自相關(guān)性檢驗

實驗五自相關(guān)性【實驗?zāi)康摹空莆兆韵嚓P(guān)性的檢驗與處理方法?！緦嶒瀮?nèi)容】利用表5-1資料，試建立我國城鄉(xiāng)居民儲蓄存款模型，并檢驗?zāi)Ｐ偷淖韵嚓P(guān)性。表5-1 我國城鄉(xiāng)居民儲蓄存款與GDP統(tǒng)計資料(1978年=100)年份存款余額YGDP指數(shù)X年份存款余額YGDP指數(shù)X1978210.60100.019895146.90271.31979281.00107.619907034.20281.71980399.50116.019919107.00307.61981523.70122.1199211545.40351.41982675.40133.1199314762.39398.81983892.50147.6199421518.80449.319841214.70170.0199529662.25496.519851622.60192.9199638520.84544.119862237.60210.0199746279.80592.019873073.30234.0199853407.47638.219883801.50260.7【實驗步驟】一、回歸模型的篩選1?相關(guān)圖分析SCATXY相關(guān)圖表明，GDP指數(shù)與居民儲蓄存款二者的曲線相關(guān)關(guān)系較為明顯?，F(xiàn)將函數(shù)初步設(shè)定為線性、雙對數(shù)、對數(shù)、指數(shù)、二次多項式等不同形式，進而加以比較分析。2?估計模型，利用LS命令分別建立以下模型⑴線性模型：LSYCXy=—14984.84+92.5075xt=(-6.706)(13.862)R2=0.9100 F=192.145 S.E=5030.809⑵雙對數(shù)模型：GENRLNY=LOG(Y)GENRLNX=LOG(X)LSLNYCLNX

Iny=-8.0753+2.95881nxt=(—31.604)(64.189)R2=0.9954 F=4120.223 S.E=0.1221⑶對數(shù)模型：LSYCLNXy=—118140.8+23605.821nxt= (—6.501) (7.200)S.E=8685.043XS.E=0.5049R2S.E=8685.043XS.E=0.5049⑷指數(shù)模型：LSLNYCIny=5.3185+0.010005xt=(23.716) (14.939)R2=0.9215 F=223.166⑸二次多項式模型：GENRX2二X"2LSYCXX2y=2944.56-44.5485x+0.1966x2t=(3.747)(—8.235)(25.886)R2=0.9976 F=3814.274S.E=835.9793.選擇模型比較以上模型，可見各模型回歸系數(shù)的符號及數(shù)值較為合理。各解釋變量及常數(shù)項都通過了t檢驗，模型都較為顯著。除了對數(shù)模型的擬合優(yōu)度較低外，其余模型都具有高擬合優(yōu)度，因此可以首先剔除對數(shù)模型。比較各模型的殘差分布表。線性模型的殘差在較長時期內(nèi)呈連續(xù)遞減趨勢而后又轉(zhuǎn)為連續(xù)遞增趨勢，指數(shù)模型則大體相反，殘差先呈連續(xù)遞增趨勢而后又轉(zhuǎn)為連續(xù)遞減趨勢，因此，可以初步判斷這兩種函數(shù)形式設(shè)置是不當?shù)?。而且，這兩個模型的擬合優(yōu)度也較雙對數(shù)模型和二次多項式模型低，所以又可舍棄線性模型和指數(shù)模型。雙對數(shù)模型和二次多項式模型都具有很高的擬合優(yōu)度，因而初步選定回歸模型為這兩個模型。二、自相關(guān)性檢驗1.DW檢驗；⑴雙對數(shù)模型因為n=21,k=1,取顯著性水平a=0.05時，查表得d=1.22,d=1.42,LU而0<0.7062=DW<d，所以存在(正)自相關(guān)。L⑵二次多項式模型d=1.22，d=1.42，而d<1.2479=DW<d，所以通過DW檢驗并不能判LULU斷是否存在自相關(guān)。

