季节ARIMＡ模型建模与预测实验指导————————————————————————————————作者: ————————————————————————————————日期:ﻩ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：（1)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; （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6,0007,0008,0009,00010,00011,00012,000510152025303540455055606570SIWANGRENSHU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)1,200800400-400-800-1,200-1,600510152025303540455055606570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)1,6001,200800400-400-800-1,200510152025303540455055606570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) has a unit rootExogenous: ConstantLag Length: 1 (Automatic - based on SIC, maxlag=10)t-Statistic Prob.*Augmented Dickey-Fuller test statistic-7.938879 0.0000Test critical values:1% level-3.5503965% level-2.91354910% level-2.594521*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(NEW,2)Method: Least SquaresDate: 05/10/16 Time: 15:07Sample (adjusted): 16 72Included observations: 57 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob.D(NEW(-1))-1.7125340.215715-7.9388790.0000D(NEW(-1),2)0.2604880.130940 1.9893620.0517C41.9937948.897790.8588070.3942R-squared0.702461 Mean dependent var-2.789474Adjusted R-squared0.691442 S.D. dependent var660.1922S.E. of regression366.7238 Akaike info criterion14.69829Sum squared resid7262264. Schwarz criterion14.80582Log likelihood-415.9013 Hannan-Quinn criter.14.74008F-statistic63.74455 Durbin-Watson stat 2.033371Prob(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):Dependent Variable: NEW2Method: Least SquaresDate: 05/10/16 Time: 15:16Sample (adjusted): 16 72Included observations: 57 after adjustmentsConvergence achieved after 3 iterationsVariable Coefficient Std. Error t-Statistic Prob.C24.5214328.364330.8645160.3911AR(1)-0.4520470.130914-3.4530130.0011AR(2)-0.2604880.130940-1.9893620.0517R-squared0.188919 Mean dependent var23.40351Adjusted R-squared0.158879 S.D. dependent var399.8619S.E. of regression366.7238 Akaike info criterion14.69829Sum squared resid7262264. Schwarz criterion14.80582Log likelihood-415.9013 Hannan-Quinn criter.14.74008F-statistic 6.288925 Durbin-Watson stat 2.033371Prob(F-statistic)0.003505Inverted AR Roots-.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。
Dependent Variable: NEW2Method: Least SquaresDate: 05/10/16 Time: 15:16Sample (adjusted): 15 72Included observations: 58 after adjustmentsConvergence achieved after 3 iterationsVariable Coefficient Std. Error t-Statistic Prob.C27.3052736.264940.7529380.4546AR(1)-0.3561150.124802-2.8534400.0061R-squared0.126939 Mean dependent var27.05172Adjusted R-squared0.111348 S.D. dependent var397.3115S.E. of regression374.5389 Akaike info criterion14.72314Sum squared resid7855644. Schwarz criterion14.79419Log likelihood-424.9711 Hannan-Quinn criter.14.75082F-statistic8.142118 Durbin-Watson stat 2.182200Prob(F-statistic)0.006051Inverted AR Roots -.36剔除AR(2)项后的模型显著。
Dependent Variable: NEW2Method: Least SquaresDate: 05/10/16 Time: 15:16Sample (adjusted): 14 72Included observations: 59 after adjustmentsConvergence achieved after 7 iterationsMA Backcast: 13Variable Coefficient Std. Error t-Statistic Prob.C26.7013721.98022 1.2147910.2295MA(1)-0.5378890.111431-4.8270840.0000 R-squared0.192889 Mean dependent var28.83051Adjusted R-squared0.178729 S.D. dependent var394.1084S.E. of regression357.1567 Akaike info criterion14.62754Sum squared resid7270974. Schwarz criterion14.69796Log likelihood-429.5123 Hannan-Quinn criter.14.65503F-statistic13.62226 Durbin-Watson stat 1.903991Prob(F-statistic)0.000502Inverted MA Roots .54ＭA（１):ﻫ模型显著。
ＡRMA(2,1):Dependent Variable: NEW2Method: Least SquaresDate: 05/10/16 Time: 15:18Sample (adjusted): 16 72Included observations: 57 after adjustmentsConvergence achieved after 73 iterationsMA Backcast: OFF (Roots of MA process too large)Variable Coefficient Std. Error t-Statistic Prob.C 6.67139213.560420.4919750.6248AR(1)0.2555470.140150 1.8233880.0739AR(2)-0.0195060.134431-0.1451040.8852MA(1)-1.2054420.061808-19.502970.0000R-squared0.427047 Mean dependent var23.40351Adjusted R-squared0.394616 S.D. dependent var399.8619S.E. of regression311.1182 Akaike info criterion14.38581Sum squared resid5130111. Schwarz criterion14.52919Log likelihood-405.9957 Hannan-Quinn criter.14.44153F-statistic13.16776 Durbin-Watson stat 1.773991Prob(F-statistic)0.000002Inverted AR Roots .13-.06i .13+.06iInverted MA Roots 1.21Estimated MA process is noninvertible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。