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：

2、（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SIWANGRENSHU11,00010,0009,0008,0007,00012,00070566055o54540533052o25 di o di5o&Cnncp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

3、为12,所以对原序列作12步差分，得到新 序列如下图所示。Ghor.1Objects to dispa y in a single 'indoA d (sfA'a ngrenshu ,0r 12)Siter one of the following-an Object or Obrject.View-a Series Formula like LOG凶 or X 十丫(-1)* a l»stofStrie£r Groupsr and Formulas-a k± of GraphsD(SIWANGRENSHU,0,12)1,200800400 -0-

4、400-800-1,200-1,60010152025303540455055606570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。Objects to display in a single windoyv d(new)|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NuLHypothesis: D(NEW) has a unit rootExogenous: ConstantLag Length: 1 (Automatic - based on SIC, maxlag=10)t-StatisticProb.*A

5、ugmented Dickey-Fuller test statistic-7.9388790.0000Test critical values:1% level5% level 10% level-3.550396-2.913549-2.594521*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 72I

6、ncluded observations: 57 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(NEW(-1)-1.7125340.215715-7.9388790.0000D(NEW(-1),2)0.2604880.1309401.9893620.0517C41.9937948.897790.8588070.3942R-squared0.702461Mean dependent var-2.789474Adjusted R-squared0.691442S.D. dependent var660.1922S.E

7、. of regression366.7238Akaike info criterion14.69829Sum squared resid7262264.Schwarz criterion14.80582Log likelihood-415.9013Hannan-Quinn criter.14.74008F-statistic63.74455Durbin-Watson stat2.033371Prob(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Date

8、: 05/10/16 rime: 15:12Sample: 1 72Included observations: 59Autoeoirrelation Partial Correlation .AC PAC Q-Stat Prob11二11 -C 356 -0.356 7.S649 0.0051匸1a2 -0 09S -0.2 5S 8.4795 0.01411 H3 C.096 -0.04Q "他 0 02S1匸1 14 -C.113 -0.U0 93029 0.04211'015 0 042 -0.052 1Q.01B 0 0751111S 0 114 0.094 10.

9、902 0 0911匚1< 17 -0J04 -0.134 13.782 0.05511< 口B 43.007 -0.150 1X786 0.0Bfi1J 19 0.100 -0.029 14.507 0.1051 111 0110 -0.092 4),067 14.996 0.13211J111 C.19& 0.156 17.859 Q.Q3511112 -0.333 -0.296 26.3&9 0 01013 |1 0II13 C 090 -0.084 26.995 0 01213 I1 114 0.116 -0.015 28.077 0 0141 111111

10、5 -C.041 0.012 28.212 0.0201 11 口116 -0.064 -0.121 28.550 0 027111 117 018S 0J36 31.428 001B1匚1II 1113 -0.19? -0,023 34.679 0.010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):Dependent Variable: NEW2Method: Least SquaresDate: 05/10/16 Time: 15:16Sample (adjusted

11、): 16 72Included observations: 57 after adjustmentsConvergence achieved after 3 iterationsVariableCoefficientStd. Errort-StatisticProb.C24.5214328.364330.8645160.3911AR(1)-0.4520470.130914-3.4530130.0011AR(2)-0.2604880.130940-1.9893620.0517R-squared0.188919Mean dependent var23.40351Adjusted R-square

12、d0.158879S.D. dependent var399.8619S.E. of regression366.7238Akaike info criterion14.69829Sum squared resid7262264.Schwarz criterion14.80582Log likelihood-415.9013Hannan-Quinn criter.14.74008F-statistic6.288925Durbin-Watson stat2.033371Prob(F-statistic)0.003505Inverted AR Roots-.23+.46i-.23-.46i由P值检

13、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Depe ndent Variable: NEW2Method: Least SquaresDate: 05/10/16 Time: 15:16Sample (adjusted): 15 72In eluded observati ons: 58 after adjustme nts Con verge nee aehieved after 3 iterati onsVariableCoeffieie ntStd. Errort-StatistieProb.C27.3052736.264940.7529380.

14、4546AR(1)-0.3561150.124802-2.8534400.0061R-squared0.126939Mean depe ndent var27.05172Adjusted R-squared0.111348S.D. dependent var397.3115S.E. of regressi on374.5389Akaike info eriteri on14.72314Sum squared resid7855644.Sehwarz eriteri on14.79419Log likelihood-424.9711Hannan-Qu inn eriter.14.75082F-s

15、tatistie8.142118Durb in -Watson stat2.182200Prob(F-statistie)0.006051In verted AR Roots-.36剔除AR(2)项后的模型显著。MA(1):Depe ndent Variable: NEW2Method: Least SquaresDate: 05/10/16 Time: 15:16Sample (adjusted): 14 72In cluded observati ons: 59 after adjustme ntsCon verge nee achieved after 7 iterati onsMA B

16、aekeast: 13VariableCoeffieie nt Std. Error t-Statistie Prob.C26.7013721.980221.2147910.2295MA(1)-0.5378890.111431-4.8270840.0000R-squared0.192889Mean depe ndent var28.83051Adjusted R-squared0.178729S.D. dependent var394.1084S.E. of regressi on357.1567Akaike info eriteri on14.62754Sum squared resid72

17、70974.Sehwarz eriteri on14.69796Log likelihood-429.5123Hannan-Quinn eriter.14.65503F-statistie13.62226Durb in-Watson stat1.903991Prob(F-statistie)0.000502In verted MA Roots.54模型显著ARMA(2,1):Dependent Variable: NEW2Method: Least SquaresDate: 05/10/16 Time: 15:18Sample (adjusted): 16 72Included observa

18、tions: 57 after adjustmentsConvergence achieved after 73 iterationsMA Backcast: OFF (Roots of MA process too large)VariableCoefficientStd. Errort-StatisticProb.C6.67139213.560420.4919750.6248AR(1)0.2555470.1401501.8233880.0739AR(2)-0.0195060.134431-0.1451040.8852MA(1)-1.2054420.061808-19.502970.0000

19、R-squared0.427047Mean dependent var23.40351Adjusted R-squared0.394616S.D.dependent var399.8619S.E. of regression311.1182Akaike info criterion14.38581Sum squared resid5130111.Schwarz criterion14.52919Log likelihood-405.9957Hannan-Quinn criter.14.44153F-statistic13.16776Durbin-Watson stat1.773991Prob(

20、F-statistic)0.000002Inverted AR Roots.13-.06i.13+.06iInverted MA Roots1.21Estimated 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。Dependent Variable: NEW2Method: Least SquaresDate: 05/10/16 Time: 15:19Sample (adjusted): 15 72Included observations: 58 after adjustments Co

21、nvergence achieved after 19 iterations MA Backcast: 14VariableCoefficientStd. Errort-StatisticProb.C21.343354.2651915.0040780.0000AR(1)0.4891990.1276673.8318230.0003MA(1)-0.9993490.069455-14.388410.0000R-squared0.275064Mean dependent var27.05172Adjusted R-squared0.248703S.D.dependent var397.3115S.E.

22、 of regression344.3792Akaike info criterion14.57170Sum squared resid6522837.Schwarz criterion14.67828Log likelihood-419.5794Hannan-Quinn criter.14.61322F-statistic10.43440Durbin-Watson stat2.188525Prob(F-statistic)0.000144Inverted AR Roots.49Inverted MA Roots1.00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DV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D樹：仙216 Time: 15:26Sample： 1 72Included observations: 58Q-statistic prababili-ties adjusted far 2 ARMA termsAutocorrelation