Seasonal Adjustment Of Time Series And Case Study

Time series analysis can quantitatively reveal the development and changes of a phenomenon or portray the intrinsic relationship and the change rule between a phe-nomenon and other phenomena from the dynamic point of view. This helps us to achieve the purpose of understanding the objective world. Moreover, time series mod-els can predict and control behavior in the future of the phenomenon, so that we can modify or redesign system to achieve the purpose of using and transforming the ob-jectives. A large number of facts show that, a time series is often the superposition or coupling of the following forms:(1) the trends (2) the seasonal variation (3) the irreg-ular change (it is usually divided into sudden change and stochastic change, according to the central limit theorem, random changes are usually considered approximately to obey the normal distribution). To deal with the time series that has the seasonal characteristic, we can first eliminate the seasonal item, then remove the trend, finally choose a model for stationary time series obtained. Unit root test is used to judge the stationarity of the time series. Dicky-Fuller stationary test method is used widely, but it could not overcome the difficulty of judging when to include the constant term and when to include the trends. Therefore, we introduce a new test method. In the testing, the critical value can not be obtained from t distribution, but it can be estimated by Monte Carlo method. WOLD theorem guarantees that the stationary time series can be fitted by ARMA model. It is difficult to determine the order of ARMA model, we can decide the order of the model through residual analysis chart, F test, AIC criterion and BIC criterion. The prediction can be divided into the within sample prediction, the out of sample prediction and forecast in advance. Advance prediction is what we are most concerned about. We achieve a reasonable evaluation of model through the out of sample prediction. Prom a longer time series, the process of economic opera-tion has certain rules because of the role of market mechanism, which provides a basis for prediction. This paper studies the GDP time series. First, we get trend through smoothing, then we get the seasonal index and remove the seasonal terms. Using first order difference to eliminate the trend, we finally obtan the stationary time series. We use EVIEWS software for stationary time series fitting. We also use the Holt-Winters model for the prediction. The results of forecasting from both methods are compared.