Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review
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高维因子模型的拟极大似然估计：批判性综述
- 研究问题
- 在特质成分具有温和横截面与序列相关的高维近似因子模型中，拟似然方法能否识别、估计和推断，维度增长有何作用？
- 方法与思路
- 作者综述不显式设定因子动态的估计，以及结合 Kalman 平滑与 EM 的动态估计，并与主成分和固定维精确似然比较。
- 材料陈述的贡献
- 摘要称，横截面维度增长可使精确因子似然的误设误差消失；维度和时间长度共同增长时，可一致估计参数及潜因子。
- 阅读关注点
- 应核对近似因子结构、相关性强度和维度增长条件，并比较各方法的识别规范、因子估计误差与效率结论适用范围。
- 阅读边界
- 仅据 arXiv 预印本摘要解读，同行评审及期刊接收未经核实；摘要未列具体正则条件、收敛速度或估计量效率排序。
原文摘要
We review Quasi Maximum Likelihood estimation of factor models for high-dimensional panels of time series. We consider two cases: (1) estimation when no dynamic model for the factors is specified (Bai and Li, 2012, 2016); (2) estimation based on the Kalman smoother and the Expectation Maximization algorithm thus allowing to model explicitly the factor dynamics (Doz et al., 2012, Barigozzi and Luciani, 2019). Our interest is in approximate factor models, i.e., when we allow for the idiosyncratic components to be mildly cross-sectionally, as well as serially, correlated. Although such setting apparently makes estimation harder, we show, in fact, that factor models do not suffer of the {\it curse of dimensionality} problem, but instead they enjoy a {\it blessing of dimensionality} property. In particular, given an approximate factor structure, if the cross-sectional dimension of the data, $N$, grows to infinity, we show that: (i) identification of the model is still possible, (ii) the mis-specification error due to the use of an exact factor model log-likelihood vanishes. Moreover, if we let also the sample size, $T$, grow to infinity, we can also consistently estimate all parameters of the model and make inference. The same is true for estimation of the latent factors which can be carried out by weighted least-squares, linear projection, or Kalman filtering/smoothing. We also compare the approaches presented with: Principal Component analysis and the classical, fixed $N$, exact Maximum Likelihood approach. We conclude with a discussion on efficiency of the considered estimators.