第五章作业

5.1 该序列时序图如图。对原序列进行差分运算，选择1阶差分。一阶差分后序列时序图。时序图显示出差分后序列在均值附近比较稳定地波动。为了进一步确定平稳性，考察差分后序列的自相关图。对其进行白噪声检验。延迟P值延迟P值1234560.11140.27610.37930.41610.54520.51977891011120.25620.31930.39070.33100.38110.46335.2该序列时序图如图。先进行一阶差分再进行12步差分。考虑到差分后序列具有短期相关性显著，尝试拟合乘积模型Coefficients: ar1 ar2 ar3 ma1 sma1 intercept 0.2422 -0.2157 -0.1163 -0.3483 -1.0000 0.0130s.e. 0.3144 0.0827 0.1209 0.3140 0.1322 0.0072sigma2 estimated as 0.3697: log likelihood = -158.73, aic = 331.45模型检验：延迟阶数P值延迟阶数P值20.9033110.771830.9708120.67140.9962130.711650.993140.758660.9591150.791870.9213160.829680.9608180.456490.9236240.2251100.9388300.2702Time Series:Start = 169 End = 173 Frequency = 1 1 0.4889905 -0.5583821 0.7111743 0.1095789 0.72973293.4. 时间序列的时序图为进行单位根检验可得Augmented Dickey-Fuller Testdata: sheept Dickey-Fuller = -1.8653, Lag order = 4, p-value = 0.6302alternative hypothesis: stationary通过单位根检验，可知序列非平稳。对其进行一阶差分，差分后的时序图为进行单位根检验可得Augmented Dickey-Fuller Testdata: d1 Dickey-Fuller = -3.8456, Lag order = 4, p-value = 0.02169alternative hypothesis: stationary可知一阶差分后序列平稳。Coefficients: ar1 ar2 ar3 intercept 0.4869 -0.2414 -0.2626 -5.5264s.e. 0.1219 0.1297 0.1141 7.7306sigma2 estimated as 4370: part log likelihood = -398.33延迟阶数P值延迟阶数P值20.75970.899830.670880.94740.7072120.912150.7977180.759360.828240.8526Time Series:Start = 73 End = 77 Frequency = 1 1 78.946632 3.207663 -66.182214 -59.352090 -19.3863015.该序列的时序图显示序列显著非平稳。对原序列进行一阶差分，差分后残差序列显示出均值平稳但方差递增的性质。因此该序列方差非齐性。对原序列进行对数变换：对数序列图显示它保持了原序列的变化趋势，对它进行一阶差分：，差分后残差图如图残差图直观显示残差序列波