我國(guó)居民消費(fèi)價(jià)格指數(shù)時(shí)間序列模型與預(yù)測(cè)

1、 我國(guó)居民消費(fèi)價(jià)格指數(shù)時(shí)間序列模型與預(yù)測(cè)摘要: 居民消費(fèi)價(jià)格指數(shù)CPI 是具有重要經(jīng)濟(jì)意義的指標(biāo)，它的增長(zhǎng)具有一定的內(nèi)在規(guī)律性，而大多數(shù)經(jīng)濟(jì)時(shí)間序列存在慣性或者說(shuō)是遲緩性，通過(guò)對(duì)這種慣性的分析可以由時(shí)間序列的當(dāng)前值和過(guò)去值對(duì)未來(lái)值進(jìn)行預(yù)測(cè)。本文利用了ARMA模型對(duì)我國(guó)1993年8月2014年10月的月度CPI的時(shí)間序列數(shù)據(jù)進(jìn)行建模分析，并利用所建立的模型對(duì)我國(guó)的居民消費(fèi)價(jià)格指數(shù)進(jìn)行了短期預(yù)測(cè)。關(guān)鍵詞: CPI ARMA模型 時(shí)間序列 預(yù)測(cè) 時(shí)間序列預(yù)測(cè)是通過(guò)對(duì)預(yù)測(cè)目標(biāo)自身時(shí)間序列的處理來(lái)研究其變化趨勢(shì)的。即通過(guò)時(shí)間序列的歷史數(shù)據(jù)揭示現(xiàn)象隨時(shí)間變化的規(guī)律，將這種規(guī)律延伸到未來(lái)從而對(duì)該現(xiàn)象的未來(lái)作

2、出預(yù)測(cè)。文中所用的ARMA 模型是目前最常用的隨機(jī)時(shí)間序列擬合模型。其基本思想是:某些時(shí)間序列是依賴于時(shí)間t的一組隨機(jī)變量，構(gòu)成該時(shí)序的單個(gè)序列值雖然具有不確定性。但整個(gè)序列的變化卻有一定的規(guī)律性，可以用相應(yīng)的數(shù)學(xué)模型近似描述。通過(guò)對(duì)該數(shù)學(xué)模型的分析研究，能夠更本質(zhì)地認(rèn)識(shí)時(shí)間序列的結(jié)構(gòu)與特征達(dá)到最小方差意義下的最優(yōu)預(yù)測(cè)。 研究我國(guó)的居民消費(fèi)價(jià)格指數(shù)CPI的統(tǒng)計(jì)規(guī)律性和變動(dòng)趨勢(shì)，對(duì)于我國(guó)相關(guān)的經(jīng)濟(jì)發(fā)展政策有特別重要的意義。本文利用我國(guó)1993年8月2014年10月的月度CPI歷史數(shù)據(jù)為樣本，利用在研究一個(gè)國(guó)家或地區(qū)經(jīng)濟(jì)和商業(yè)預(yù)測(cè)中比較先進(jìn)適用的時(shí)間序列模型之一的ARMA 模型對(duì)樣本進(jìn)行統(tǒng)計(jì)分析，

3、以揭示我國(guó)居民消費(fèi)價(jià)格指數(shù)CPI變化的內(nèi)在規(guī)律性，并進(jìn)行后期預(yù)測(cè)。1、 數(shù)據(jù)預(yù)處理1. 平穩(wěn)性檢驗(yàn)（1）時(shí)序圖從上圖可知，該數(shù)據(jù)有截距項(xiàng)，無(wú)明顯變動(dòng)趨勢(shì)。（2） ADF 單位根檢驗(yàn)Null Hypothesis: CPI has a unit rootExogenous: ConstantLag Length: 12 (Automatic - based on SIC, maxlag=15)t-Statistic  Prob.*Augmented Dickey-Fuller test statistic-4.798075 0.0001Test critical v

4、alues:1% level-3.4572865% level-2.87328910% level-2.573106*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(CPI)Method: Least SquaresDate: 11/26/14 Time: 22:25Sample (adjusted): 14 255Included observations: 242 after adjustmentsVariableCoefficientStd. Er

5、rort-StatisticProb.  CPI(-1)-0.0320850.006687-4.7980750.0000D(CPI(-1)0.1683830.0531343.1690210.0017D(CPI(-2)0.0757100.0533471.4191910.1572D(CPI(-3)0.0433810.0532180.8151670.4158D(CPI(-4)0.1069930.0531572.0127670.0453D(CPI(-5)0.0592080.0526981.1235340.2624D(CPI(-6)0.0227020.0521430.4353740.

