季節(jié)ARIMA模型建模與預(yù)測實驗指導

1、季節(jié)ARIMA模型建模與預(yù)測實 驗指導作者：日期:實驗六季節(jié)ARI MA模型建模與預(yù)測實驗指導學號:2 01 3 136 3 0 38姓名：闕丹鳳班級：金融工程1班一、實驗?zāi)康膶W會識別時間序列的季節(jié)變動，能看出其季節(jié)波動趨勢。學會剔除季節(jié)因素的方 法，了解A RI MA模型的特點和建模過程，掌握利用最小二乘法等方法對A RIMA模型進行 估計，利用信息準則對估計的ARIMA莫型進行診斷，以及如何利用ARIMA模型進行預(yù)測。 掌握在實證研究如何運用Evi ews軟件進行ARIMA模型的識別、診斷、估計和預(yù)測。二、實驗內(nèi)容及要求1、實驗內(nèi)容：根據(jù)美國國家安全委員會統(tǒng)計的1973 1 9 78年美國

2、月度事故死亡率數(shù)據(jù)，請選 擇適當模型擬合該序列的發(fā)展。2、實驗要求：(1)深刻理解季節(jié)非平穩(wěn)時間序列的概念和季節(jié)ARIMA模型的建模思想；(2)如何通過觀察自相關(guān)，偏自相關(guān)系數(shù)及其圖形，利用最小二乘法，以及信息準則建 立合適的ARIMA模型；如何利用ARIMA模型進行預(yù)測；(3)熟練掌握相關(guān)E vi e ws操作。三、實驗步驟第一步：導入數(shù)據(jù)Excel Spreadsheet Import atflofderUpper deft data celExcel 5+!h wt name口？ By Observation - series in CDlumnsB20¥ Series - s

3、erits inTrnes for series of Humber if named ri filesiuvangre nehu,Write dale/obs EViews date format First calendar day Last calendar dayWrite series names1 72Rjeset sample to: Current aarnple Worfcfte range To end ofOKCrttel第二步：畫出時序圖第三步：季節(jié)差分法消除季節(jié)變動由時序圖可知，波動的周期大約為12,所以對原序列作12步差分，得到新 序列如 下圖所示。ShowD(SI

4、WANGRENSHU,0,12)Cancel由12步差分后的新序列可知，由上升趨勢，再進行序步差分得到進一步的新 列，結(jié)果如下圖所示。ShowObjects to display in a single wrdow d(new)|Enter one of the fulowing an Object or Object Vie 腳 a Series Formula 歐e LOG(X) or X +Y(-1) a list of Seriesr Groups, and Fomnulas a list of GraphsD(NEW)所以經(jīng)過12步差分、 又經(jīng)過一階差分后的序列平穩(wěn)。第四步：平穩(wěn)性檢

5、驗Null_Hy pothesis: D(NEW) has a unit rootExogenous: ConstantLag Length: 1 (Automatic - based on SIC, maxlag=10)t-StatisticP rob. *Augmented Dickey-Fuller test statistic-7.9388790. 0000Test critical values:1% level-3.5503965% level-2.91354910% level-2.594521*MacKinnon (1996) one-sided p-values.Augmen

6、ted Dickey-Fuller Test EquationDep endent Variable: D(NEW, 2)Method: Least SquaresDate: 05/10/16 Time: 15:07Sam pie (adjusted): 16 72Included observations: 57 after adjustmentsVariableCoefficientStd. Errort-StatisticP rob.D(NEW(-1)-1.7125340.215715-7.9388790. 0000D (NEW (-1),2)0.2604880. 1309401. 98

7、93620. 0517C41.9937948.897790.8588070. 3942R-squared0.702461Mean dep endent var-2.789474Adjusted R-squared0. 691442S.D. dep endent var660.1922S.E. of regression366.7238Akaike info criterion14.69829Sum squared resid7262264.Schwarz criterion14.80582Log likelihood-415. 9013Hannan-Quinn criter.14. 71008

8、F-statistic63. 74455Durbin-Watson stat2.033371P rob(F-statistic)0. 000000由AD F檢驗結(jié)果表明，在0.0 1的顯著性水平下拒絕存在單位根的原假設(shè),所以驗證了序列是平穩(wěn)的，可以對其進行ARMA模型建模分析。第五步：模型的確定Date; 0S/1CW1S Time： 15. ： 13Sample： 1 72Included observations： 59Autocorrelation Partial Correlation AC PAC Q-Stat Prabrn1U11 -o 356 -o. 356 7. S649 0.

9、 00511n12 -0. 099 -0. 256 S. 47ffi 0. OU11 11 n13 0. O&e dCi4S 3. 0700 0 02S11111 -0.113 -0 140 9 9029 0. 0421111 D15 0. 042 £1052 10. 018 0. 07511111S 0. 114 0094 10. 902 0. 091>1<17 -0. 204 00.134 13. 702 0. 055111a -0 007 -0. 15C n. 796 o. oae13 19 0.100 -0. 02S 14- 50T 0.105111 Q1

10、ia -0. 0B2 -00a? 14. 996 0. 1321口1口，11 0.195 D ISe 17, 059 0, 085匚1口112 -0. 333 0 296 26. 359 0. 010111 D113 0 090 -0 034 Ze 995 0.0f 12111(114 0 116 -0. 015 28 077 0 014111115 -0 041 0.012 28 212 0. 02011116 -0. 0S4 -0.121550 0. 0371F11117 0.1S3 0 ne 31428 0. 0181111113 -0, 1&2 -0 023 34.679 0.

