混频时间序列的潜在因子分析及其应用

Latent Factor Analysis for Time Series with Mixed Frequencies and Its Application

宏观经济产生的时间序列通常假设被少数潜在因子所控制,其共同作用表现为序列之间的联动效应。因子对于时间序列的分析和预测有重要的作用,但是宏观经济的实证分析往往包含混频数据,使得因子分析不能直接使用。为此,本文提出了混频时间序列的两种因子分析方法MIDAS-LF和EM-LF,前者得益于多变量MIDAS模型对低频序列的插值,后者利用EM算法进行迭代求解。模拟数据分析显示,相比于文献中的计算方法,MIDAS-LF对混频时间序列的分析有较好的效果,计算简便而且保留了原始数据的信息,可以更好地估计因子的成分和载荷,具有较低的拟合误差和预测误差。宏观经济的实际数据分析也证实了MIDAS-LF方法的可行性和正确性。

Time series generated by macroeconomics are usually assumed to be controlled by a few latent factors.The joint effects of factors lead to the co-movement of series.Factors are important in the analysis and forecasting of time series.However,empirical macroeconomic studies always contain time series with mixed frequencies,which make factor analysis impossible to implement.To this end,this paper proposes two factor analysis methods for time series with mixed frequencies,namely MIDAS-LF and EM-LF.The former benefits from the interpolation of low-frequency sequences by the multivariate MIDAS model,while the latter uses the EM algorithm for iterative solution.The simulation data analysis shows that,compared with methods existing in the literature,MIDAS-LF is better for the analysis of time series with mixed frequencies.The calculation procedure of MIDAS-LF is simple and retains most of the information in original data,which can better estimate the factors and loading matrix,leading to low fitting error and prediction error.The actual data analysis of the macro-economy also confirms the feasibility and correctness of the proposed methods.