Modeling And Application Of The Seasonal Time Series Based On The Structural Time Series Models

Seasonal fluctuations are the most significant features of the seasonal time series.Therefore,in the macroeconomic analysis,first need to deal with is the seasonal fluc-tuations in the data.Although the use of seasonal adjustment software to eliminate seasonal fluctuations can make economic analysis more convenient,but the traditional seasonal adjustment method will cause distortions in information contained in the data.In addition,in terms of China,foreign seasonal adjustment softwares may not be able to completely eliminate the abnormal fluctuations caused by traditional Chinese holidays such as the Spring Festival.In order to avoid the influence of seasonal adjustment and make full use of the information contained in the data,this paper considers directly modeling the season-al time series under the framework of the structure time series models.For season-al growth rate data,we proposed univariate seasonal growth rate(SGR)model,the Markov-switching seasonal growth rate(MS-SGR)model,and the multivariate sea-sonal dynamic factor(SDF)model.For seasonal level data,we proposed a Plucking model with seasonal component.In addition,the application of these models in fitting and forecasting,the extraction of chain-based data,the construction of macroeconomic coincident index and the dating of business cycle are discussed.First,this paper presents a seasonal growth rate(SGR)model that can not only fit and forecast the original seasonal growth rate,but also extract the seasonally adjusted growth rate series from the unadjusted growth rate data directly.Monte Carlo simula-tion results show that the proposed MLE estimation method for SGR model have good large sample performance.Through the empirical applications to China's real GDP and CPI data,we find that the seasonally adjusted growth rate extracted by the SGR mod-el is smoother than by the other seasonally adjustment methods.Moreover,the fitting and forecasting performance of the SGR model is significantly improved compared to that of the BSM model and the SARIMA model.In addition,the SGR model also has the advantage of being easily extended to the nonlinear or multivariate cases.Finally,based on the MS-SGR model,we can more accurately dating the business cycle phases compared to that of the traditional Markow-switching model.Secondly,this paper presents a seasonal dynamic factor(SDF)model which can directly use the seasonal growth rate data to extract the coincident index.The advantage of this model is that it can make full use of the information in the original data and avoid the repeatedly deleting of the information at the seasonal frequency.The general form of the model and its estimation method are given.The empirical results show that,compared with the traditional dynamic factor model,the seasonal dynamic factor model can better identify the turning point of China's economy.In addition,based on this model,we further confirmed that traditional seasonal adjustment will cause outliers in the chain-based data,which have a negative impact on the coincident index.Finally,this paper developed a Plucking model with seasonal component,which can capture all the information contained in the data.By using the original seasonal unadjusted real GDP data,we can not only depict the dynamics of the business cy-cle during 1978-2015,but also correctly identify the business cycle phase from 1992,which is unable to achieve if the seasonal adjusted GDP data was used.Moreover,through the comparison of the Plucking model with seasonal component and MS-SGR model,we can conclude that both of these models can give consistent conclusions on the changes of business cycle phases.