时间序列论文timeseiesproject

1、Abstract : This article collects a series quarterly data of C hina GsDP from 1992 to 2010, and we use the method of factor decomposition to collect the long-term increasing trend and seasonality, then use ARMA model to fit the residuals, do analysis to get the final model and use it to generate a sh

2、ort-term GDP-forecast of china.Key words : factor decomposition; ARMA model; GDP forecast ；1. Introduction1.1BackgroundFrom 1978, since the reform and opening up, chinaeconomy is devesloping rapidly andsteadily. After joining the WTO, the developing speed has reached a new level. GDP (Gross Domestic

3、 Product) , which is the basis of national economic production of statistical indicators, can be used to reflect a country s economy. It is the core of Statistical indicators in the national economy. GDP combines responses of the most basic aspects of macroeconomic, can not only measure the overall

4、national output and income scale, but also can explore the economic fluctuations and cycles. Hence, it is of great importance to fit and analyze GDP accurately for exploring a country smacroeconomics trend. The aim of this article is to generate a GDP forecast model and use it to predict the future

5、GDP of china.1.2 MethodA lot of methods have been used to analysis economy phenomenon, time series analysis is one of the most efficient methods. A time series is a collection of observations of well-defined data items obtained through repeated measurements over time. Time-series methods use economi

6、c theory mainly as a guide to variable selection, and rely on past patterns in the data to predict the future. An observed time series can be decomposed into three components: the trend (long term direction), the seasonal (systematic, calendar related movements) and the irregular (unsystematic, shor

7、t term fluctuations). When these factors occur, we can use the method of decomposition, from which can we collect useful information of the data, we defined it as factor decomposition here.The trend component typically represents the longer term developments of the time series of interest and is oft

8、en specified as a smooth function of time.The recurring but persistently changing patterns within the years are captured by the seasonal component. It is quite common in economic time series, when it occurs, we should use seasonal adjustment method. Seasonal adjustment is the process of estimating a

9、nd then removing from a time series influences that are systematic and calendar related. Observed data needs to be seasonally adjusted as seasonal effects can conceal both the true underlying movement in the series, as well as certain non-seasonal characteristics which may be of interest to analysts

10、.Theirregular component represents the irregular fluctuations which are affected by causal factors. It usually defined as residual. Considering the Insufficiency of the deterministic decomposition, we should test the residuals, if there is no autocorrelation among the residual, it means that the inf

11、ormation of the time series is totally recovered by the deterministic decomposition.In the case of the existence of autocorrelation, ARMA model can be used to fit the residuals. ARMA is a one of those most common time series model which was used to make precise estimation according to short term dat

12、a. Its main idea can be concluded as a combination of several time- related components which can be used to predict the future data. The time series components from the ARMA model is a set of random variables which related to time itself, which shows uncertainty when observed individually combined w

13、ith each other shows some kinds of regularity and can be expressed by corresponding statistical model. The ARMA model consists of two parts, an autoregressive (AR) part and a moving average (MA) part. The model is usually then referred to as the ARMA(p,q) model where p is the order of the autoregres

14、sive part and q is the order of the moving average part.2. Data An alysis2.1 DatasetThe data we collected contains historical GDP from 1992-2010, the reas on we choose this time duration rather than the 1978-2011 which most other prediction article would like to use is that during the first 10-15 ye

15、ars the economic growth rate is relatively slow compared with the later year s (1990bw) growth. So we would like to wipe out the interferenee of the early data. Another reason we use recent years data (1992-2011) is that it is hard for us to look for the quarterly GDP data before 1992 due to the imp

16、erfection of the statistical system of China in the end of 20th cen tury.Tableqluarter GDP data from 1992-2010 (Unit: 1000 million CNY)timeGDPtimeGDPtimeGDPTimeGDP1992.149741997.1162572002.01253762007.0154755.91992.2 16358P 1997.2186972002.02279652007.02612431992.371191997.3191482002.03297162007.036

