The Short Economic Time Series Analysis Models With Applications

With the research and practice of time series analysis method in recentyears,more and more practical workers have started to understand andmaster it with the further development of reform and ecomomy ,amountsof data in ecnomy has to be analysized , forcasted and decision-mademoreover with more scientific method .The current methods could notmeet the need of dealing with the practical data,hence it is necessary to doa lot of further work to discuss the way of dealing with the practical datawidely and deeply on base of the current anylysis method . The mostfundmental theory of time series analasis is given by Norbort Wienerand Andrei Kolmogorov .who contributed a lot to parameter estimatingand modeling and gave the important relational article which promotethe application of time series analysis method in engineering field. In1970's ,The masterpiece <>written by G.P.Box and G.M.Jenkins has put forward ARMA model forthe stationary time series and gave the complet way of modeling ,estimating, diagnostic checking ,controling, and made it possible for thetime series to be widely applied .The time series analysis has developed in two different ways inwhich there are not apparent differences between them..First one isfrequency domain method,which empasised on spectral density andtime series spectral decomposition and discribe the time series innon-parameter way,it widely used in engineering and physics,and hasbeen paid more attention in economic .The second one is time-domainmethod by which we use correlation function to deal with stochastic ,suchas we use the ARIMA parameter model to approximate the observedsequence and make correlation analysis on it,and for more compicatedones we use transfer function and multiple ARMA model, One importantpattern of them is ARMA,it is the compound of AR and MA..Until now,the ARIMA model is the most commonly used forcastingmethod for time series.In the progress of using ARIMA,first ,thenonstatinary sequece should be transformed into stationary ones,and thenbe used for the model building which includes tentativeidentification,estimation and forcasting by the SACF,SPACF SIACF andthe MA(p)progress,AR(q)progress.Box-Jenking method or the ARIMA method needs more than50.historical statistical data.It is difficult to collect the material ofeconomy that is in light of month,season and year.If the data is less than50,the forcasting model we get from the Box-Jenking will be lack ofaccuracy and even the model could not be built. pattern.With the help ofSAS and Visual C++, this paper put up the smoothing Box-Jenkingmethod aimed at the sequence which consists of less data .This methoddeals with data first in order to get the sequence with more data,and buildpattern with these dealt sequence in Box-Jenking method, then thepredictions of the sequence become feasible. Meanwhile,we use greyforecasting method to deal with the small sample data.By the pratticalanalysis and comparing with the grey forecasting method,we come to theconclusion that the smoothing ARIMA modeling method has highaccuracy in forecasting .The grey system theory is a crossing subject set up by the famousscholar Deng Ju long in 1982 .Its work object is indefinite system inwhich the sample with part known information and part unknowninformation is little and the information is poor.It mainly bygenerating,developing, and abstracting valued information from theknown segment information to get the exact cognition and effectivecontrol on behavior of the system.. Since the time when Dengjulongprofessor created it , Gray System Theory has been widely been used inmany field,and many new gray modeling method have been presented bysome researcher of gray system theory,such as SCGM(1,h)model, Grayerror-modified model, buffer operator interventionn processing modeland so on. As the gray modelingn ask for less data, the ideal munber ofdata for the modeling of the above model is 10 or so, so to the rich datathis paper put forward the Separated-Modeling method in which way firstwe divide the original data sequence into two groups, then get modelingby the two sequences respectively and caculate the forecast value usingthe two models,at last incorporate the two forecast date and get theforecast value of the original sequence applying proper method.Because of the historical reason,we have only 27 available year data ofGDP in our country from 1978 to now,and recent seasonal data,it's unableto get ARIMA model with such less available data,so the model putforward by this paper is valuable for the government decision-making.The paper consists of 3 parts. Part one is preliminary knowledge inwhich the progress of modeling for GM(1,1) model and ARIMA modelare introducedand a few useful conclusion for some ARIMA model ofpoint time series .The second part is the main body of this paper,itincludes the innovation of this paper ,that is the Gray separatingmodeling method,smoothing ARIMA modeling method. Part three isexperimental analysis of the models,it established the model using thedata since 1978 to now,and has obtainde the forecast for future withhigher accuracy compared with the common GM(1,1) model andARIMA model.