時間序列分析結(jié)課報告

1、列3.13對等時間間隔，連續(xù)70個某次化學(xué)反應(yīng)的過程數(shù)據(jù)構(gòu)成的時間序列47715150483868643557715559382357505645555071406074574160385845505053396444575862495955805045443440415545546435575937253643545448745954524523建立時間序列模型一、數(shù)據(jù)平穩(wěn)性檢驗（1）用時序圖進行檢驗30-60-50-40-30-20從時序圖可以看出該序列無明顯趨勢性和周期性，可以初步認為是平穩(wěn)的，（2）用序列相關(guān)性進行檢驗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從相關(guān)圖看出，自相關(guān)系數(shù)，偏系相關(guān)系數(shù)均在2階后迅速衰減為0，說明序列是平穩(wěn)的。二、對序列進行的隨機性進行檢驗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由圖可見Q統(tǒng)計量對應(yīng)的P0.05,表明序列存在相關(guān)性并且相關(guān)性顯 著，因此序列為非白噪聲序列。三、模型識別從自相關(guān)圖可以看出自相關(guān)系數(shù)和偏自相關(guān)系數(shù)均有大于百分之九 十五的數(shù)據(jù)都在兩倍標準差范圍內(nèi)，所以可以考慮用MAC2)和AR(1) 進行擬合；還可以考慮用ARMA (1,2)進行擬合。四、對模型的參數(shù)進行估計(判定條件:統(tǒng)計量的相伴概率非常顯著， 且模型的特征根在單位圓內(nèi)，說明該過程是平穩(wěn)的)(1)用AR (1)進行擬合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經(jīng)檢驗符合擬合條件得到如下AR

10、 (1)模型:Xt=51.29213-0.424903(t-1)+Et(2)用MA (2)模型進行擬合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經(jīng)檢驗符合擬合條件得到MA(2)模型Xt=51.04935+0.319506E(t-2)用ARMA (1, 2 )模型擬合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由參數(shù)估計結(jié)果看出，各系數(shù)均不顯著，說明模型并不適合擬合ARMA(1, 2)模型。經(jīng)過進一步篩選，逐步剔除不顯著的滯后項或 移動平均項，最后得到如下ARMA(1，1)模型，其中剔除過程略。用ARMA(1,

15、1)進行擬合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、模型檢驗殘差的自相關(guān)-偏自相關(guān)圖和模型擬合圖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