11、 010由ACF和PAC F可知，AC F在1階截尾,PACF在2階截尾，所以可選擇的 模型有 AR(2)、MA(1 )、ARM A(2, 1 )等。第六步:模型的參數(shù)估計AR(2):Dependent Variable： NEW2Method: Least SquaresDate: 05/10/16 Time： 15:16Sam pie (adjusted)： 16 72Included observations: 57 after adjustments Convergence achieved after 3 iterationsVariableCoefficientStd. Error

12、t-StatisticP rob.C24.5214328. 364330. 8645160. 3911AR-0.4520470. 130914-3.4530130. 0011AR (2)-0.2604880. 130940T. 9893620. 0517R-squared0. 188919Mean dep endent var23. 40351Adjusted R-squared0. 158879S. D. dep endent var399.8619S.E. of regression366.7238Akaike info criterion14. 69829Sum squared resi

13、d7262264.Schwarz criterion14.80582Log likelihood-415.9013Hannan-Quinn criter.14.74008F-statistic6. 288925Durbin-Watson stat2.033371P rob(F-statiStic)0. 003505Inverted AR Roots23+. 46i一 23-. 46i由P值檢驗可知，在5%顯著水平下，AR (2)系數(shù)不顯著，剔除AR ( 2 )項后再一次估計結(jié)果如下。Dependent Variable： NEW2Method: Least SquaresDate: 05/10

14、/16 Time： 15:16Sam pie (adjusted)： 15 72In eluded observati ons： 58 after adjustme ntsCon verge nee achieved after 3 iterati onsVariableCoeffieie ntStd. Errort-StatistieP rob.C27.3052736.264940. 7529380. 4546AR-0. 3561150.124802-2. 8534400. 0061R-squared0.126939Mean dependent var27.05172Adjusted R-s

15、quared0. 111348S.D. dependentvar397.3115S.E. of regressi on374.5389Akaike info eriteri on14.72314Sum squared resid7855644.Sehwarz eriteri on14.79419Log likelihood-424.9711Hannan-Quinn eriter.14.75082F-statistie8.142118Durb in-Watson stat2. 182200P rob(F-statiStic)0.006051In verted AR Roots一 36剔除AR (

16、2)項后的模型顯著。Dependent Variable： NEW2Method： Least SquaresDate： 05/10/16 Time: 15:16Sam pie (adjusted)： 14 72In eluded observati ons： 59 after adjustme ntsCon verge nee achieved after 7 iterati onsMA Baekeast: 13VariableCoeffieie ntStd. Errort-StatistieP rob.C26. 7013721.980221.2147910. 2295MA(1)-0.537

17、8890. 111431-4.8270840. 0000R-squared0.192889Mean dependent var28.83051Adjusted R-squared0. 178729S.D.dependent var394. 1084S.E. of regressi on357.1567Akaike info eriteri on14.62754Sum squared resid7270974.Sehwarz eriteri on14.69796Log likelihood-429.5123Hannan-Qui nn eriter.14.65503F-statistie13. 6

18、2226Durbi n Watson stat1. 903991P rob(F-statistie)0. 000502In verted MA Roots. 54MA (1 ):模型顯著。A RMA(2, 1):Dependent Variable： NEW2Method: Least SquaresDate: 05/10/16 Time： 15:18Sam pie (adjusted)： 16 72Included observations： 57 after adjustmentsConvergence achieved after 73 iterationsMA Backcast: OF

19、F (Roots of MA process too large)VariableCoefficientStd. Errort-StatisticProb.C6.67139213. 560420. 4919750. 6248AR0.2555470. 1401501. 8233880. 0739AR (2)-0.0195060.134431-0. 1451040. 8852MAT. 2054420.06180819, 502970. 0000R-squared0.427047Mean dep endent var23. 40351Adjusted R-squared0.394616S. D. d

20、ependent var399.8619S.E. of regression311. 1182Akaike info criterion14.38581Sum squared resid5130111.Schwarz criterion14.52919Log likelihood-405. 9957Hannan-Quinn criter.14.44153F-statistic13.16776Durbin-Watson stat1.773991P rob(F-statiStic)0.000002Inverted AR Roots.131 06i. 13+ 06iInverted MA Roots

21、1. 21Estimated MA p rocess is noninvertible由P值檢驗可知，在5%顯著水平下，AR(2)系數(shù)不顯著，剔除AR(2)項后再一次估 計結(jié)果如下。Dependent Variable： NEW2Method: Least SquaresDate: 05/10/16 Time： 15:19Sam pie (adjusted)： 15 72Included observations： 58 after adjustments Convergence achieved after 19 iterations MA Backcast： 14VariableCoeff

22、icientStd. Errort-StatisticProb.C21. 343354.2651915. 0040780.0000AR(1)0.4891990. 1276673.8318230.0003MA(1)-0.9993490.069455-14.38841n aaaaR-squared0.275064Mean dep endent var27.05172Adjusted R-squared0.248703S.D. dependent var397.3115S.E. of regression344.3792Akaike info criterion14. 57170Sum square

23、d resid6522837.Schwarz criterion14. 67828Log likelihood-419. 5794Hannan-Quinn criter.14.61322F-statistic10. 43440Durbin-Watson stat2.188525P rob(F-statiStic)0.000144Inverted AR Roots.49Inverted MA Roots1.00剔除AR(2 )項后的模型顯著。步確認,由三個模型的最小信息準則AIC、BI C檢驗可知，且由DV統(tǒng)計量進 ARMA (1, 1)為最佳擬合模型。第七步：模型適應(yīng)性檢驗Time: 15:26Date:Sample： 1 72Indudedl observations： 5QQ-statistic pro ba bi I Hies adjusted for 2 ARWAt&rms *Lito correl