6、6637D(CPI(-7)0.0779840.0513911.5174690.1305D(CPI(-8)0.1125750.0512732.1956070.0291D(CPI(-9)0.0285000.0515860.5524760.5812D(CPI(-10)-0.0392580.051568-0.7612950.4473D(CPI(-11)0.2105990.0514514.0931880.0001D(CPI(-12)-0.4817730.049770-9.6800530.0000C3.2611750.6932664.7040720.0000R-squared0.474112 &

7、#160;  Mean dependent var-0.100000Adjusted R-squared0.444127    S.D. dependent var0.690841S.E. of regression0.515070    Akaike info criterion1.567081Sum squared resid60.48765    Schwarz criterion1.768920Log likelihood-175.6168

8、0;   Hannan-Quinn criter.1.648389F-statistic15.81172    Durbin-Watson stat2.004497Prob(F-statistic)0.000000由檢驗(yàn)結(jié)果可知，在5%的置信度水平下，p=0.0001<0.05, 通過(guò)單位根檢驗(yàn)，數(shù)據(jù)平穩(wěn)。2、 .參數(shù)估計(jì)Date: 11/26/14 Time: 22:24Sample: 1 255Included observations: 255AutocorrelationPartial CorrelationA

9、C  PAC Q-Stat Prob       .|*       .|*10.9860.986250.740.000       .|*       *|. |20.968-0.151493.240.000      

10、; .|*       *|. |30.945-0.133725.650.000       .|*       *|. |40.920-0.077946.840.000       .|*|       *|. |50.891-0.138

11、1155.00.000       .|*|       *|. |60.857-0.1301348.50.000       .|*|       *|. |70.819-0.1451525.70.000       .|*|  

12、;     .|. |80.778-0.0191686.50.000       .|* |       .|. |90.736-0.0321830.90.000       .|* |       .|. |100.693-0.0031959.40.000 

13、      .|* |       .|. |110.649-0.0142072.40.000       .|* |       .|. |120.602-0.0652170.30.000       .|* |    

14、;   .|* |130.5590.1372254.90.000       .|* |       .|. |140.516-0.0232327.30.000       .|* |       .|. |150.473-0.0242388.30.000   

15、;    .|* |       .|. |160.431-0.0062439.20.000       .|* |       .|* |170.3920.0882481.50.000       .|* |      

16、; .|. |180.3550.0262516.40.000       .|* |       .|. |190.3220.0142545.20.000       .|* |       .|. |200.2900.0112568.70.000     &

17、#160; .|* |       .|. |210.261-0.0042587.70.000       .|* |       .|. |220.233-0.0542603.00.000       .|* |       .|. |2

18、30.207-0.0082615.00.000       .|* |       .|. |240.1840.0302624.60.000       .|* |       .|. |250.1650.0522632.40.000       .

19、|* |       *|. |260.146-0.0702638.50.000       .|* |       .|. |270.1290.0042643.30.000       .|* |       .|. |280.113-0.0422

20、647.00.000       .|* |       .|. |290.098-0.0102649.80.000       .|* |       .|. |300.085-0.0092651.90.000       .|. | &

21、#160;     .|. |310.072-0.0492653.40.000       .|. |       .|. |320.059-0.0112654.40.000       .|. |       .|. |330.046-0.0252655.00.000

22、       .|. |       .|. |340.0340.0082655.30.000       .|. |       .|. |350.0230.0022655.50.000       .|. |   &

23、#160;   .|. |360.0110.0062655.50.000由自相關(guān)與偏自相關(guān)圖可知，自相關(guān)函數(shù)拖尾，偏自相關(guān)函數(shù)一階截尾，可建立ar（1）模型3、 模型估計(jì)1.帶截距項(xiàng)的ar（1）模型Dependent Variable: CPIMethod: Least SquaresDate: 11/26/14 Time: 22:26Sample (adjusted): 2 255Included observations: 254 after adjustmentsConvergence achieved after 4 iterationsVariableC

24、oefficientStd. Errort-StatisticProb.  C99.998774.16048524.035360.0000AR(1)0.9865170.007274135.62690.0000R-squared0.986486    Mean dependent var104.2622Adjusted R-squared0.986432    S.D. dependent var6.356552S.E. of regression0.740426   

25、; Akaike info criterion2.244660Sum squared resid138.1540    Schwarz criterion2.272513Log likelihood-283.0718    Hannan-Quinn criter.2.255865F-statistic18394.65    Durbin-Watson stat1.288678Prob(F-statistic)0.000000Inverted AR Roots

26、0;     .992. 不帶截距項(xiàng)的ar（1）模型Dependent Variable: CPIMethod: Least SquaresDate: 11/26/14 Time: 22:26Sample (adjusted): 2 255Included observations: 254 after adjustmentsConvergence achieved after 2 iterationsVariableCoefficientStd. Errort-StatisticProb.  AR(1)0.9993930.0004462238.8260.0000R-squared0.986317