时间序列实验

学生学号0121315940324实验课成绩学生实验报告书实验课程名称应用时间序列分析理学院理学院开课学院指导教师姓名桂预风魏丽魏丽学生姓名学生专业班级金融sy130120152016学年第2学期实验一:实验项目名称 平稳序列建模 实验成绩实验者魏丽 专业班级 金融sy1301 实验日期 2016年4月5日一、实验目的在某个时间序列经过预处理后为平稳非白噪声序列时，可继续学会通过Eviews软件利用ARMA模型对该序列建模，熟悉建模步骤，并且利用拟合模型对序列的将来走势进行预测。二、实验原理1.ARMA模型定阶原则：AR（p）模型自相关图拖尾，偏自相关图q阶截尾，MA（q）模型自相关图q阶截尾，偏自相关图拖尾，ARMA（p,q）模型自相关图和偏自相关图均拖尾。2.未知参数估计可用矩估计、极大似然估计、和最小二乘估计3.模型显著性检验即对残差序列的白噪声检验，3.模型显著性检验即对残差序列的白噪声检验，检验统计量为:x2（m）Q=T（T+x2（m）L 尸iT-j三实验步骤一）模型一模型识别1）选择1950-2008年我国邮路及农村投递线路每年新增里程数作为实验序列，在Eviews中做出时序图，如图1-1

X图1-1由时序图可以看出，序列在均值0附近上下波动，序列平稳，可用来建立模型2）自相关性检验在Eviews中点击Correlogram，检验序列是否为白噪声序列，以及通过自相关、偏自相关图确定模型形式。uorrelogramoTXDate:03^30/16Time:2039Samptle:1950200SIncludedobservations:59AutocorrelationPartialCorrelationACFACa-statProb1 11 110.4730.47313.0650.0001匚111 12-0.199-0.54416.3620.0001iL13-0.456-0.09829.7230.000EZ1114-0.2560.00934.0050.0001111[150.0S4-0.05734.0830.0001n1□160.2320.12037.7540.0001□11[170.175-0.06439.3640.0001111Q-000(30.00739.3650.000IC11[19-0.162-0.06841.7520.000IE11110-0.161-0.02043.6580.0001111111-0.0110.05642.6680.0001:11[1120.112-0.03544.6200.000由上图可知，Q统计量对应的p值均为0,拒绝序列不相关的假设，即序列不是白噪声，同时自相关图拖尾，偏自相关图2阶截尾，因此，可建立AR⑵模型。模型建立与参数估计在Eviews中点击Quick，在空白框输入'/car(1)ar(2)”，得到图2-1DependentVariable:XMethod:LeastSquaresDate:04/0&f16Time:19:41Sample(adjusted}:19522008Includedobservations:57afteradjustmentsConvergenceachievedafter3iterationsVariableCoefficientStd.Er「o「t-StatisticProb.C10.836363.233950 3.3509660.0015AR⑴0.7236120.113S34 6397S660.0000AR(2)-0.5445970.1U075 -4-.7740230.0000R-squared0.453934Meandependentvar10.9526SAdjustedR-squared0.433709S.D.dependentvar26.47381S.E.ofregression19.92215Akaikeinfocriterion8.872737Sumsquaredresid21432.17Schwarzcriterion3.930267Loglikelihood-249.8730Hannan-Quinncriter.8.914527F-statistic2244457Durbin-Watsonstat2.104130Prob(F-statistic)0.000000InvertedARRoots.36-64136+641图2-1各项系数t统计量对应的p值都小于0.05，说明在95%的显著水平下拒绝系数为0的假设，说明系数均显著，则模型为：x=10.83686+0.728612x1-0.544597x2+£模型检验在Eviews中点击View-Residualdiagnostics，对残差序列进行白噪声检验，判断序列是否正确，结果如图3-1

□ate:0W5J16Time:19:42Sample:19522008Includedabservations:57□-statisticprobabilitiesadjustedfarZARMAterm(s)AutocorrelationPartialCorrelationACPACQ-StatProb|[1■111-0.0&4-Q.0&40.177411111120.0350.0330.25401匚11113-0.088-0.DS50.7J52[1.3911]111140.04-70.03S0.3769Ci.6451匚11匚15-0113-0.11017S44[1.6131]111160.0760.0572.1612Ci.70611111了-0.045-0.0292.30510.80S11118-0.010-0.037231260.8391[1119-0.030-0.0122376709361[1■1110-0.052-0.0792.57370.953111111-0.0050.0052.57S809791]11110.0560.0452.3091o.gss从上图看出，Q统计量对应的p值均大于0.05，接受序列不具有相关性的假设，即残差序列是白噪声序列，说明模型拟合效果较好。