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1、实验六实验名称：拟合残差自回归模型实验目的与要求：掌握用统计软件实现拟合残差自回归模型方法和步骤。实验内容：教材171页的例5.6 （续）实验环境与器材：北203机房-minitab统计软件实验过程（步骤）或程序代码：键入数据统计T时间序列T简单T选择C2 T确定线性拟合：时间序列T趋势分析T变量实验结果与分析 xt的时间序列图 xt的趋势分析数据xt长度37缺失数据数0拟合趋势方程Yt = 66.15 + 4.52*t准确度度量平均百分误差（MAPE） 14.759平均绝对误差（MAD） 20.841平均偏差平方和553.812Xt的趋势分析图 回归分析：Tt与t回归方程为Tt = 66.1
2、 + 4.52 t自变量系数系数标准误TP常量66.1498.1208.150.000t4.51580.372612.120.000S = 24.1962 R-Sq=80.8%R-Sq（调整）=80.2%方差分析来源自由度SSMSFP残差误差3520491:585合计36 106505异常观测值拟合值标准化观测值tTt拟合值标准误残差残差37 37.0279.40 233.237.8046.172.02RR表示此观测值含有大的标准化残差 回归分析：xt与xt-1回归方程为xt = 18.2 + 0.927 xt-1自变量系数系数标准误TP常量18.1548.2102.210.034xt-10.
3、926580.0531617.430.000S = 17.7290 R-Sq = 89.7% R-Sq （调整）=89.4%方差分析来源自由度SSMSFP回归195504 95504 303.85 0.000残差误差3511001314合计36 106505异常观测值拟合值标准化观测值 xt-1xt 拟合值 标准误残差 残差10 100.0018.158.2181.855.21RX37273 279.40 271.297.448.110.50 XR 表示此观测值含有大的标准化残差X表示受X值影响很大的观测值。回归分析：xt与xt-1回归方程为xt = 1.04 xt-1自变量系数 系数标准误T
4、P无常数项xt-11.036450.01986 52.180.000S = 18.6620方差分析来源自由度SSMSFP回归1 948238 948238 2722.71 0.000残差误差3612538348合计37 960776异常观测值拟合值标准化观测值 xt-1xt 拟合值 标准误残差 残差10 100.000.000.00100.005.36R37273 279.40 283.165.43-3.76-0.21 XR 表示此观测值含有大的标准化残差X表示受X值影响很大的观测值。 自相关函数：残差1滞后ACFTLBQ10.8580735.2229.5120.6497702.5146.92
5、30.4330361.4554.8840.2056150.6556.7350.0018440.0156.736-0.132743-0.4257.557-0.216002-0.6759.798-0.206314-0.6461.919-0.161411-0.4963.2510-0.151776-0.4664.4811-0.126886-0.3865.3812-0.102208-0.3165.9813-0.102679-0.3166.6114-0.118259-0.3567.4915-0.129545-0.3868.5916-0.125660-0.3769.6817-0.097002-0.2970.
6、3618-0.099145-0.2971.1019-0.138576-0.4172.6420-0.177660-0.5275.3221-0.228044-0.6680.0122-0.311090-0.8989.3223-0.378048-1.06104.0524-0.401812-1.10121.97残差1的自相关 偏自相关函数：残差1滞后PACFT10.8580735.222-0.328081-2.003-0.110138-0.674-0.198267-1.215-0.071217-0.4360.0627050.387-0.039807-0.2480.2051631.259-0.083272
7、-0.5110-0.231817-1.41110.0715380.4412-0.062013-0.3813-0.006191-0.0414-0.052089-0.32150.0001830.00160.0625630.3818-0.172466-1.0519-0.145155-0.8820-0.078179-0.4821-0.104789-0.6422-0.188685-1.1523-0.022760-0.14240.0010300.01残差1的偏自相关 综合自回归移动平均(ARIMA)模型：残差1每次迭代中的估计值迭代SSE参数014926.6 0.1000.100 0.080112179.
