Research On Time Series Modeling Of Quarterly Data

In our daily life,a lot of time series data contain significant seasonal factors,such as various monthly data,quarterly data.China's gross domestic product-the season value(the text referred to as quarterly GDP)is a typical quarterly time series data.Time series analysis is a method for observing,researching,and analyzing time series data.The purpose of this method is to seek the law of time series development and change.And we can use this law to predict the random events' future trend.Time series analysis can be divided into traditional time series analysis and modern time series analysis according to the development stage and the statistical analysis method it used.In this paper,we use the time series analysis method to model and forecast china's quarterly GDP data,and then explore the experience and method of quarterly(monthly)data modeling.The data in this paper is china's quarterly GDP data from 1992 first quarter to the fourth quarter of 2016.The data comes from Official Website of the Statistical Office of the People's Republic of China(http://www.stats.gov.cn/),the main work in this paper is:(A)Different time series analysis methods are used to fit the quarterly GDP data from the first quarter of 1992 to the fourth quarter of 2016.This part uses the following two ideas:(1)The combination of traditional and modern time series analysis methods.First,the seasonal index of each season is obtained by the traditional method,with the original sequence divided by the corresponding seasonal index,we can get the sequence that doesn't contain seasonal factors.This sequence does not include seasonal factors,only including the trend and random fluctuations,then two methods,curve fitting and modern time series ARIMA modeling,are fitted to this sequence.Last,the fitting value and the predicted value of the model are multiplied by the corresponding seasonal index to get the fitting and the predicted value about the raw data.(2)Directly model the raw data.The methods used are Holt-Winters exponential smoothing and non-stationary season ARIMA model.(B)Compare the advantages and disadvantages of the four methods established in the text and find the optimal model to forecast quarterly GDP data for the next two years in 2017 and 2018.The standards of the model comparison are the fitting effect of the model and the strength of the residual pure randomness.At last,by comparison the four models we found,for the quarterly GDP data studied in this paper,to extract seasonal factors,seasonal index are better than seasonal differences.Therefore,when we model the time series containing significant seasonal factors,we can give priority to try first to use the seasonal index of traditional method to separate the seasonal factors,and then to model the seasonal separation sequence,this method may significantly improve the fitting accuracy of the model.