Bootstrap校准的谱散度检验用于协方差矩阵变化的在线检测
Bootstrap-Calibrated Spectral Divergence Tests for Online Detection of Covariance Matrix Changes
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中文总结 AI 辅助
本文提出Bootstrap校准的谱散度检验，用于在线检测协方差矩阵变化，控制误报率并证明一致性，在金融数据中验证了有效性。
中文摘要 AI 辅助
协方差矩阵很少在单一方向上发生扭曲：一次偏移可以同时扩大所有方差，沿一个或两个主方向移动方差，在不改变边际均值的情况下转移谱质量，或旋转依赖结构。默认的均值偏移检测器对这些效应视而不见，且现有的在线程序无法在时间和跟踪窗口选择上同时以可证明的误报控制来校准一族谱偏差检验；本文填补了这一空白。我们考虑四种谱散度：$D_{KL}(P_{1}\\|P_{0})$、$D_{KL}(P_{0}\\|P_{1})$、Jeffreys和Bhattacharyya，每种都在经验相对协方差算子$\widehat{\Sigma}_{0}^{-1/2}\widehat{\Sigma}_{t}\widehat{\Sigma}_{0}^{-1/2}$的特征值上进行评估。临界值来自条件参数Bootstrap，该Bootstrap考虑了过去窗口和跟踪窗口中的估计不确定性，这是渐近方法通常忽略的一个方面。该程序在预定义的监测周期和一系列候选窗口大小上逐族控制误报率；当需要单个操作窗口时，基于功效的准则选择它。我们通过具有接近零假设的二阶敏感性的局部谱展开证明了在恒定备择下的一致性。模拟在零假设下是保守的，并表明检测功效主要取决于谱形状而非幅度：$D_{KL}(P_{1}\\|P_{0})$在全局膨胀下表现出色，而Jeffreys和Bhattacharyya覆盖了更广泛的备择范围。我们在三个金融应用中展示了该方法：欧洲股票指数、Fama-French行业投资组合和大盘科技股。
英文摘要
A covariance matrix rarely distorts in a single direction: a shift can expand all variances simultaneously, shift variance along one or two principal directions, displace spectral mass without changing marginal means, or rotate the dependence structure. Default mean-shift detectors are blind to these effects, and no existing online procedure calibrates a family of spectral deviation tests with provable false alarm control across both time and tracking window selection; this paper fills that gap. We consider four spectral deviations: $D_{KL}(P_{1}\|P_{0})$, $D_{KL}(P_{0}\|P_{1})$, Jeffreys, and Bhattacharyya, each evaluated on the eigenvalues of the empirical relative covariance operator $\widehatΣ_{0}^{-1/2}\widehatΣ_{t}\widehatΣ_{0}^{-1/2}$. Critical values come from a conditional parametric bootstrap that accounts for estimation uncertainty in both the past and tracking windows, an aspect asymptotic approaches typically overlook. The procedure controls the false alarm rate family-by-family over a predefined monitoring period and a range of candidate window sizes; when a single operational window is needed, a power-based criterion selects it. We prove consistency under constant alternatives via local spectral expansions with second-order sensitivity near the null. Simulations are conservative under the null and show detection power depends largely on spectral shape rather than magnitude: $D_{KL}(P_{1}\|P_{0})$ excels under global inflation, while Jeffreys and Bhattacharyya cover a broader range of alternatives. We illustrate the approach on three financial applications: European stock indices, Fama-French sector portfolios, and large-cap technology stocks.
发表机构
- Cumhuriyet University（居米舍特大学）
- Linköping University（林雪平大学）
机构由 AI 辅助整理，请以论文原文为准。
