时间序列分析结课报告

1、列3.13对等时间间隔，连续70个某次化学反应的过程数据构成的时间序列47715150483868643557715559382357505645555071406074574160385845505053396444575862495955805045443440415545546435575937253643545448745954524523建立时间序列模型一、数据平稳性检验（1）用时序图进行检验30-60-50-40-30-20从时序图可以看出该序列无明显趋势性和周期性，可以初步认为是平稳的，（2）用序列相关性进行检验Date: 04/21/12 Time: 21:28Sample:

2、1 70Included observations: 70Autocorrelation Partial Correlation AC PAG Q-Stat ProbII111 -0.390 -0.390 11.103 0.001II112 0.304 0.180 17.970 0.000I匚I113 -0 1&6 0 002 20.032 0 000I1 11 114 0.071 -0.044 20.414 0.000i L11 115 -0.097 -0.069 21.144 0.001| 11匚16 -0.047 -0.121 21.319 0.002I1111 0.035 0.020

3、21.419 0.003I 1118 -0.043 0.005 21.572 0.006I11 119 -0.005 -0.056 21 574 0.010I11110 0.014 0.004 21.592 0.017I111|11 0.110 0.143 22.624 0.020I 11112 -0。69 -0 009 23.035 0 027I|1113 0.148 0.092 24.972 0.023I11114 0.036 0.167 25.088 0.034I11115 -0 007 -0 001 25.092 0 049I11116 0.173 0.221 27.885 0.033

4、i E111 117 -0.111 0.053 29.064 0.034I1| E118 0 020 -0.105 29.103 0 047I 111 119 -0.047 0.042 29.324 0.061I111 120 0 01& 0 050 29.350 0 081从相关图看出，自相关系数，偏系相关系数均在2阶后迅速衰减为0，说明序列是平稳的。二、对序列进行的随机性进行检验Date: 04/21/12 Time: 21:28Sample: 1 70Included observations: 70Autocorrelation Partial Correlation AC PAG Q

5、-Stat Prob11111 -0.390 -0.390 11.103 0.00111112 0.304 0.180 17.970 0.0001匚1113 -0 1&6 0 002 20.032 0 00011 11 114 0.071 -0.044 20.414 0.000| L11 115 -0.097 -0.069 21.144 0.001| 11匚16 -0.047 -0.121 21.319 0.00211111 0.035 0.020 21.419 0.0031 1118 -0.043 0.005 21.572 0.006111 119 -0.005 -0.056 21 574

6、0.010111110 0.014 0.004 21.592 0.0171111|11 0.110 0.143 22.624 0.0201 11112 -0。69 -0 009 23.035 0 0271|1113 0.148 0.092 24.972 0.023111114 0.036 0.167 25.088 0.034111115 -0 007 -0 001 25.092 0 049111116 0.173 0.221 27.885 0.033| E111 117 -0.111 0.053 29.064 0.03411| E118 0 020 -0.105 29.103 0 0471 1

7、11 119 -0.047 0.042 29.324 0.0611111 120 0 01& 0 050 29.350 0 081由图可见Q统计量对应的P0.05,表明序列存在相关性并且相关性显 著，因此序列为非白噪声序列。三、模型识别从自相关图可以看出自相关系数和偏自相关系数均有大于百分之九 十五的数据都在两倍标准差范围内，所以可以考虑用MAC2)和AR(1) 进行拟合；还可以考虑用ARMA (1,2)进行拟合。四、对模型的参数进行估计(判定条件:统计量的相伴概率非常显著， 且模型的特征根在单位圆内，说明该过程是平稳的)(1)用AR (1)进行拟合Dependent. Variable: A

8、SMethod: Least SquaresDate: 04721/12 Time: 21:31Sam pie (adjusted): 2 70Included obsen/ations: 69 after adjusting endpointsConvergence achieved after 3 iterationsVariableCoefficientStd. Errort-StatisticProb.C51.292130.93184455.04J680 0000AR-0.4249030.11&343-3.6521670 0006R-squared0.166027Mean depend

