1、应用时间序列分析实验报告二学生姓名张亚平学号20091315030院系数学与统计学院专业统计学指导教师尚林二0一二年三月三十日应用时间序列分析第二次实验报告实验题目118某地区连续74年的谷物产量(单位：千吨)如表3-21所示(具体数据见课本102页表-21)(1)判断该序列的平稳性与纯随机性。(2)选择适当模型拟合该序列的发展。(3)利用拟合模型，预测该地区未来5年的谷物产量。实验步骤1(1) 根据题目所给数据得到了样本的自相关序列图，和纯随机性检验结果如下所示。AutocoiTelationsCovarianceCorrelation-19864 3 2 10 1 2 3 4 567891
2、Std Error0. 0864011. 0000000. 0313720. 363090. 1162480. 0230380. 266640.1306780.22648M 杵0. 1378340.0195680.21287*年0. 1427750. 0162880.188510. 1470010.0178200. 206250. 1502320.0126210. 146080.1540110. 00325250. 03764*0. 1558720.0137470. 159100. 1559950.163021 1581730-0. 122780.00872490.100980. 161692
3、0.0001540-.001780.1625420. .00222878026480. 1625420. 000348880. OO lO l0. 162601-0.002918903378*0. 162602-0.013364154670. 162697-0.01292814963*0.164672.markstwostandarderrorsTheARIMAProcedureAutocorrelationCheckforWhiteNoiseToLagChi-SquareDFPr)ChiSq-AutocoiTelations-629.836.00010.3630.2670.2260.213
4、0.1890.2061238.54120.00010.1460.0380.1590.1630.1230.1011843.32180.0007-0.002-0.0260.004-0.034-0.155-0.150样本自相关图显示延迟3阶以后，自相关系数都落在2倍标准差范围内，而且样本自相关系数向零衰减的速度非常快，延迟6阶以后自相关系数即在零值附近波动，这是一个典型的短期相关的样本自相关图。由时序图和样本自相关图的性质可知该序列平稳。由纯随机性检验结果可知，在各阶延迟下LB检验统计量的P值都非常小，所以我们可以认定该序列属于非白噪声序列。(2) 为了找到合适的模型来拟合模型的发展，首先进行相对最
5、优定阶得到结果如下。MinimumInformationCriterionLassMA0MAIMA2MA3MA4MA5MA6MA7MA8f0-2.79799-2.78999-2.7739-2.78743-2.75304-2.69948-2.68152-2.65277-2.65428AFR1-2.84654-2.81935-2.78066-2.76348-2.72155-2.66356-2.63419-2.60857-2.62838AFR2-2.8204-2.77522-2.7284-2.70539-2.66343-2.60543-2.57646-2.5504-2.57975AR3-2.8160
6、4-2.7671-2.70934-2.671-2.61654-2.5587-2.52868-2.50716-2.52992AR4-2.78555-2.72802-2.672-2.61766-2.56047-2.50358-2.47071-2.45152-2.47179AR5-2.73049-2.6724-2.61915-2.56253-2.5044-2.49831-2.45023-2.41837-2.41498afR6-2.69706-2.64005-2.60074-2.54338-2.49039-2.45514-2.42308-2.41261-2.41245afR7-2.68859-2.63
7、045-2.58514-2.52739-2.47028-2.42293-2.40985-2.35937-2.35495AF8-2.68654-2.62839-2.57117-2.51912-2.46548-2.41621-2.41293-2.35656-2.29893Errorseriesmodel:AR(9)MinimumTableValue:BIC(i,0)=-2.84654最后一条信息显示，在自相关延迟阶数小于等8时，移动平均阶数也小于8的所有ARMA(P,q)模型中，BlC信息量相对最小的是ARMA(1,0)模型，即AR(I)模型。然后对参数进行估计，得到如下结果：Conditiona
8、lLeastSquaresEstimationParameterEstimateStandardErrortValuepWagAR1,10.927220.0443820.89.00010.1178250. 34325652.7427855.04684log determinant.VarianceEstimateStdErrorEstimateAICSBC*AICa混跳第懦懦船deAutoregressiveFactorsFactor1:1-0.92722B*(l)因此可得该序列拟合的模型为：x,=0.92722x(3) 利用模型(1)对该地区未来五年的谷产量进行预测得到结果如下:Foreca
9、stsforvariablegrainObsForecastStdError95%ConfidcnccLimits750.42650.3433-0.24621.0993760.39550.4681-0.52201.3130770.36670.5534-0.71791.4513780.34000.6173-0.86991.5500790.31530.6674-0.99291.6234并画出拟合、预测图如图1所示:图1该地区谷产量拟合、预测图相序：datagrain_1;inputgrain;time=_n_;cards;O.970.451.611.261.371.431.321.230.840.
