On the number of common factors with high-frequency data
提出一种局部主成分分析方法，利用高频数据估计时变因子载荷连续时间因子模型中的共同因子数量，通过最小化惩罚聚合均方残差得到一致估计量，模拟和真实数据验证了方法有效性。
In this paper, we introduce a local principal component analysis approach to determining the number of common factors of a continuous-time factor model with time-varying factor loadings using high-frequency data. The model is approximated locally on shrinking blocks using discrete-time factor models. The number of common factors is estimated by minimizing the penalized aggregated mean squared residual error over all shrinking blocks. While the local mean squared residual error on each block converges at rate |$\min(n^{1/4}, p)$|, where |$n$| is the sample size and |$p$| is the dimension, the aggregated mean squared residual error converges at rate |$\min(n^{1/2}, p)$|; this achieves the convergence rate of the penalized criterion function of the global principal component analysis method, assuming restrictive constant factor loading. An estimator of the number of factors based on the local principal component analysis is consistent. Simulation results justify the performance of our estimator. A real financial dataset is analysed.