1、时间序列分析课后习题答案1时间序列分析课后习题答案（上机）第二章2、（1）时序图如上：序列具有明显的趋势和周期性，该序列非平稳。（2）样本自相关系数：（3）该样本自相关图上，自相关系数衰减为0的速度缓慢，且有正弦波状，显示序列具有趋势和周期，非平稳。3、（1）样本自相关系数：（2）序列平稳。（3）因Q统计量对应的概率均大于0.05，故接受该序列为白噪声的假设，即序列为村随机序列。5、（1）时序图和样本自相关图：（2）序列具有明显的周期性，非平稳。（3）序列的Q统计量对应的概率均小于0.05，该序列是非白噪声的。6、（1）根据样本相关图可知：该序列是非平稳，非白噪声的。（2）对该序列进行差分运算
2、： 的样本相关图：该序列平稳，非白噪声。第三章：17、（1）结论：序列平稳，非白噪声。（2）拟合MA(2) model: VariableCoefficientStd. Errort-StatisticProb. C80.405684.63030817.365080.0000MA(1)0.3367830.1146102.9385190.0047MA(2)0.3438770.1168742.9422970.0046R-squared0.171979 Mean dependent var80.29524Adjusted R-squared0.144379 S.D. dependent var23.
3、71981S.E. of regression21.94078 Akaike info criterion9.061019Sum squared resid28883.87 Schwarz criterion9.163073Log likelihood-282.4221 F-statistic6.230976Durbin-Watson stat2.072640 Prob(F-statistic)0.003477Inverted MA Roots -.17+.56i -.17 -.56iResidual tests（3）拟合AR(2)model： VariableCoefficientStd.
4、Errort-StatisticProb. C79.719565.44261314.647290.0000AR(1)0.2586240.1288102.0077940.0493AR(2)0.2274690.1251141.8181020.0742R-squared0.154672 Mean dependent var79.50492Adjusted R-squared0.125522 S.D. dependent var23.35053S.E. of regression21.83590 Akaike info criterion9.052918Sum squared resid27654.7
5、9 Schwarz criterion9.156731Log likelihood-273.1140 F-statistic5.306195Durbin-Watson stat1.939572 Prob(F-statistic)0.007651Inverted AR Roots .62 -.36Residual tests:(4) 拟合ARMA（2，1）model：VariableCoefficientStd. Errort-StatisticProb. C79.175034.08290819.391830.0000AR(1)-0.5868340.118000-4.9731700.0000AR
6、(2)0.3761200.0820914.5817560.0000MA(1)1.1139990.09712211.470120.0000R-squared0.338419 Mean dependent var79.50492Adjusted R-squared0.303599 S.D. dependent var23.35053S.E. of regression19.48617 Akaike info criterion8.840611Sum squared resid21643.51 Schwarz criterion8.979029Log likelihood-265.6386 F-st
7、atistic9.719104Durbin-Watson stat1.963688 Prob(F-statistic)0.000028Inverted AR Roots .39 -.97Inverted MA Roots -1.11Estimated MA process is noninvertible残差检验：（5）拟合ARMA（1，（2）model:VariableCoefficientStd. Errort-StatisticProb. C79.521004.62191017.205230.0000AR(1)0.2705060.1256062.1536030.0354MA(2)0.23
8、39140.1307731.7887010.0788R-squared0.157273 Mean dependent var79.55161Adjusted R-squared0.128706 S.D. dependent var23.16126S.E. of regression21.61946 Akaike info criterion9.032242Sum squared resid27576.65 Schwarz criterion9.135167Log likelihood-276.9995 F-statistic5.505386Durbin-Watson stat1.981887
9、Prob(F-statistic)0.006423Inverted AR Roots .27残差检验：(6)优化modelAICSCMA(2)9.06109.1631AR(2)9.05299.1567ARMA(2，1)8.84068.9790ARMA(1,（2）)9.03229.1352根据SC准则，最优模型为ARMA(2,1)模型。(7)预测：年份预测值标准差95的置信下限95的置信上限1964 83.80630 19.4861745.61341121.99921965 88.05114 22.0280144.87624131.2261966 75.70815 22.0663932.4580
10、3118.95831967 84.54800 22.2831140.87310128.22291968 74.71802 22.3227730.96539118.470618、（1）平稳性判断与纯随机性检验：序列平稳，非白噪声。（2）拟合AR（1）model:VariableCoefficientStd. Errort-StatisticProb. C0.8454410.05201316.254270.0000AR(1)0.3725640.1115693.3393220.0013R-squared0.135739 Mean dependent var0.849589Adjusted R-squ
11、ared0.123566 S.D. dependent var0.297627S.E. of regression0.278633 Akaike info criterion0.309169Sum squared resid5.512162 Schwarz criterion0.371921Log likelihood-9.284669 F-statistic11.15107Durbin-Watson stat2.068675 Prob(F-statistic)0.001341Inverted AR Roots .37残差检验：（3）拟合MA（6）model:VariableCoefficie
12、ntStd. Errort-StatisticProb. C0.8372700.06564112.755260.0000MA(1)0.2018530.1102891.8302250.0715MA(2)0.3011180.1048142.8728750.0054MA(4)0.2785660.1105282.5203220.0140MA(6)0.2700840.1159842.3286360.0228R-squared0.189662 Mean dependent var0.851216Adjusted R-squared0.142686 S.D. dependent var0.295913S.E
13、. of regression0.273989 Akaike info criterion0.313720Sum squared resid5.179833 Schwarz criterion0.469400Log likelihood-6.607637 F-statistic4.037420Durbin-Watson stat1.867536 Prob(F-statistic)0.005328Inverted MA Roots .61+.50i .61 -.50i -.04 -.77i -.04+.77i -.68+.53i -.68 -.53i残差检验：（4）拟合ARMA(2),1)mod