2?偏相關(guān)系數(shù)檢驗在方程窗口中點擊View/ResidualTest/Correlogram-Q-statistics，并輸入滯后期為10,則會得到殘差e與e,e,e的各期相關(guān)系數(shù)和偏相關(guān)系數(shù),t t—1t—2 t—10如圖5-11、5-12所示。il111il11111:PAGQ-StatProb□.5370.5376.95430.00B-□.OB?-0.5277.14810.02B-□.3400.02710.2570.017-□.300-0.15412.8170.012-□.238-0.21214.5290.013-□.206-0.14915.S940.014-□.106-0.0681E.2810.023□.112O.OSO1E.7480.0330.3440.16521.5160.0110.2B9-0.13125.1800.005圖5-1雙對數(shù)模型的偏相關(guān)系數(shù)檢驗ACPAGQ-StatProbAutocorrelationPartialCorrelationACPAGQ-StatProbi匚 ii匚 i匚 ii匚 ii匚 i＞匚 i0.31B0.3162.4428-0.572-074910754-0.6B1-0.31623.197-0.080-0.25123.3780.450-0.22129.4970.306-0.47532.503-0.062-0.17432.596-0.180-0.24433.SOO0.11B0.0050.0000.0000.0000.0000.0000.0009-0.046-0.10933.886W0.046-0.15433.9700.0000.000圖5-2二次多項式模型的偏相關(guān)系數(shù)檢驗從5-11中可以看出,雙對數(shù)模型的第1期、第2期偏相關(guān)系數(shù)的直方塊超過了虛線部分,存在著一階和二階自相關(guān)。圖5-2則表明二次多項式模型僅存在二階自相關(guān)。3.BG檢驗在方程窗口中點擊View/ResidualTest/SeriesCorrelationLMTest,并選擇滯后期為2,則會得到如圖5-13所示的信息。Breusch-GodfreySerialCorrelatioriLMTestF-statistic9.931164Probability0.001390Ot＞s*R-squar&d11.31531Probability0.003491

VariableCoefficientStd.Errort-StatisticProb.C-0.019571O.1B0281-0.1039450.91B4LNX0.0035210.0340550.1034060.91B9RESID(-1)0.9062200.2050594.4193140.0004RESID(-2)-0.6016160.211596-2.8432300.0112R-squared0.538824Meandependentvar-1.40E-15AdjustedR-squared0.457440S.D.dependentvar0.119023S.E.ofregression0.067671Akaikeinfocriterion-1.860611Sumsquaredresid0.130665Schwarzcriterion-1.661854Loglikelihciod23.53B51F-statisticE.6207G9Durbin-Watsonstat1.534084ProL(F-statistic)0.003653圖5-13雙對數(shù)模型的BG檢驗圖中，nR2=11.31531,臨界概率P=0.0034，因此輔助回歸模型是顯著的,即存在自相關(guān)性。又因為e，e的回歸系數(shù)均顯著地不為0說明雙對數(shù)模型t—1 t—2存在一階和二階自相關(guān)性。二次多項式BG檢驗BG檢驗與偏相關(guān)系數(shù)檢驗結(jié)果不同三、自相關(guān)性的調(diào)整：加入AR項1?對雙對數(shù)模型進行調(diào)整；在LS命令中加上AR(1)和AR(2),使用迭代估計法估計模型。鍵入命令:LSLNYCLNX AR(1)AR(2)則估計結(jié)果如圖5-16所示。Convergerceachievedafter4iterationsVariableCoefficientStd.Errort-StatisticProb.C-7.B4452B0.310490-25.2649?0.0000LNX2.9192840.05541252.682910.0000AR(1)0.9450690.2040204.63G1070.0003AR(2)-0.5913530.194324-3.0431310.0002R-squared0.998158Meandependentvar8.525164AdjustedR-squared0.997790S.D.dependentvar1.582174S.E.ofregression0.074378Akaikeinfo匚riterion-2.174642Sumsquaredresid0.082982Schwarzcriterion-1.975813Loglikelihoad24.65910F-statistic2709.985Durbir-Watsonstat1.644516Prob(F-statistic)0.000000InvertedARRoois.47+.611.47-,61i圖5-16加入AR項的雙對數(shù)模型估計結(jié)果圖5-16表明，估計過程經(jīng)過4次迭代后收斂；p,p的估計值分別為0.945912和-0.5914,并且t檢驗顯著，說明雙對數(shù)模型確實存在一階和二階自相關(guān)性。調(diào)整后模型的DW=1.6445,n=19,k=1,取顯著性水平a=0.05時，查表得d=L1.18,d=1.40,而d<1.6445=DW<4-d，說明模型不存在一階自相關(guān)性；UUU再進行偏相關(guān)系數(shù)檢驗(圖5-17)和BG檢驗(圖5-18),也表明不存在高階自相關(guān)性，因此，中國城鄉(xiāng)居民儲蓄存款的雙對數(shù)模型為：Iny=—7.8445+2.91931nxt=(-25.263)(52.683)R2=0.9982 F=2709.985 S.E=0.0744 DW=1.6445Q-statisticprobabilitiesadjustedfor2ARMAterm(s)AutcicorrelationPartialCorrelationACPACQ-StatProb1to11■110.1440.1440.4627■匚11■12-0.294-0.3212.48061111□130.0510.1752.55330.110111iE140.065-0.0902.66620.264111115-0.0630.0132.77770.4271匚11匚16-0.206-0.2444.10180.3921匚11匚17-0.206-0.1585.51460.3561111匚1B-0.097-0.1885.B5300.4401匚11匚19-0.119-0.2016.41770.492111111100.0020.0976.71840.6E?圖5-17雙對數(shù)模型調(diào)整后的偏相關(guān)系數(shù)檢驗結(jié)果Breusch-Godfre/SerialCorrelatioriLMTestF-statistic0.412721Probability0.890480Obs*R-squared8.591566Probability0.571253VariableCoefficientStd.Errort-StatislicProb.C-0.6816970.785604-0.86773S0.4252LNX0.1273600.1495580.8615810.4333AR(1)0.4170010.7030600.5931240.5789AR(2)-0.2927960.535478-0.5467930.6080RESID(-1)-0.2870900.850201-0.3376740.7493RESID(-2)-0.7802960.623645-1.2511860.2662RESID(-3)0.3952180.8378140.4717260.6670RESID(-4)-0.0339740.553061-0.OB143O0.9634RESID(-5)0.1686100.7660150.2070590.8441RESID(-6)-0.2971920.559800-0.5308900.6182RESID(-7)-0.5125770.540149-0.9489560.3862RESID(-8)0.1371901.3349490.1027680.9221RESID(-9)-0.0119381.13S151-0.0104890.9920RESID(-10)1.2248502.9752620.4116780.6976R-squared0.4521SeMeandependentvar4.74E-11AdjustedR-squared-0.972124S.D.dependentyar0.06789BS.E.ofregression0.095350Akaikeinfouriterion-1723833Sumsquaredresid0.045459Schwarzcriterion-1.027931Loglikelihood30.37G41F-statistic0.31747BDurbin-Watsonstat2.005774Prob(F-statistic)0.955691圖5-18雙對數(shù)模型調(diào)整后的BG檢驗結(jié)果2?對二次多項式模型進行調(diào)整；鍵入命令：LSYCXX2AR(2)則估計結(jié)果如圖5-19所示。加上ar12調(diào)整后不存在自相關(guān)性，但僅有AR(2)項調(diào)整后用偏相關(guān)系數(shù)檢驗仍然存在2階和6階自相關(guān)，且BG檢驗結(jié)果與偏相關(guān)系數(shù)檢驗結(jié)果不同，且BG檢驗滯后期不同，結(jié)果不同。3.從雙對數(shù)模型和二次多項式模型中選擇調(diào)整結(jié)果較好的模型。四、重新設(shè)定雙對數(shù)模型中的解釋變量：模型1：加入上期儲蓄LNY(-l)；模型2：解釋變量取成：上期儲蓄LNY(-1)、本期X的增長DLOG(X)。1?檢驗自相關(guān)性；⑴模型1鍵入命令：LSLNYCLNXLNY(-1)則模型1的估計結(jié)果如圖5-21所示。