实验预测用该模型对1950到2009的数据进行拟合预测，得到静态预测图4-1图4-1实验结论从上述实验过程及分析可知，该序列可用AR（2）模型进行拟合，且拟合效果较好。模型拟合为x=10.83686+0.728612x1-0.544597x2+£二）模型二模型识别1）选择美国科罗拉多州某个加油站连续57天的OVERSHORT作为实验序列，在Eviews中做出时序图，如图1-1图1-1由时序图可以看出，序列在均值0附近上下波动，序列平稳，可用来建立模型2）自相关性检验在Eviews中点击Correlogram，检验序列是否为白噪声序列，以及通过自相关、偏自相关图确定模型形式。CorrelogramofOVERSHOTDate:04706Time:19:50Samp-le:157Includedobservations:57AutocorrelationPartialCorrelationACPACProb1 11 11-0.5-04-0.50415.^370.0001□11匚120.122-0.17716.1470.0001匚1匚13-0.211-031518.9130.000111匚140.080-0.26319.3150.001111■150.019-0.15319.3380.0021□111160.1170.04320.2390.0031匚11匚17-0.216-0.19123.3840.0011ZD11180_2520.12127.7320.001匚1111g-0.19J0.05030.3460.00011111110Q.Q&6-0.07030.57Q0.0011匚11匚1-1-1-0.104-0.15331.3550.00-111匚1120.012-024931.3660.002图1-2由上图可知，Q统计量对应的p值均小于0.05，拒绝序列不相关的假设，即序列不是白噪声，同时自相关图1阶截尾，偏自相关图拖尾，因此，可建立MA(1)模型。模型建立与参数估计在Eviews中点击Quick，在空白框输入“0VERSHORTcMA(1)，得到图2-10Equation;UNTITLEDWorkfile;UNTTTLEDt;;Untitled\ -□X[viewProcObjectPrintNameFreezeEstimateJForecastStatsResids□ependentVariable:OVERSHOTMethod:LeastSquaresDate:0W5/16Time:19:51Sample:157Includedobservations:57Convergenceachievedafter24iterationsMABackcast:0VariableCoefficient&td.Errort-Statistic：Prob.C)-5H71034-0.9778610.379501 -13.362J80.019953 -49.00846ci.ooaod.ooaoR-squaredAcjustedR-squaredS.E.ofregressionSuesquaredresidLoglikelihoodF-statisticPrcbfF-statistic}0.43-23730.42205344.82&98110535.0-296.625541.894700.000000MeandependentvarSDdependentvarAkaikeinfocriterionSchwarzcriterionHannan-Quinncriter.□urbin-Wateonstat-4.03503358.9691110.4780910.54977-10.E05951.73S0S4InvertedMARoots.98图2-1各项系数t统计量对应的p值都小于0.05，说明在95%的显著水平下拒绝系数为0的假设，说明系数均显著，则模型为：x=-5.071034+£-0.977861£1模型检验在Eviews中点击View-Residualdiagnostics，对残差序列进行白噪声检验，判断序列是否正确，结果如图3-1CorrelogramofR&siduals□ate:0470^16Time:19:52S-atriple:157Includedobservations:57Q-statistieprobabilitiesadjustedfor1ARMAtermfs}AutocorrelationPartialCorrelation ACPACQ-StatProbibi i21i 101180.1180.83S-0|□i 'J' 20.12+0.112178050.132|[i ■C' 3-0.0&4-Q.0S21.96220.375iJi iJi 40.1010.1062.61260455i□i iZli 50.1300.1283.6991044-8i□i i]i 60.1240.070471670.451iEi i匚i 7-0.091-0.1355.27050510i1i iJi 30.0790.0985.69780.575i匚i i匚i 9-0.208-0.227B.73-610.365iEi i匚i 10-0.170-0.21610.7970.290i匚i 'ri 11-0.177-0.09613.079021911 1 1' 12-0.0370.00213.1830.232图3-2从上图看出，Q统计量对应的p值均大于0.05，接受序列不具有相关性的假设，即残差序列是白噪声序列，说明模型拟合效果较好。实验结论从上述实验过程及分析可知，该序列可用MA（1）模型进行拟合，且拟合效果较好。模型拟合为工=-5.071034+£-0.97786181三）模型三模型识别1）选择1880-1985年全球气表平均温度做为序列，并对其进行一阶差分，在Eviews中做出时序图，如图1-1