9、ent var51.18841Adjusted R-squared0.153580S.D. dependent var11.98552S.E. of regression11.02691Akaike info criterion7.667111Sum squared resid8146.708Schwarz criterion7.731867Log likelihood-262.5153F-statistic13.33832Dubin-Watson stat1.738796Prob(F-statistic)0 000511Inverted AR Roots-.42经检验符合拟合条件得到如下AR

10、 (1)模型:Xt=51.29213-0.424903(t-1)+Et(2)用MA (2)模型进行拟合Dependent Variable: AS Method: Least Squares Date: 04/21/12 Time: 21:33 Sample: 1 70Included observations: 70Convergence achieved after 5 iterations Backcast: -1 0VariableCoefficientStd. Error t-StatiaticProb.C51.049351.78890828.536600.0000MA0.31950

11、60 1220202.6184660.0109R-squared0.096990Mean dependent var51.12857Adjusted R-squared0 083711S.D. dependent var11.90898S.E. of regression11.39963Akaike infb criterion7.733194Sum squared res id8836709Schwarz criterion7.797437Log likelihood-268.6618F-statistic7.303747Durbin-Watson stat2.488438Pro -stat

12、istic：)0.008682经检验符合拟合条件得到MA(2)模型Xt=51.04935+0.319506E(t-2)用ARMA (1, 2 )模型拟合Dependent Variable: AS Method: Least Squares Date: 04/21/12 Time: 21:37 Sam pie (adjusted): 2 70Included observations: 69 after adjusting end points Convergence achieved after 11 iterations Backcast: 0 1VariableCoefficientSt

13、d. Errort-StatisticProb.C51.177261.23278641.513500.0000AR-0.2551200.355732-0.7171700.4758MA-0.1004210.343262-0.29254907708MA2)0.2739180 1594341.7180570.0905R-squared0.195286Mean dependent var51.18841Adjusted R-squared0.158U5S.D. dependent var11.98562S.E. of regression10.99713Akaike info criterion7.6

14、89368Sum squared resid7860.890Schwarz criterion7.818881Log likelihood-261.2832F-statistic5.258010urbin-Watson stat1.878947ProbfF-statistic)0 002610Inverted AR Roots.26Inverted MA Roots05 S3 .05+.52i由参数估计结果看出，各系数均不显著，说明模型并不适合拟合ARMA(1, 2)模型。经过进一步筛选，逐步剔除不显著的滞后项或 移动平均项，最后得到如下ARMA(1，1)模型，其中剔除过程略。用ARMA(1,

15、1)进行拟合Dependent Variable: ASMethod: Least SquaresDate: 04/21/12 Time: 21:38Sam pie (adjusted): 2 70Included observations: 69 after adjusting end pointsConvergence achieved after 9 iterationsBackcast: 1VariableCoefficientStd. Error t-StatisticProb.C51.241371.09630146.740240.0000AR-0.7733570.146716 -5

16、.2711000.0000MA0.4881100.2090782.3345850.0226R-squared0.203097Mean dependent var51.18841Adjusted R-squared0.178949S.D. dependent var11.98562S.E. of regression10.86040Akaike info criterion7.660628Sum squared res id7784.58&Schwarz criterion7.747763Log likelihood-260.9467F-statistic8.410322Durbin-Watson stat1E51249ProbfF-statistic)0.000558Inverted AR RootsInverted MA Roots-11-49五、模型检验残差的自相关-偏自相关图和模型拟合图AutocorrelationPartial CorrelationAC FAC Q-Stat Probii 111 -0.034 -0.034 0.0834I1 1112 0.057 0.056 0.3191I1 111 13 0.031 0.035 0.3925 0.531I 11 14 -0.082 -0.084 0.9008 0.637I 11 11