季節(jié)ARIMA模型建模與預測試驗指導

1、實驗六季節(jié)ARIMA莫型建模與預測實驗指導學號：20131363038姓名：闕丹鳳班級：金融工程1班一、實驗目的學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ARIMA真型的特點和建模過程，掌握利用最小二乘法等方法對ARIMA模型進行估計，利用信息準則對估計的ARIMAf型進行診斷，以及如何利用ARIMA模型進行預測。掌握在實證研究如何運用Eviews軟件進行ARIMA1型的識別、診斷、估計和預測。二、實驗內容及要求1、實驗內容：根據美國國家安全委員會統(tǒng)計的1973-1978年美國月度事故死亡率數據，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

2、節(jié)非平穩(wěn)時間序列的概念和季節(jié)ARIMA真型的建模思想；(2)如何通過觀察自相關，偏自相關系數及其圖形，利用最小二乘法，以及信息準則建立合適的ARIMA1型；如何利用ARIMA真型進行預測；(3)熟練掌握相關Eviews操作。三、實驗步驟第一步：導入數據第二步：畫出時序圖由時序圖可知，死亡人數雖然沒有上升或者下降趨勢，但由季節(jié)變動因素影響。第三步：季節(jié)差分法消除季節(jié)變動得到新由時序圖可知，波動的周期大約為12,所以對原序列作12步差分,序列如下圖所示。Ghor.1Objectstodisf命yinasingle'MndowdtsfA'angrenshu,0r12)Siterone

3、oftheftlld'Mng- anObjectoObrject.View- aSeriesFormulalikeLOGOQorX+¥(-1)- al»stofStrie£rGroupsr3ndFormulas- ak±ofGraphsD(SIWANGRENSHU,0,12)1,200800-400_-800_-1,200_-1,600510152025303540455055606570由12步差分后的新序列可知，由上升趨勢，再進行一步差分得到進一步的新序列，結果如下圖所示。D(NEW)所以經過12步差分、又經過一階差分后的序列平穩(wěn)第四步：平穩(wěn)

4、性檢驗NuU_Hypothesis:D(NEW)hasaunitrootExogenous:ConstantLagLength:1(Automatic-basedonSIC,maxlag=10)t-StatisticProb.*AugmentedDickey-Fullerteststatistic-7.9388790.0000Testcriticalvalues:1%level-3.5503965%level-2.91354910%level-2.594521*MacKinnon(1996)one-sidedp-values.AugmentedDickey-FullerTestEquation

5、DependentVariable:D(NEW,2)Method:LeastSquaresDate:05/10/16Time:15:07Sample(adjusted):1672Includedobservations:57afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.D(NEW(-1)-1.7125340.215715-7.9388790.0000D(NEW(-1),2)0.2604880.1309401.9893620.0517C41.9937948.897790.8588070.3942R-squared0.702

6、461Meandependentvar-2.789474AdjustedR-squared0.691442S.D.dependentvar660.1922S.E.ofregression366.7238Akaikeinfocriterion14.69829Sumsquaredresid7262264.Schwarzcriterion14.80582Loglikelihood-415.9013Hannan-Quinncriter.14.74008F-statistic63.74455Durbin-Watsonstat2.033371Prob(F-statistic)0.000000由ADF檢驗結

7、果表明，在0.01的顯著性水平下拒絕存在單位根的原假設,所以驗證了序列是平穩(wěn)的，可以對其進行ARMA1型建模分析第五步：模型的確定Date:05/10/16rime:15:12Sample:172Includedobservations:59AutocoirrelationPartialCorrelation.ACPACQ-StatProb1口1-C356-0.3567.S6490.0051匚a2-009S-0.25S8.47950.01411U3C,096-0.04Q002SL4-C.113-0.14口930290.0421'050042-0.05210.01800751150114

8、0.09410.90200911匚!7-0J04-0.13413.7820.0551"B43.007-0.1501X786OOSS1J90,100-0.02914.5070.105111010-0,0924),06714.9960.1321111C.19&0.15617.859Q,Q351-129,333-0.29626.3590010131口13C090-0.08426.99500121311140,116-0.01528.0770014111115-C0410.01228.2120.0201n1fi-0.064-0.12128.55000271Jl117018S0J363

9、1.42800181匚II113-0.19?-0,C2334.6790.010由ACF和PACFW知，ACFft1階截尾，PACFft2階截尾，所以可選擇的模型有AR(2)、MA(1)、ARMA(2,1型。第六步：模型的參數估計AR(2):DependentVariable:NEW2Method:LeastSquaresDate:05/10/16Time:15:16Sample(adjusted):1672Includedobservations:57afteradjustmentsConvergenceachievedafter3iterationsVariableCoefficientSt

