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摘要翻译：
本文研究了大面元时间序列动态因子模型的拟极大似然估计。具体地说，我们考虑了显式地考虑因素的自相关性，从而使模型具有状态空间形式的情况。利用期望最大化(EM)算法和Kalman平滑器实现了因子及其加载的估计。~我们证明了，当面元维数$n$和样本容量$t$都发散到无穷大时:(i)当$sqrt/n\到0$时，估计的加载是$sqrt-sqrt-一致的且是渐近正态的，当t/n\到0$时，估计的加载是$sqrt-sqrt-sqrt-sqrt-sqrt-sqrt-sqrt-sqrt一致的；(ii)当$\sqrtn/t\到0$时，估计因子是$\sqrtn$-一致且渐近正态的；(iii)估计的公共分量是$\min(\sqrt T,\sqrt n)$一致且渐近正态的，无论相对散度为$n$和$T$。尽管模型被估计为特质项是横截面和序列不相关的，但我们表明这些错误规范并不影响一致性。此外，估计的加载量与主成分估计量一样是渐近有效的，而数值结果表明，估计因子的效率损失随n和t的增加而变得可以忽略不计。然后，我们提出了渐近协方差的稳健估计，该估计可用于对加载量进行推断，并可用于计算因子和公共分量的置信区间。在MonteCarlo模拟练习和对美国宏观经济数据的分析中，我们研究了我们的估计量的性能，并与传统的主成分方法进行了比较。
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英文标题：
《Quasi Maximum Likelihood Estimation and Inference of Large Approximate
Dynamic Factor Models via the EM algorithm》
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作者：
Matteo Barigozzi, Matteo Luciani
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最新提交年份：
2020
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
This paper studies Quasi Maximum Likelihood estimation of dynamic factor models for large panels of time series. Specifically, we consider the case in which the autocorrelation of the factors is explicitly accounted for and therefore the model has a state-space form. Estimation of the factors and of their loadings is implemented by means of the Expectation Maximization (EM) algorithm, jointly with the Kalman smoother.~We prove that, as both the dimension of the panel $n$ and the sample size $T$ diverge to infinity: (i) the estimated loadings are $\sqrt T$-consistent and asymptotically normal if $\sqrt T/n\to 0$; (ii) the estimated factors are $\sqrt n$-consistent and asymptotically normal if $\sqrt n/T\to 0$; (iii) the estimated common component is $\min(\sqrt T,\sqrt n)$-consistent and asymptotically normal regardless of the relative rate of divergence of $n$ and $T$. Although the model is estimated as if the idiosyncratic terms were cross-sectionally and serially uncorrelated, we show that these mis-specifications do not affect consistency. Moreover, the estimated loadings are asymptotically as efficient as those obtained with the Principal Components estimator, whereas numerical results show that the loss in efficiency of the estimated factors becomes negligible as $n$ and $T$ increase.~We then propose robust estimators of the asymptotic covariances, which can be used to conduct inference on the loadings and to compute confidence intervals for the factors and common components. In a MonteCarlo simulation exercise and an analysis of US macroeconomic data, we study the performance of our estimators and we compare them with the traditional Principal Components approach.
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PDF链接：
https://arxiv.org/pdf/1910.03821
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