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特定因子模型样本相关矩阵有界与发散特征值的渐近位置及成分保留规则AI 解读

Let the dimension $N$ of data and the sample size $T$ tend to $\infty$ with $N/T \to c > 0$. The spectral properties of a sample correlation matrix $\mathbf{C}$ and a sample covariance matrix $\mathbf{S}$ are asymptotically equal whenever the population correlation matrix $\mathbf{R}$ is bounded (El Karoui 2009). We demonstrate this also for general linear models for unbounded $\mathbf{R}$, by examining the behavior of the singular values of multiplicatively perturbed…

等相关正态总体的相关矩阵：最大特征值波动、谱主体缩放与股票市场AI 解读

Given an $N$-dimensional sample of size $T$ and form a sample correlation matrix $\mathbf{C}$. Suppose that $N$ and $T$ tend to infinity with $T/N $ converging to a fixed finite constant $Q>0$. If the population is a factor model, then the eigenvalue distribution of $\mathbf{C}$ almost surely converges weakly to Marčenko-Pastur distribution such that the index is $Q$ and the scale parameter is the limiting ratio of the specific variance to the $i$-th variable $(i\to\infty)$.…