10、d.Errort-StatisticProb.C24.5214328.364330.8645160.3911AR(1)-0.4520470.130914-3.4530130.0011AR(2)-0.2604880.130940-1.9893620.0517R-squared0.188919Meandependentvar23.40351AdjustedR-squared0.158879S.D.dependentvar399.8619S.E.ofregression366.7238Akaikeinfocriterion14.69829Sumsquaredresid7262264.Schwarzc

11、riterion14.80582Loglikelihood-415.9013Hannan-Quinncriter.14.74008F-statistic6.288925Durbin-Watsonstat2.033371Prob(F-statistic)0.003505InvertedARRoots-.23+.46i-.23-.46i由P值檢驗可知，在5%著水平下，AR(2)系數不顯著，剔除AR(2)項后再一次估計結果如下。DependentVariable:NEW2Method:LeastSquaresDate:05/10/16Time:15:16Sample(adjusted):1572In

12、cludedobservations:58afteradjustmentsConvergenceachievedafter3iterationsVariableCoefficientStd.Errort-StatisticProb.C27.3052736.264940.7529380.4546AR(1)-0.3561150.124802-2.8534400.0061R-squared0.126939Meandependentvar27.05172AdjustedR-squared0.111348S.D.dependentvar397.3115S.E.ofregression374.5389Ak

13、aikeinfocriterion14.72314Sumsquaredresid7855644.Schwarzcriterion14.79419Loglikelihood-424.9711Hannan-Quinncriter.14.75082F-statistic8.142118Durbin-Watsonstat2.182200Prob(F-statistic)0.006051InvertedARRoots-.36剔除AR(2)項后的模型顯著。MA(1):DependentVariable:NEW2Method:LeastSquaresDate:05/10/16Time:15:16Sample

14、(adjusted):1472Includedobservations:59afteradjustmentsConvergenceachievedafter7iterationsMABackcast:13VariableCoefficientStd.Errort-StatisticProb.C26.7013721.980221.2147910.2295MA(1)-0.5378890.111431-4.8270840.0000R-squared0.192889Meandependentvar28.83051AdjustedR-squared0.178729S.D.dependentvar394.

15、1084S.E.ofregression357.1567Akaikeinfocriterion14.62754Sumsquaredresid7270974.Schwarzcriterion14.69796Loglikelihood-429.5123Hannan-Quinncriter.14.65503F-statistic13.62226Durbin-Watsonstat1.903991Prob(F-statistic)0.000502InvertedMARoots.54模型顯著ARMA(2,1):DependentVariable:NEW2Method:LeastSquaresDate:05

16、/10/16Time:15:18Sample(adjusted):1672Includedobservations:57afteradjustmentsConvergenceachievedafter73iterationsMABackcast:OFF(RootsofMAprocesstoolarge)VariableCoefficientStd.Errort-StatisticProb.C6.67139213.560420.4919750.6248AR(1)0.2555470.1401501.8233880.0739AR(2)-0.0195060.134431-0.1451040.8852M

17、A(1)-1.2054420.061808-19.502970.0000R-squared0.427047Meandependentvar23.40351AdjustedR-squared0.394616S.D.dependentvar399.8619S.E.ofregression311.1182Akaikeinfocriterion14.38581Sumsquaredresid5130111.Schwarzcriterion14.52919Loglikelihood-405.9957Hannan-Quinncriter.14.44153F-statistic13.16776Durbin-W

18、atsonstat1.773991Prob(F-statistic)0.000002InvertedARRoots.13-.06i.13+.06iInvertedMARoots1.21EstimatedMAprocessisnoninvertible由P值檢驗可知，在5%著水平下，AR(2)系數不顯著，剔除AR(2)項后再一次估計結果如下。DependentVariable:NEW2Method:LeastSquaresDate:05/10/16Time:15:19Sample(adjusted):1572Includedobservations:58afteradjustmentsConve

19、rgenceachievedafter19iterationsMABackcast:14VariableCoefficientStd.Errort-StatisticProb.C21.343354.2651915.0040780.0000AR(1)0.4891990.1276673.8318230.0003MA(1)-0.9993490.069455-14.388410.0000R-squared0.275064Meandependentvar27.05172AdjustedR-squared0.248703S.D.dependentvar397.3115S.E.ofregression344

20、.3792Akaikeinfocriterion14.57170Sumsquaredresid6522837.Schwarzcriterion14.67828Loglikelihood-419.5794Hannan-Quinncriter.14.61322F-statistic10.43440Durbin-Watsonstat2.188525Prob(F-statistic)0.000144InvertedARRoots.49InvertedMARoots1.00剔除AR(2)項后的模型顯著。由三個模型的最小信息準則AIC、BIC檢驗可知，且由D慚計量進一步確認,ARMA(1,1)為最佳擬合模型。第七步：模型適應性檢驗Date:05/10/KTime:15:26Sample：172Includedobservations:58Q-statisticprababili-tiesadjusted