季节ARIMA模型建模与预测实验指导

实验六季节ARIMA模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模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ARIMA模型进行诊断，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ARIMA模型的识别、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：深刻理解季节非平稳时间序列的概念和季节ARIMA模型的建模思想；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ARIMA模型；如何利用ARIMA模型进行预测；(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。由12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新序列，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Null-Hypothesis:D(NEW)hasaunitrootExogenous:ConstantLagLength:1(Automatic-basedonSIC,maxlag=10)t-StatisticProb.*AugmentedDickey匚iillerteststatistic793887900000Testcriticalvalues:1%level-3.5503965%level-2.91354910%level-2.594521*MacKinnon(1996)one-sidedp-values.AugmentedDickey-FullerTestEquationDependentVariable:D(NEW,2)Method:LeastSquaresDate:05/10/16Time:15:07Sample(adjusted):1672Ineludedobservations:57afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.D(NEW(-1))-1.7125340.215715-7.9388790.0000D(NEW(-1),2)0.2604880.1309401.9893620.0517C41.9937948.897790.8588070.3942R-squared0.702461Meandependentvar-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ARMA模型建模分析。第五步：模型的确定□ate:05J10/16Time:15:12Sample;172Includedobservations:5-9AutocorrelationPartialCorrelationACPACQ-StatProb11111-0.356-0.^567.864900051匚1匸12-0.099-0.2588.479500141]111130.096-0.0499.0700C-02S1匚11匚14-0.113--0.1409.902900421111[150.042-0.05210.018007513|11160.1140.09410.9020.0911匚11匚11-020斗-0.13413.7320.0S5111匚13-0.007-0.15013.7S60OSS1J11190.100-0.Q2914.S07Q.1Q51[111110-0.082-0.06714.996013211□'110.195-0.16617.859003511匚112-0.333--0.29626.J590.0101]1111130.090-0.08426.9950012121111140.116-0.01528.077001411111115-0.0410.01228.21200201[11匚116-0.064--0.12120.5500.0271□11□1170.183-0.13631.42800181匚11113-0.192-0.02334.6790.010由ACF和PACF可知，ACF在1阶截尾，PACF在2阶截尾，所以可选择的模型有AR(2)、MA(1)、ARMA(2,1)等。第六步：模型的参数估计AR(2)：DependentVariable:NEW2Method:LeastSquaresDate:05/10/16Time:15:16Sample(adjusted):1672Includedobservations: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.dependentvar399.8619S.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%显著水平下，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:05/10/16Time:15:16Sample(adjusted):1572Includedobservations:58afteradjustmentsConvergeneeachievedafter3iterationsVariableCoefficientStd.Errort-StatisticProb.C27.3052736.264940.7529380.4546AR(1)-0.3561150.124802-2.8534400.0061R-squared0.126939Meandependentvar27.05172AdjustedR-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)项后的模型显著。MA(1)：DependentVariable:NEW2Method:LeastSquaresDate:05/10/16Time:15:16Sample(adjusted):1472Includedobservations:59afteradjustmentsConvergeneeachievedafter7iterationsMABackcast:13VariableCoefficientStd.Errort-StatisticProb.C26.7013721.980221.2147910.2295MA(1)-0.5378890.111431-4.8270840.0000R-squared0.192889Meandependentvar28.83051AdjustedR-squared0.178729S.D.dependentvar394.1084S.E.ofregression357.1567Akaikeinfocriterion14.62754Sumsquaredresid7270974.Schwarzcriterion14.69796Loglikelihood-429.5123Hannan-Quinncriter.14.65503F-statistic13.62226Durbin-Watsonstat1.903991Prob(F-statistic)0.000502InvertedMARoots.54模型显著。ARMA(2,1):

DependentVariable:NEW2Method:LeastSquaresDate:05/10/16Time:15:18Sample(adjusted):1672Includedobservations:57afteradjustmentsConvergenceachievedafter73iterationsMABackcast:OFF(RootsofMAprocesstoolarge)VariableCoefficientStd.Errort-StatisticProb.C6.67139213.560420.4919750.6248AR(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.Schwarzcriterion14.52919Loglikelihood-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%显著水平下，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: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-squared0.275064Meandependentvar27.05172AdjustedR-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、IC检验可知，且由DW统计量进一步确认,ARMA(1,1)为最佳拟合模型。第七步：模型适应性检验

Date;05/10/16Time;15;26Sample:172Includedobservations:58Q-statisticprobabilitiesadjustedfor2ARMAtermsAutocorrelationP