季节ARIMA模型建模与预测试验指导

1、实验六季节ARIMA莫型建模与预测实验指导学号：20131363038姓名：阙丹凤班级：金融工程1班一、实验目的学会识别时间序列的季节变动，能看出其季节波动趋势。学会剔除季节因素的方法，了解ARIMA真型的特点和建模过程，掌握利用最小二乘法等方法对ARIMA模型进行估计，利用信息准则对估计的ARIMAf型进行诊断，以及如何利用ARIMA模型进行预测。掌握在实证研究如何运用Eviews软件进行ARIMA1型的识别、诊断、估计和预测。二、实验内容及要求1、实验内容：根据美国国家安全委员会统计的1973-1978年美国月度事故死亡率数据，请选择适当模型拟合该序列的发展。2、实验要求：(1)深刻理解季

2、节非平稳时间序列的概念和季节ARIMA真型的建模思想；(2)如何通过观察自相关，偏自相关系数及其图形，利用最小二乘法，以及信息准则建立合适的ARIMA1型；如何利用ARIMA真型进行预测；(3)熟练掌握相关Eviews操作。三、实验步骤第一步：导入数据第二步：画出时序图SIWANGRENSHU由时序图可知，死亡人数虽然没有上升或者下降趋势，但由季节变动因素影响。第三步：季节差分法消除季节变动由时序图可知，波动的周期大约为12,所以对原序列作12步差分，得到新序列如下图所示。D(SIWANGRENSHU,0,12)1,200800-400_-800_-1,200_-1,600由新序列,51015

3、202530354045505560657012步差分后的新序列可知，由上升趋势，再进行一步差分得到进一步的结果如下图所示。D(NEW)所以经过12步差分、又经过一阶差分后的序列平稳第四步：平稳性检验NuU_Hypothesis:D(NEW)hasaunitrootExogenous:ConstantLagLength:1(Automatic-basedonSIC,maxlag=10)t-StatisticProb.*AugmentedDickey-Fullerteststatistic-7.9388790.0000Testcriticalvalues:1%level-3.5503965%le

4、vel-2.91354910%level-2.594521*MacKinnon(1996)one-sidedp-values.AugmentedDickey-FullerTestEquationDependentVariable:D(NEW,2)Method:LeastSquaresDate:05/10/16Time:15:07Sample(adjusted):1672Includedobservations:57afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.D(NEW(-1)-1.7125340.215715-7.93

5、88790.0000D(NEW(-1),2)0.2604880.1309401.9893620.0517C41.9937948.897790.8588070.3942R-squared0.702461Meandependentvar-2.789474AdjustedR-squared0.691442S.D.dependentvar660.1922S.E.ofregression366.7238Akaikeinfocriterion14.69829Sumsquaredresid7262264.Schwarzcriterion14.80582Loglikelihood-415.9013Hannan

6、-Quinncriter.14.74008F-statistic63.74455Durbin-Watsonstat2.033371Prob(F-statistic)0.000000由ADF检验结果表明，在0.01的显著性水平下拒绝存在单位根的原假设,所以验证了序列是平稳的，可以对其进行ARMA1型建模分析第五步：模型的确定Date:05/10/1CTime：15:12Sample:172includedobservations:59AutocorrelationPartialCorrelationACPACQ-StstProb111-035ft-0.356786490.0051匚匚2-0.D9

7、9-0.2588475500141二*130.09S-0.049S0700005S1匚1匚4-0113-0.1409.90290.042111150042-C.05210.0130.07511160.114Q,09410.9020091匚*7-0.204*0.13413.7620.05511匚S-0007-0.15013.7860.06B11190.100-Q.02914.5C70.105E110-0.082-0.06714.9960.13211110,195O.lfiS17.35900351-二12H333-0.29526.35903101L130090-0.06425.9950.01211

8、|140.11S-0.01528.077001411115-0.0410.01228.2120020116-0.064-0.12129.S500111701830,13631.4260016匚118-0,192-0.02334.579Q.010由ACF和PACFW知，ACFft1阶截尾，PACFft2阶截尾，所以可选择的模型有AR(2)、MA(1)、ARMA(2,1型。第六步：模型的参数估计AR(2):DependentVariable:NEW2Method:LeastSquaresDate:05/10/16Time:15:16Sample(adjusted):1672Includedobse

9、rvations:57afteradjustmentsConvergenceachievedafter3iterationsVariableCoefficientStd.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.dependentvar399.861

