.實驗報告----穩(wěn)時間序列模型建立08經(jīng)濟統(tǒng)計I60814030王思瑤..

.一．實驗?zāi)康膹挠^察到的化工生產(chǎn)過程產(chǎn)量的70個據(jù)樣本出發(fā)，通過對模型的識別、模型的定價、模型的參數(shù)估計等步驟建立起適合序列的模型。以下是化工生產(chǎn)過程的產(chǎn)量數(shù)據(jù)：obsBF147264323

obs58455445678910111213141516171819

71386455415948713557405844805537

20212223242526272829303132333435

74515750604557504525595071567450

53493435544568385060395940575423可以明顯看出序列均值顯著非零，所以用樣本均值作為其估計對序列進行零均值化。obsBF零值化后的數(shù)據(jù)obsBF零值化后的數(shù)據(jù)Y147-4.12857

6.8714326412.87143-6.12857..

.323-28.12857

2.8714347119.87143

538-13.12857

2.8714366412.871437553.8714355

-3.128573.87143841-10.12857

-6.128579597.8714357

5.871431048-3.12857

-1.12857117119.87143

1235-16.12857

-7.1285713575.8714364

1440-11.12857

-8.1285715586.8714352

0.871431644-7.12857178028.87143

7.8714318553.8714355

3.871431937-14.12857207422.871432151-0.12857

1.87143-2.1285722575.8714334

2350-1.1285724608.871432545-6.12857

2.87143-6.1285726575.8714368

2750-1.128572845-6.128572925-26.1285730597.871433150-1.12857

-1.128578.871437.87143327119.8714333564.8714357347422.87143

5.871432.871433550-1.12857

二．實驗步驟1.模識別零均值平穩(wěn)序列的自相關(guān)函數(shù)與偏相關(guān)函數(shù)的統(tǒng)計特性如下：模型AR(n)MA(m)ARMA(n,m)自相關(guān)函數(shù)拖截拖尾偏自相關(guān)函數(shù)截拖拖尾所以，作零均值化后數(shù)據(jù)的自相關(guān)函數(shù)與偏自相關(guān)函數(shù)圖Date:04/25/11Time:22:35Sample:20012070Includedobservations:..

.Autocorrelation***|.|.|**|**|.|.|*.|.*|.|.|.|.|.|.*|.|.|.|.|.|.|*.|.*|.|.|.|.|.|.|.|.|*.|.*|.|.|.|.*|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.*|.|.|.|

PartialCorrelation***|.|.|**|.|.|.|.|.*|.|.*|.|.|.|.*|.|.|.|.|*.|.|*.|.|.|.|.|.|*.|.|*.|.|*.|.|.|.*|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|.|

ACQ-StatProb1-0.382-0.38210.6380.00120.3250.20918.4440.0003-0.193-0.01821.2340.00040.090-0.04921.8570.0005-0.162-0.12623.9000.00060.014-0.09423.9160.00170.0120.06523.9280.0018-0.085-0.07924.5190.00290.039-0.05124.6440.003100.0330.08024.7360.006110.0900.12525.4260.00812-0.077-0.05425.9420.011130.063-0.04526.2910.016140.0510.13426.5240.02215-0.0060.07926.5280.033160.1260.14528.0160.03117-0.090-0.04028.7920.036180.017-0.08428.8200.05119-0.099-0.01729.7950.054200.006-0.03629.7980.073210.0150.05529.8200.09622-0.037-0.01529.9680.119230.013-0.05129.9850.150240.0100.01029.9970.185250.015-0.01630.0230.223260.0360.02330.1720.26127-0.016-0.03630.2020.305280.0330.03030.3350.34729-0.057-0.01530.7350.378300.051-0.00331.0640.41231-0.070-0.05331.7060.431320.057-0.00332.1410.460由上圖可知Autocorrelation與PartialCorrelation

序列均有收斂到零的趨勢，可以認為Y的自相關(guān)函數(shù)與偏自相關(guān)函數(shù)均是拖尾的，所以初步判斷該序列適合ARMA模。模型定（1根據(jù)Pandit-Wu建模方法，擬建ARMA，）模型，在EViews命令欄中輸入：YAR(1)AR(2)MA(1)，得到如下結(jié)果：DependentVariable:YMethod:LeastSquaresDate:04/27/11Time:16:11Sample(adjusted):2003..

