基于函数型主成分分析的季节调整和混合频率时间序列模型：理论与应用

Seasonal Adjustment is of great practical importance in the analysis of economic time series. Proper use of seasonal adjustment method removes those fluctuations caused by seasonal reasons, and helps people make correct and timely decisions according to the seasonal-adjusted information in the time series. Traditional seasonal adjustment methods include moving average method based on nonparametric filtering theory, TRAMO/SEATS method based on ARIMA model and signal extraction theory, and structure time series model with seasonal component. The first two methods lack flexibility, and are not suitable for dealing with time varying seasonality. Although state space models with seasonal component are very flexible, their estimates rely on the dynamic specifications and distributional assumptions, which causes the results less robust. In addition, all the methods cannot be applied to the time series data with different frequencies. The aim of this proposal is to propose a new seasonal adjustment time series model based on functional principal component analysis, and overcomes some of those disadvantages in traditional methods. In the new model, the extraction of seasonal component is fully data-driven, which is both flexible and robust. Also, the model can be directly applied to mixed frequencies time series. This research has wide application prospects in macroeconomic analysis and forecasting of China.

季节调整在经济时间序列分析中有重要的现实意义。 恰当的季节调整方法可剔除时间序列因季节因素导致的波动，帮助决策者们根据经济变量短期内变化趋势及时、正确的作出经济决策。传统的季节调整方法包括基于非参数滤波的移动平均法、基于ARIMA模型和信号提取的TRAMO/SEATS法、对季节成分建立结构时间序列模型的方法。前两种方法缺乏灵活性，不适用于带时间趋势的季节特征。而带季节成分的状态空间模型虽然具有很灵活，但是其结果却十分依赖模型的动态设定和分布假设，使得模型结果的稳健性不足。另外，这些办法都不能直接应用在含有混合频率的时间序列数据。而本项目的研究目标就是在函数型主成分分析法的框架下提出新的季节调整方法，试图克服传统方法的一些不足。新方法的优势主要体现在灵活性和稳健性兼备——季节成分的提取是完全以数据为导向的，并且可以直接用于混合频率数据。本研究在中国宏观经济的分析与预测方面也有广阔的应用前景。