DIF图1-1由时序图可以看出，差分序列在均值0附近上下波动，序列平稳，可用来建立模型2）自相关性检验在Eviews中点击Correlogram，检验序列是否为白噪声序列，以及通过自相关、偏自相关图确定模型形式。CorrelogramofDIFDate:04/06/16Time:20:01Sample:13801985Includedobservations:105AutocorrelationPartialCorrelationACFACd-StatProbEZ1EZ11-0.253-0.2536.90620.009iL1匚12-0.116-0.192837790.015i匚1EZ13-0.151-0.26010.S910.0121]1ill140.041-0.13011.0000.026iC1匚15-0.102-0.24312.2430.0321n1]160.2140.05517.4S60.008匚1匚17-0.202-0.23222.0930.0021JI11Q0.107-0.029234130.003IE1匚19-0.106-0.16S24.7300.00311111100.104-0.04626.0010.004-11卜111-0.013-0.01326.0220.0061]111120.045-0.05126.2660.010由上图可知，Q统计量对应的p值均小于0.05，拒绝序列不相关的假设，即序列不是白噪声，同时自相关图和偏自相关图均拖尾，因此，可建立ARMA(1,1)模型。模型建立与参数估计在Eviews中点击Quick，在空白框输入“DIFcAR(1)MA(1)，得到图2-1[=}Equation:UNTITLEDWorkfile:UNTTTLED::Untitled\ _□X[viewProcObjectPrintNameFreezeEstimateForecastStatsResidsDependentVariable:DIFMethod:LeastSquares□ate:04/06/16Time:20:03Sample(adjusted):18321935Includedobservations:104-afteradjustmentsConvergenceachievedafter10iterationsMABackcast1831VariableCoefficientStd.Errort-StatisticProb.C0.0056790.002495 2.2763230.0249AR(1)0.3300580.120663 3.1497330.0021MA⑴-0.3353450.060663 -14.593280.0000R-squared0.231156Meandependentvar0.004033AdjustedR-squared0.215931S.D.dependentvar0.142512S.E.ofregression0.126191Akaikeinfocriterion-1.273614Sumsquaredresid1.603348Schwarzcriterion-1197333Loglikelihood69.22792Hannan-Quinncriter.-1.242710F-statistic15.18301Durbin-Watsonstat1.94-4673ProbfF-statistic)0.000002InvertedARRoots.38InvertedMARoots.89图2-1各项系数t统计量对应的p值都小于0.05，说明在95%的显著水平下拒绝系数为0的假设，说明系数均显著，则模型为：x=0.002495+0.380058%+£-0.885345s1模型检验在Eviews中点击View-Residualdiagnostics，对残差序列进行白噪声检验，判断序列是否正确，结果如图3-1(=]Equation:UNTTLEDWorfcfile!LrmTLECh:lfntitled\_□XViewProcObject|PrintNameFreezeEstimateForecastStatsResidsCorrelogramofResidualsDate:04V06J16Time:20:05£amp-le:13-821985Includedobservations:104Q-statisticprobabilitiesadjustedfor2ARMAterm(E；AutocorrelationPartialCorrelationACPACQ-StatProb1111110.0260.0260.07511[11112-0.029-0.0300.16581[11[13-0.097-0.095-1.15570.276111140.0190.0241.22680.&411[11[15-0.0&9-0.066-1.61-120.6&71□1oE0.17S0.1775.19230.26S1匚11匚17-0.122-0.1406.S9130.2291]11□1&0.0860.1067.73360.2&81[11119-0.042-0.0347.93600.3351■11■I100.1150.1059.49950.3021111J111O.a^g0.0669.67B703771]111120.0670.01710.2190.422图3-3从上图看出，Q统计量对应的p值均大于0.05，接受序列不具有相关性的假设，即残差序列是白噪声序列，说明模型拟合效果较好。实验结论从上述实验过程及分析可知，该序列可用ARMA（1，1）模型进行拟合，且拟合效果较好。模型拟合为工=0.002495+0.380058%+£-0.885345s1四）模型四模型识别1）选择等时间间隔连续70个某次化学反应的过程数据作为时间序列，在Eviews中做出时序图，如图1-1