10、891.181.331.210.980.910.611.230.971.100.740.800.81O.800.600.590.630.870.360.810.910.770.960.93O.950.650.980.700.861.320.880.680.781.250.791.190.690.930.860.860.850.900.540.321.401.14O.690.910.680.570.940.350.390.450.990.840.62O.850.730.660.760.630.320.170.46procarimadata=grain_1;identifyvar=grainmin
11、icp=(0:8)q=(0:8);estimatep=lnoint;forecastlead=5id=timeout=results;runjprocgplotdata=results;plotgrain*time=lfrecast*time=2195*time=3u95*time=3overlay;symbol1c=blacki=nonev=star;symbo!2c=redi=joinv=none;symbo!3c=greeni=joinv=none1=32;run;实验题目23-19现有201个连续的生产纪录，如表3-22所示(具体数据见课本102T03页表3-22)(1)判断该序列的平
12、稳性与纯随机性。(2)如果序列平稳且非白噪声，选择适当模型拟合该序列的发展。(3)利用拟合模型，预测该序列下一时刻95%的置信区间。实验步骤2(1)根据题目所给数据我们得到了样本的时序图和自相关序列图以及序列的纯随性检验结果，如下所示。producetimc图2该201连续生产记录时序图AutorrelationCheck for White NoiseTo Chi-ag Square DF-AutocorreIat ions33. 116.0001-0. 310-0. 088-0. 03536.05120. 0003-0.0510.016-0. 00846. 79180. 00020.011
13、0. 062-0. 02657.8824O-O(X)I0. 162-0. 0590.072ChiSq侬.05140.03 0.0.0.0.-0.125O. 169-O. 080-0.044-0.114-O.106-0.115O. OOlAutorrelationsLagCovarianceCorrelation-197in4321.012456891StdErrorO8.4532741.000000-2.624378.31046*0.070535-0.741078.087670.077034“-0.291722-.03451-米0.077528,59M2650.10851-.12456价.0.
14、0776050.078356G1.-126,710.16874料0.07933571321401-.05115米.0.081101.M0M40.015590.081261-0.085979-.00781A0.08127810iM6i-0.05029取0.08128011-0.674349.07977A0.08143412130bW-.043720.01143*0.0818220.081938140.5234620.06192.0.081946150.223152-.026400.082179161.1856920.140260.08222117-0.964737-.11413树：0.08340
15、318-0.895019-.105880.0841761;1.3688160.16193,o20-0.498726-.05900申0.086360Jl,Q6/，一,0.071570.08656122QL0.033650.086854-0.968268-.IMM*0.086919240.00958040.001130.087667-markstwostandarderrors由图2可以看出该序列大致在定的范围内随机波动。样本自相关图自延迟2阶以后，自相关系数都落入2倍标准差范围内，而且自相关系数随机分布在零值附近随机波动。因比由时序图和自相关图的性质可以认为该序列平稳。由纯随机性检验结果可以看出
16、LB统计量P值很小，因此该序列为非白噪声序列。为了找出合适的模型来拟合该序列的发展，首先对该序列进行最优定阶，得到结果如下。MinimumInformationCriterionLagSMAOMA1MA2MA3MA4MA5MA6AR02.0620421.9410871.9584441.9842131.9831562.002351.998232AR11.9740661.9673581.9724461.9979751.995772.0206532.022319AR21.9596491.9817641.9987882.0233392.0207762.0145952.048667AR31.962879
17、1.9884872.0138662.0374022.0435052.0690372.075029AR41.98472.0110172.0317012.0576252.0683812.0836692.097585%区O2.0226942.0489182.0659422.0594812.0841212.107518.UUUZOo2.0160552.042382.O6W552IOT3882124C35Errorseriesmciel:AR(12)MinimumTableValue:BIC(0.1)=1.941087ConditionalLeastSquaresEstimationParameterE
18、stimateStandardErrortValueApproxPrXUMUMALI84.123210.446020.106140.06363792.547.01.0001duceminicP=(0:6)q=(0:6);estimateq=l;forecastlead=31id=timeout=results;runiprocgplotdata=results;plotproduce*time=lfbrecasttime=2195*time=3u95time=3overlay;symbolIc=blacki=nonev=star;symbol2c=redi=joinv=none;symbo!3c=greeni=joinv=none1=32;run;Prodice751200
