Python中用于相关矩阵与协方差矩阵预测的矩阵感知真评分规则及显著性检验
Matrix-Aware Proper Scoring Rules and Significance Testing for Correlation and Covariance Forecasts in Python
AI总结：
针对相关与协方差矩阵预测的评估难题，研发Python包corrscore，提供矩阵感知的真评分规则、几何感知变异函数评分、零重叠回测工具及配套显著性检验套件，并完成示例演示。
AI中文摘要：
在风险管理与投资组合构建中，相关矩阵或协方差矩阵的预测十分常见，但对这类预测进行正确评估并非常规操作：朴素的矩阵比较指标并非真评分规则，滚动向前评估窗口极易与估计窗口重叠，造成信息悄然泄露，且对序列依赖的预测误差序列进行显著性检验，需要分析师自行实现的专用工具。corrscore是一个Python包，针对该场景提供了两种成熟真评分规则的矩阵感知实现——能量评分与变异函数评分，其实现覆盖了闭式可处理范围（点预测、离散混合预测及各向同性高斯混合预测可精确评分；通用蒙特卡洛集成预测则采用采样方式），还包含基于相关流形上仿射不变距离构建的变异函数评分的几何感知变体、按构造实现零重叠的滚动向前回测工具，以及配套的显著性检验套件（循环块自举法、Diebold-Mariano检验与模型置信集）。我们描述了该包的设计、其与现有scoringRules和properscoring包的差异点，并完整演示了一个示例。
英文摘要：
Forecasting a correlation or covariance matrix is common in risk management and portfolio construction, but evaluating such a forecast correctly is not routine: naive matrix-comparison metrics are not proper scoring rules, walk-forward evaluation windows are easy to overlap with the estimation window in ways that silently leak information, and significance testing on serially dependent forecast-error sequences needs machinery few analysts implement from scratch. corrscore is a Python package that provides matrix-aware implementations of two established proper scoring rules for this setting -- the energy score and the variogram score -- dispatched across a closed-form tractability spectrum (point, discrete-mixture, and isotropic-Gaussian-mixture forecasts are scored exactly; a general Monte Carlo ensemble falls back to sampling), a geometry-aware variant of the variogram score built from the affine-invariant distance on the correlation manifold, a zero-overlap-by-construction walk-forward backtest harness, and a bundled significance-testing suite (circular block bootstrap, the Diebold-Mariano test, and the Model Confidence Set). We describe the package's design, its point of departure from the existing scoringRules and properscoring packages, and walk through a complete worked example.