14、elVariableCoefficientStd. Errort-StatisticProb. C0.8522990.06125513.913900.0000AR(2)0.2607380.1237112.1076400.0387MA(1)0.4527770.1175963.8502790.0003R-squared0.219781 Mean dependent var0.855139Adjusted R-squared0.197166 S.D. dependent var0.295887S.E. of regression0.265118 Akaike info criterion0.2234
15、90Sum squared resid4.849841 Schwarz criterion0.318351Log likelihood-5.045646 F-statistic9.718346Durbin-Watson stat2.041391 Prob(F-statistic)0.000191Inverted AR Roots .51 -.51Inverted MA Roots -.45残差检验：（5）优化modelAICSCAR(1)0.30920.3719MA(6)0.31370.4694ARMA(2)，1)0.22350.3184根据SC准则，最优模型为ARMA(2),1)模型。(6)
16、预测：年份预测值标准差95的置信下限95的置信上限19750.647740.265120.128101.1673719760.750010.291030.179601.3204219770.798960.299120.212681.3852419780.825630.300760.236151.4151119790.838390.301300.247851.4289318.(1)序列平稳，非白噪声（2）拟合AR（3）模型：VariableCoefficientStd. Errort-StatisticProb. C84.130280.100370838.20040.0000AR(1)-0.39
17、50220.070460-5.6062930.0000AR(2)-0.2986340.072652-4.1104760.0001AR(3)-0.1863350.070027-2.6609180.0084R-squared0.161289 Mean dependent var84.12980Adjusted R-squared0.148320 S.D. dependent var2.877053S.E. of regression2.655132 Akaike info criterion4.810861Sum squared resid1367.647 Schwarz criterion4.8
18、77291Log likelihood-472.2752 F-statistic12.43581Durbin-Watson stat2.001728 Prob(F-statistic)0.000000Inverted AR Roots .06 -.60i .06+.60i -.52残差检验：（3）拟合AR(1,2,3,6)模型：VariableCoefficientStd. Errort-StatisticProb. C84.142840.108789773.45150.0000AR(1)-0.3955270.070754-5.5901340.0000AR(2)-0.3042730.07344
19、0-4.1431280.0001AR(3)-0.1818640.070624-2.5751100.0108AR(6)0.1481990.0652402.2716090.0242R-squared0.186539 Mean dependent var84.13128Adjusted R-squared0.169414 S.D. dependent var2.889386S.E. of regression2.633285 Akaike info criterion4.799648Sum squared resid1317.496 Schwarz criterion4.883571Log like
20、lihood-462.9657 F-statistic10.89251Durbin-Watson stat1.985492 Prob(F-statistic)0.000000Inverted AR Roots .59 .27 -.71i .27+.71i -.37 -.64i -.37+.64i -.79残差检验：（4）拟合MA（1）模型：VariableCoefficientStd. Errort-StatisticProb. C84.130420.099045849.42010.0000MA(1)-0.4807400.062375-7.7073120.0000R-squared0.1481
21、10 Mean dependent var84.11940Adjusted R-squared0.143830 S.D. dependent var2.906625S.E. of regression2.689485 Akaike info criterion4.826477Sum squared resid1439.433 Schwarz criterion4.859346Log likelihood-483.0610 F-statistic34.59833Durbin-Watson stat1.872891 Prob(F-statistic)0.000000Inverted MA Root
22、s .48残差检验：（5）拟合ARMA(1),(1,6)模型：VariableCoefficientStd. Errort-StatisticProb. C84.115530.126943662.62530.0000AR(2)-0.1679700.074565-2.2526560.0254MA(1)-0.3751340.068739-5.4573760.0000MA(6)0.1681230.0658122.5545780.0114R-squared0.175501 Mean dependent var84.10402Adjusted R-squared0.162816 S.D. depende
23、nt var2.892726S.E. of regression2.646779 Akaike info criterion4.804460Sum squared resid1366.061 Schwarz criterion4.870657Log likelihood-474.0437 F-statistic13.83572Durbin-Watson stat2.001830 Prob(F-statistic)0.000000Inverted MA Roots .72 -.36i .72+.36i .06+.73i .06 -.73i -.59 -.37i -.59+.37i残差检验：（6）
24、拟合ARMA(3，(6)模型：VariableCoefficientStd. Errort-StatisticProb. C84.127080.119520703.87620.0000AR(1)-0.3883170.070662-5.4954300.0000AR(2)-0.3204610.072472-4.4218740.0000AR(3)-0.1837540.070018-2.6243940.0094MA(6)0.2275260.0714533.1842540.0017R-squared0.196499 Mean dependent var84.12980Adjusted R-squared
25、0.179846 S.D. dependent var2.877053S.E. of regression2.605527 Akaike info criterion4.778075Sum squared resid1310.232 Schwarz criterion4.861112Log likelihood-468.0294 F-statistic11.79970Durbin-Watson stat1.990809 Prob(F-statistic)0.000000Inverted AR Roots .05+.61i .05 -.61i -.49Inverted MA Roots .68+.39i .68 -.39i .00 -.78i -.00+.78i -.68+.39i -.68 -.39i残差检验：（7）优化modelAICSCAR(3)4.81094.8773AR(6)4.79964.8836MA(1)4.82654.8593ARMA(2,6)4.80454.8707ARMA(3,6)4.77814.8611根据SC准则，最优模型为MA(1)模型。(8)预测：预测值标准差95的置信下限95的置信上限20285.692222.68948580.4208390.96361