)-(2.)-(2Includedobservations:afteradjustmentsConvergenceafter16iterationsBackcast:2002VariableAR(1)AR(2)MA(1)

Coefficient-0.837128-0.0794100.531360

Std.Error0.3270870.1905900.317114

t-Statistic-2.559343-0.4166521.675609

Prob.0.01280.67830.0986R-squaredAdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihood

0.223430Meandependentvar0.199535S.D.dependentvar10.71062Akaikeinfocriterion7456.629Schwarzcriterion-256.1978Durbin-Watsonstat

-0.12857011.971367.6234637.7213831.824445InvertedARRootsInvertedMARoots

-.11-.53

-.73令a2=resid，在Eviews命行中輸入genr再輸入：a2a2(-1)看該模型的殘差與其滯后一期之間的散點圖：3020101A

0-10-20-30-30-20-100A2

102030從上圖看不出有相關(guān)趨勢，而且D.W值1.824445，明不存在相關(guān)性，因此可以初步認為（2，1）模型是適應(yīng)的。（2根據(jù)Pandit-Wu建模方法，再建ARMA，）模型，在EViews命令欄中輸入：YAR(1)AR(2)AR(3)AR(4)MA(1)MA(2)MA(3)，到如下結(jié)果：DependentVariable:YMethod:LeastSquaresDate:04/27/11Time:16:36Sample(adjusted):2005Includedobservations:afteradjustmentsConvergenceafter191iterations..

.Backcast:2002VariableAR(1)AR(2)AR(3)AR(4)MA(1)MA(2)MA(3)

Coefficient-0.5988740.3121000.8709760.1743630.328836-0.288747-0.940054

Std.Error0.1451980.1230010.1186350.1293780.0492180.0561560.053871

t-Statistic-4.1245442.5373797.3416631.3477026.681214-5.141834-17.45006

Prob.0.00010.01380.00000.18290.00000.00000.0000R-squaredAdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihood

0.236761Meandependentvar0.159143S.D.dependentvar10.43479Akaikeinfocriterion6424.210Schwarzcriterion-244.7297Durbin-Watsonstat

-0.00735811.379497.6281727.8604091.907327InvertedARRootsInvertedMARoots

.94.97

-.22-.65+.74i

-.66-.64i-.65-.74i

-.66+.64i由上面結(jié)果可以看出（，3模型的殘差平方和Sumsquaredresid為（，）模型的殘差平方和Sumsquaredresid為，此ARMA（，3）擬合效果更好；而且（4）模型的D.W值為1.907327大于（21）模型的D.W值1.824445說明ARMA（4，）模型的擬合效果更好（4）模型值為比ARMA（1模型的稍但不明顯此模型ARMA（，）比模型（2,1）更好。（3根據(jù)模方法，再建模型（，5命欄中輸入YAR(1)AR(2)AR(3)AR(4)AR(6)MA(1)MA(3)MA(5),得到如下結(jié)果：DependentVariable:YMethod:LeastSquaresDate:04/27/11Time:16:46Sample(adjusted):2007Includedobservations:afteradjustmentsConvergenceafter124iterationsBackcast:OFF(RootsofMAprocesstoolarge)VariableAR(1)AR(2)AR(3)AR(4)AR(5)AR(6)MA(1)

Coefficient0.1548380.0190600.1427820.2354670.6786490.115784-0.610975

Std.Error0.2155130.2076730.1214870.1697330.2092390.1815760.318997

t-Statistic0.7184610.0917811.1752861.3872823.2434150.637661-1.915302

Prob.0.47560.92720.24510.17120.00200.52640.0609..

.MA(2)MA(3)MA(4)MA(5)

0.584247-0.105015-0.560825-1.160571

0.3334970.3083240.3691430.430714

1.751880-0.340600-1.519263-2.694526

0.08560.73480.13460.0094R-squaredAdjustedR-squaredS.E.ofregressionsquaredresidLoglikelihoodInvertedARRoots

0.596802Meandependentvar0.520727S.D.dependentvar7.839709Akaikeinfocriterion3257.435Schwarzcriterion-216.5661Durbin-Watsonstat1.07.28+.89i.28-.89i-.65+.51i-.65-.51iEstimatedARprocessisnonstationary

-0.00357011.324237.1114397.4824972.318205-.18InvertedMARoots

1.17

.35+1.15i.35-1.15i

-.63-.54i-.63+.54iEstimatedMAprocessisnoninvertible從回歸結(jié)果可以看出，（6）模型估計的AR已不穩(wěn)定的MA是可逆的，因此不用