YIELD5 10 1520253035+04&&0 55 606570图1-1由时序图可以看出，差分序列在均值0附近上下波动，序列平稳，可用来建立模型2）自相关性检验在Eviews中点击Correlogram，检验序列是否为白噪声序列，以及通过自相关、偏自相关图确定模型形式。Date:04/05/16Time:20:09Sample:170Includedobservations:70AutocorrelationPartialCorrelationACRACCl-StatProbI I1 11-0.390-0.390111030.001IZZI1□I20.3040.1S017.9700.000I匚I113-0.1660.00220.0320.000I1111140.071-0.04420.4140.000Ic11115-0.097-0.06921.1440.001I[11匚16-0.047-012121.3190.002I111170.0350.02021.4190.003I[1118-0.0430.00521.5720.006I11119-0.005-0.05621.574-0.010I111100.0140.00421.5920.017IJ11■1110.1100.14322.6240.020I[11112-0.069-0.00923.0S50.027图1-2由上图可知，Q统计量对应的p值均小于0.05，拒绝序列不相关的假设，即序列不是白噪声，同时自相关图2阶截尾，偏自相关图1阶截尾，可先建立MA(2)模型。模型建立与参数估计在Eviews中点击Quick，在空白框输入“YIELDcMA(1)MA(2)，得到图2-1(=]Equation:UNTTTLEDWorldfleLTMETERUntitl迎1_nxViewProcObjectPrintNameFreezeEstimateForecastStatsResidsDependentVariable:YIELDMethod:LeastSquaresDate:04/05/16Time:20:10Sample:170Includedobservations:70Convergenceachievedafter8iterationsMABackcast-10VariableCoefficientStd.Errort-StatisticFJrob.CGIA⑴MA(2)51.16344-032200703131431.290537 39.645080.121110 -2.6654000.121590 2.5754030.00000.00960.0122R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodF-statisticProb(F-statistic)0.1816060.15717610.933098000.600-265.21327-4338050.001214MeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionHannan-Quinncriter.Durbin-Watsonstat51.1285711.90S987M33777.7597417.7016541.975062InvertedMARoots,16-.54i.16+541图2-1各项系数t统计量对应的p值都小于0.05，说明在95%的显著水平下拒绝系数为0的假设，说明系数均显著，则模型为：x=51.16344+£-0.322807£"0.313143s2模型检验在Eviews中点击View-Residualdiagnostics，对残差序列进行白噪声检验，判断序列是否正确，结果如图3-1

CorrelogramofResiduals□ate:04V0W16Time:20:10S-ample:170Includedobservations:70Q-statisticprobabilitiesadjustedlor2ARUAtenm(s)AutocorrelationPartialCorrelation ACPACa-statProb|iiii1-0.034-0.0340.0842I I1 120.02S0.022Cd225I匚IIEi3-0.130-0.12S-1.3S0O0.239I111 14-0.010-00191.39620.4981匚11[15-0.098-a.0821.96340.&801[1iLi6-0.064-0.0872.28110.6841]1i]i70.0480.0422.46510.7821[1i[i8-0.D&9-00792.74340.8401[1i[ig-0.0+7-a.078293040.8911]1iJi100.086a.0393.55020.8951]1i]i110.0990.0794.37910.335iqii(i-12-0.0^3-004S447210.924图3