用于高维时间序列的因子调整位置检验
Factor-Adjusted Location Tests for High-Dimensional Time Series
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中文总结 AI 辅助
针对由潜在动态因子驱动的高维时间序列单样本均值检验问题，该文提出三种因子调整检验，通过理论推导验证其有效性，开发自助法校准，模拟与实际应用证实其性能。
中文摘要 AI 辅助
我们研究由潜在动态因子驱动的具有强共同序列依赖的时间序列的高维单样本均值检验。在从滞后自协方差估计动态因子载荷空间后，我们将数据投影到其正交补空间，并构建三种因子调整检验：针对稀疏备择假设的max检验、针对稠密备择假设的二次检验，以及针对未知稀疏性的Cauchy组合检验。特异成分允许为非高斯次高斯向量白噪声。我们建立了max统计量的Gumbel极限、二次统计量的正态极限与局部功效函数、它们的渐近独立性，以及Cauchy组合的有效性。在强因子情形下，精细投影展开表明，二次统计量对维度大至$p=o(n^2)$仍保持有效。我们开发了随机载荷残差自助法用于有限样本校准。模拟研究与实际数据应用表明，该方法对具有强依赖的高维观测值具备可靠的尺寸控制与有竞争力的功效。
英文摘要
We study high-dimensional one-sample mean testing for time series with strong common serial dependence driven by latent dynamic factors. After estimating the dynamic factor loading space from lagged autocovariance, we project the data onto its orthogonal complement and construct three factor-adjusted tests: a max test for sparse alternatives, a quadratic test for dense alternatives, and a Cauchy combination test for unknown sparsity. The idiosyncratic component is allowed to be non-Gaussian sub-Gaussian vector white noise. We establish the Gumbel limit of the max statistic, the normal limit and local power function of the quadratic statistic, their asymptotic independence, and the validity of the Cauchy combination. In the strong-factor case, the refined projection expansion shows that the quadratic statistic remains valid for dimensions as large as $p=o(n^2)$. A random-loading residual bootstrap is developed for finite-sample calibration. Simulation studies and a real data application demonstrate reliable size control and competitive power for high-dimensional observations with strong dependence.