17、4102.21992.484721997.4248712002.04372762007.0485709.21993.1 丁6500P 1998.1175012003.0128861.82008.0166283.81993.280441998.2197222003.0231007.12008.02741941993.390481998.3203722003.0333460.42008.0376548.31993.4 111742P 1998.4268072003.0442493.52008.0497019.31994.190651999.1187902004.0133420.62009.0169

18、816.91994.2110851999.2207652004.0236985.32009.0278386.71994.3 ”12447P 1999.3218592004.0339561.72009.0383099.71994.4156011999.4282632004.0449910.72009.04109599.51995.1118582000.1206472005.0139117.42010.0182613.41995.2 ”14110P 2000.2231012005.0242795.22010.0292265.41995.3155352000.3243402005.0344744.4

19、2010.0397747.91995.4192912000.4311272005.0458280.42010.04128886.11996 1142612001 01233002006.0145315.81996.2 1166012001.02256512006.0250112.71996.3176712001.03268672006.0351912.81996.4226442001.04338372006.0468973.1(Data source: Nati onal statistical database of Chi na)We are going to use these hist

20、orical GDP data as a time series, learn and analyze the data, then based on the past patter ns to get a forecast model, use the model to predict the future GDP.2.2 Data Graphical An alysisFigure 1 shows a plot of the data, and we can find that there is a sig nifica nt Ion g-term trend and vary ing s

21、eas on ality in the time series. The tre nd seems to be quadratic while the seas on ality illustrate a strong yearly comp onent occurri ng at lags that are multiples of s=4. For the purpose of dem on strati on, the sample ACF of the data is displayed in Figure 2, also, it appears a sig nifica nt sea

22、s on ality.Series 丫In dexIlli.Lag243. Time Series Model3.1 Factor Decompositi onAfter the previous analysis, now we are going to use the method of factor decomposition to build a time series model, its principle is that through the decomposition method, we collect the useful in formati on and measur

23、e the in flue nee of the tre nd and seas on ality. Define 丫 as GDP, x as time. We setthe decompositi on model as bellows:丫 TtStt Tt01x2x33X St01D12D23D3The reas on we use (2) as the trend model is because we can find that it seems to be a thrice model from the pattern in figure 2. D , D2 and D3 in (

24、3) is the dummy variables of seasons, andD1=c(1,0,0,0,1,0,0,0,)D2=c(0,1,0,0,0,1,0,0,)D3=c(0,0,1,0,0,0,1,0,.)3.11 Data Tran sformatio nA sig nifica nt vary ing seas on ality is observed from figure 1, si nce the vary ing seas on ality will have negative effects on the model fitting, so we should take

25、 some transformation of the GDP value to make the seas on ality con sta nt. The Box-Cox tran sformati on is part of the family of power tran sformati on, where the data is tran sformed using a power functions whilst preserv ing the rank of the data, so we take Box-Cox tra nsformati on of GDP.Figure

26、3 illustrate the box -cox plot of GDP, Looking at the BoxCox diagram in figure 3,入 is near the0.2 mark, so we use GDP as a new response variable defined asYt . Figure 4 shows the GDP plot after tran sformatio n. From the plot we can find that the seas on ality is almost con sta n t.d o dx L gp01981Y

27、6204060In dex3.12 Build ModelAfter tra nsformatio n, now the decompositi on model isYt. Using the“ Rstatisticspackage to analyse the time series and build model, the result of the full model is as follows:LM1: 5.976 0.09219X 0.001532 x230.00001472 x0.5072D10.3763D2 0.3433D3T = (110.322) (16.798)-0.2

28、81)P = 2e-16)(2&16)(9.22e-14)(10.442)(7.62*16)-(5.340)(-11.405)(-10.418)(2e16)( data=read.table(st5209new.txt,header=T) Y=data$GDP x=data$time x2=xA2 x3=xA3plot(Y,ty= ” l ”)acf(Y)D1=c(1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0, 1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0)D2=c(0,1,0,0,0,1,0,0,0