10、9S.E.ofregression366.7238Akaikeinfocriterion14.69829Sumsquaredresid7262264.Schwarzcriterion14.80582Loglikelihood-415.9013Hannan-Quinncriter.14.74008F-statistic6.288925Durbin-Watsonstat2.033371Prob(F-statistic)0.003505InvertedARRoots-.23+.46i-.23-.46i由P值检验可知，在5%著水平下，AR(2)系数不显著，剔除AR(2)项后再一次估计结果如下。Depe

11、ndentVariable:NEW2Method:LeastSquaresDate:05/10/16Time:15:16Sample(adjusted):1572Includedobservations:58afteradjustmentsConvergenceachievedafter3iterationsVariableCoefficientStd.Errort-StatisticProb.C27.3052736.264940.7529380.4546AR(1)-0.3561150.124802-2.8534400.0061R-squared0.126939Meandependentvar

12、27.05172AdjustedR-squared0.111348S.D.dependentvar397.3115S.E.ofregression374.5389Akaikeinfocriterion14.72314Sumsquaredresid7855644.Schwarzcriterion14.79419Loglikelihood-424.9711Hannan-Quinncriter.14.75082F-statistic8.142118Durbin-Watsonstat2.182200Prob(F-statistic)0.006051InvertedARRoots-.36剔除AR(2)项

13、后的模型显著。MA(1):DependentVariable:NEW2Method:LeastSquaresDate:05/10/16Time:15:16Sample(adjusted):1472Includedobservations:59afteradjustmentsConvergenceachievedafter7iterationsMABackcast:13VariableCoefficientStd.Errort-StatisticProb.C26.7013721.980221.2147910.2295MA(1)-0.5378890.111431-4.8270840.0000R-s

14、quared0.192889Meandependentvar28.83051AdjustedR-squared0.178729S.D.dependentvar394.1084S.E.ofregression357.1567Akaikeinfocriterion14.62754Sumsquaredresid7270974.Schwarzcriterion14.69796Loglikelihood-429.5123Hannan-Quinncriter.14.65503F-statistic13.62226Durbin-Watsonstat1.903991Prob(F-statistic)0.000

15、502InvertedMARoots.54模型显著ARMA(2,1):DependentVariable:NEW2Method:LeastSquaresDate:05/10/16Time:15:18Sample(adjusted):1672Includedobservations:57afteradjustmentsConvergenceachievedafter73iterationsMABackcast:OFF(RootsofMAprocesstoolarge)VariableCoefficientStd.Errort-StatisticProb.C6.67139213.560420.49

16、19750.6248AR(1)0.2555470.1401501.8233880.0739AR(2)-0.0195060.134431-0.1451040.8852MA(1)-1.2054420.061808-19.502970.0000R-squared0.427047Meandependentvar23.40351AdjustedR-squared0.394616S.D.dependentvar399.8619S.E.ofregression311.1182Akaikeinfocriterion14.38581Sumsquaredresid5130111.Schwarzcriterion1

17、4.52919Loglikelihood-405.9957Hannan-Quinncriter.14.44153F-statistic13.16776Durbin-Watsonstat1.773991Prob(F-statistic)0.000002InvertedARRoots.13-.06i.13+.06iInvertedMARoots1.21EstimatedMAprocessisnoninvertible由P值检验可知，在5%著水平下，AR(2)系数不显著，剔除AR(2)项后再一次估计结果如下。DependentVariable:NEW2Method:LeastSquaresDate:

18、05/10/16Time:15:19Sample(adjusted):1572Includedobservations:58afteradjustmentsConvergenceachievedafter19iterationsMABackcast:14VariableCoefficientStd.Errort-StatisticProb.C21.343354.2651915.0040780.0000AR(1)0.4891990.1276673.8318230.0003MA(1)-0.9993490.069455-14.388410.0000R-squared0.275064Meandepen

19、dentvar27.05172AdjustedR-squared0.248703S.D.dependentvar397.3115S.E.ofregression344.3792Akaikeinfocriterion14.57170Sumsquaredresid6522837.Schwarzcriterion14.67828Loglikelihood-419.5794Hannan-Quinncriter.14.61322F-statistic10.43440Durbin-Watsonstat2.188525Prob(F-statistic)0.000144InvertedARRoots.49InvertedMARoots1.00剔除AR(2)项后的模型显著。由三个模型的最小信息准则AIC、BIC检验可知，且由D惭计量进一步确认,ARMA(1,1)为最佳拟合模型。第七步：模型适应性检验Date:C5/1C/16Time:15:26Sample-172Includedobserv