Research On The Modeling And Forecasting Of Time Series

The time series is the sequence of the values of a statistical indicators at differenttimes, which arranged by the times. Time series is widely used in our lives.In1927, Yule put forward the concept of AR model. And then, in1937,Walker put forward the MA model. Those two models are the base of the timeseries. After that, combine that two models and produced the model calledARMA. In1970, Box and Jenkins proposed the model called ARIMA, which isused to describe the data with tendency, in Time Series Analysis Forecastingand Control. But this ARIMA model only used in single variable andhomoscedasticity case. In the multivariate and heteroscedasticity case, we needsome new models.In1982, Engle put forward the ARCH model to fitting the heteroscedasticitycase. In1985, Bollerslov put forward the GARCH model to fitting themultivariate case. In1987, Granger put forward the cointegration theory whichis important in economic theory. In1980, Hong Kong mathematician HowellTong put forward the threshold auto regression model.The general purposes of time series analysis are two aspects following. Theone is to understand the mechanism generating the observed sequence of random.In another words, this one is to establish the data generation model. Another oneis to predict the data in future base on the data in now. Actually, time seriesregression is familiar with nature regression in essentially. Both of them are themethod of getting known the population inferred from sample. However,because of the different data structures, we can’t treat the time series as the leastsquares method. The methods of time series include descriptive analysis of thetime series which is to judge by the table and chart, no mathematical theoryfoundation, and the statistical time series analysis which has strongmathematical foundation. But descriptive analysis of the time series still can usein initial determination. The statistical time series analysis includes frequencydomain analysis and time domain analysis method. Frequency domain analysishas to use Fourier analysis, which is difficult to use in reality. So in university, professor often teaches the time domain analysis method. Time domainanalysis method has strong theoretical foundation and the standardizedprocedure. The time domain analysis method always use with programming.In this paper, I use the R software to analysis the stability of the time series,and then I identified the right model, estimate the parameter, diagnosed model,forecasted and updated which above according to the observation of a timeseries data and the time series stationary theory.