the European Area GDP disaggregated by income, expenditure and output sides and by 19 countries.