8、3 0.2500.032 0.13329834.9 0.400-0.040 0.17437836.3 0.550-0.116 0.20846153.3 0.700-0.194 0.23654765.5 0.850-0.274 0.25963658.4 1.000-0.355 0.27972820.8 1.150-0.437 0.29782244.3 1.300-0.519 0.31491924.3 1.450-0.600 0.333101857.9 1.530-0.637 0.398111854.0 1.533-0.629 0.506121853.3 1.530-0.623 0.5471318
9、53.2 1.529-0.621 0.562141853.2 1.529-0.620 0.566151853.2 1.529-0.619 0.569161853.2 1.529-0.619 0.570171853.2 1.529-0.619 0.571181853.2 1.529-0.619 0.571每个估计值的相对变化不到0.0010 参数的最终估计值类型系数系数标准误TPAR 11.52870.138611.030.000AR 2-0.61890.1434-4.320.000常量0.5711.2660.450.655平均值6.3314.03观测值个数：37残差:SS = 1818.08
10、(不包括向后预测)MS = 53.47 DF = 34修正Box-Pierce(Ljung-Box)卡方统计量滞后12243648卡方12.923.833.5*自由度92133*P值0.1670.3050.444* 综合自回归移动平均(ARIMA)模型：残差1每次迭代中的估计值（模型2）迭代SSE参数014929.90.1000.100112196.10.2500.03229859.90.400-0.04137866.10.550-0.11746185.50.700-0.19654798.40.850-0.27663690.51.000-0.35872850.51.150-0.44082270
11、.21.300-0.52491944.01.450-0.606101870.41.539-0.649111867.31.544-0.644121866.91.543-0.640131866.81.543-0.638141866.81.543-0.637151866.81.543-0.637每个估计值的相对变化不到0.0010 参数的最终估计值类型系数系数标准误TPAR 11.54260.135911.350.000AR 2-0.63720.1409-4.520.000观测值个数：37残差:SS = 1811.38 （不包括向后预测）MS = 51.75 DF = 35修正Box-Pierce（
12、Ljung-Box）卡方统计量滞后12243648卡方13.324.034.0*自由度102234*P值0.2090.3460.466* xt,Xt的拟合值的时间序列图自相关函数：at滞后ACFTLBQ1-0.034928-0.210.052-0.129209-0.780.7430.1704391.021.974-0.205781-1.203.8250.0825330.464.1360.0231970.134.157-0.267176-1.497.5980.1417990.758.5990.2433331.2611.6410-0.169548-0.8413.1812-0.008613-0.04
13、13.2613-0.045873-0.2213.3914-0.072364-0.3513.7215-0.054325-0.2613.9116-0.072976-0.3514.28170.0823060.4014.77180.1474610.7116.4219-0.158618-0.7518.43200.0213690.1018.47210.1351490.6320.1222-0.171065-0.7922.9423-0.011875-0.0522.9524-0.098278-0.4524.02at的自相关自相关函数:残差2滞后ACFTLBQ10.0810820.490.2620.0049660
14、.030.2630.0278600.170.304-0.055917-0.340.435-0.046201-0.280.536-0.071956-0.430.777-0.228393-1.373.288-0.141247-0.804.2790.0205580.124.30100.0055330.034.30110.0510500.294.44120.0631930.354.67130.0303420.174.73140.0069470.044.7315-0.038367-0.214.8316-0.052168-0.295.01170.0032470.025.01180.0660200.375.
15、3519-0.007259-0.045.3520-0.037869-0.215.47210.0603620.335.8022-0.044789-0.255.9923-0.080607-0.446.6624-0.142030-0.788.90残差2的自相关自相关函数:残差2_1滞后ACFTLBQ10.4661362.808.4920.0950260.488.864-0.312987-1.5613.125-0.223632-1.0415.336-0.216898-0.9817.477-0.199177-0.8819.3480.1117420.4819.9590.1922990.8321.83100
16、.0048970.0221.8311-0.012791-0.0521.8412-0.044881-0.1921.9513-0.105238-0.4422.6114-0.126599-0.5323.6115-0.072151-0.3023.95160.0549500.2324.15170.2116690.8827.38180.2505371.0232.15190.1144410.4533.20200.1247470.4934.53210.0593930.2334.8622-0.180633-0.7038.0423-0.230868-0.8943.6524-0.278502-1.0552.50残差
17、2_1的自相关自相关函数：残差2_1滞后PACFT10.4661362.802-0.156196-0.943-0.027973-0.174-0.345435-2.0750.1170180.706-0.247196-1.4870.0026370.0280.1657220.9990.0307270.1810-0.280607-1.68110.0343210.21120.0222090.1313-0.078825-0.4714-0.187468-1.12150.2115761.27160.0099920.06170.0535710.32180.0664720.40190.0576360.35200.
18、0789160.4721-0.028220-0.1723 0.0004630.0024 -0.170539 -1.02残差2_1的偏自相关综合自回归移动平均(ARIMA)模型：残差2_1每次迭代中的估计值(模型3)迭代SSE参数02326.070.10012103.100.25021993.510.40031981.200.46641981.160.47051981.160.470每个估计值的相对变化不到0.0010 参数的最终估计值类型 系数系数标准误 T PAR 1 0.47000.1497 3.14 0.003观测值个数：36残差:SS = 1980.44 (不包括向后预测)MS = 5
19、6.58 DF = 35修正Box-Pierce(Ljung-Box)卡方统计量滞后12243648卡方13.728.8*自由度1123*P值0.2490.187* 综合自回归移动平均(ARIMA)模型：xt每次迭代中的估计值(模型1)迭代SSE参数03163.530.1005.08312675.00-0.0505.08422346.13-0.2005.07132128.51-0.3505.04341992.59-0.5005.00451927.64-0.6444.97461921.90-0.6804.99571920.82-0.6955.00381920.58-0.7025.00691920
20、.52-0.7055.008101920.50-0.7075.009111920.50-0.7085.009121920.50-0.7085.009每个估计值的相对变化不到0.0010 参数的最终估计值类型系数系数标准误TP移动平均1 -0.70820.1264-5.600.000常量5.0092.1202.360.024差值：1正规差值观测值个数:原始序列37, 36差值之后残差:SS = 1920.46 (不包括向后预测)MS = 56.48 DF = 34修正Box-Pierce(Ljung-Box)卡方统计量滞后12243648卡方7.918.7*自由度1022*-0. 8-1. 02
21、468101214161820222 4残差1的偏自相关函数（包含偏自相关的5%显著限）-0. 4 -0. 6 -0. 8 -1. 0 -1 IIIIIIIIIIr2 468101214161820222 4at的自相关函数（包含自相关的5%显著限）4O -0 8 6 4 2 0 21 o o o o o O - 关相自后12滞法二4 2 0 2 4 -0-0-0- -关相自-0. 6-0. 8 -1. 0 -1 IIiiiiiiiir2 468101214161820222 4是白噪声残差2_1的自相关函数（包含自相关的5%显著限）-0. 6-0. 8-1. 02468101214161820222 4不是1. 00. 8 一0.-0. 6-0. 8-1. 02468101214161820222 4成 绩:教师签名:
