非平稳因子模型的自适应估计及静态因子载荷检验
Adaptive Estimation for Non-stationary Factor Models And A Test for Static Factor Loadings
AI总结：
本文针对具有演化动态的局部平稳因子模型，提出自适应筛估计量估计时变载荷列空间和因子过程，并基于特征分析和 bootstrap 检验静态载荷假设，适用于高维情形。
摘要：
本文考虑一类具有演化时间动态的局部平稳时间序列因子模型的估计与检验问题。特别地，因子载荷矩阵的元素和维度允许随时间变化，而因子和 idiosyncratic 噪声分量是局部平稳的。我们提出了一种自适应筛估计量，用于估计变化载荷矩阵的列空间和局部平稳因子过程。通过对一个非负定时变矩阵进行特征分析，我们研究了一致有效的因子数量估计量。通过比较整个时间序列的协方差矩阵的核与其局部对应核，我们提出了一种可能高维的 bootstrap 辅助检验，用于检验静态因子载荷的假设。我们通过模拟研究和真实数据分析来检验我们的估计量和检验方法。最后，我们的所有结果在以下两种流行但不同的假设下成立：（a）白噪声 idiosyncratic 误差，其维度固定或发散；（b）相关 idiosyncratic 误差，其维度发散。
英文摘要：
This paper considers the estimation and testing of a class of locally stationary time series factor models with evolutionary temporal dynamics. In particular, the entries and the dimension of the factor loading matrix are allowed to vary with time while the factors and the idiosyncratic noise components are locally stationary. We propose an adaptive sieve estimator for the span of the varying loading matrix and the locally stationary factor processes. A uniformly consistent estimator of the effective number of factors is investigated via eigenanalysis of a non-negative definite time-varying matrix. A possibly high-dimensional bootstrap-assisted test for the hypothesis of static factor loadings is proposed by comparing the kernels of the covariance matrices of the whole time series with their local counterparts. We examine our estimator and test via simulation studies and real data analysis. Finally, all our results hold at the following popular but distinct assumptions: (a) the white noise idiosyncratic errors with either fixed or diverging dimension, and (b) the correlated idiosyncratic errors with diverging dimension.
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