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.

翻译：本文研究一类具有演化时域动态特征的局部平稳时间序列因子模型的估计与检验问题。具体而言，因子载荷矩阵的元素及维度允许随时间变化，而因子与特质噪声分量保持局部平稳性。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支撑空间及局部平稳因子过程。通过非负定时变矩阵的特征分析，研究了有效因子数的一致估计量。通过比较整段时间序列协方差矩阵核与其局部对应物，提出了针对静态因子载荷假设的（可能高维的）自助法辅助检验。我们通过模拟研究与实际数据分析检验了所提出的估计量与检验方法。最后，所有结果均在以下两种常见但不同假设下成立：（a）维度固定或发散的独立同分布特质误差，以及（b）发散维度下具有相关结构的特质误差。