R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat0.9991240.9990210.052259R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat0.9991240.9990210.0522590.04642732.2772G1.350468MeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProbfF-statistic)B.380B241.669792-2.927726-2.7783669690.4660.000000VariableCoefficientStd.Errort-StatisticProb.C-0.5240410.894277-0.5859940.5656LNX0.3199760.3144471.0175840.3231LNY(-1)0.B793570.105795B.311B970.0000圖5-21模型1的估計結(jié)果圖5-21表明了DW=1.358,n=20,k=2,查表得d=1.100,d=1.537,LU而d<1.358=DW<d,屬于無法判定區(qū)域。采用偏相關(guān)系數(shù)檢驗的結(jié)果如圖5-22LU所示，圖中偏相關(guān)系數(shù)方塊均未超過虛線，模型1不存在自相關(guān)性。AutocorrelationPartialCorrelationACPAGQ-StatProbI□II■110.1890.1890.83000.362I匚II■12-0.289-0.3372.86900.238I匚I113-0.225-0.1034.17700.243II1[14-0.015-0.0434.18350.382IZlI1Zl150.1980.1305.33880.376I[I1■16-0.053-0.1905.42580.490I匚I117-0.160-0.0346.29240.506I匚I1匚18-0.236-0.2678.33520.401I]I1□>90.0920.1620.67140.468I□I11W0.168-0.1219.92000.448圖5-22模型1的偏相關(guān)系數(shù)檢驗結(jié)果⑵模型2鍵入命令：GENR DLNX二D(LNX)LSLNYCLNY(-1)DLNX則模型2的估計結(jié)果如圖5-23所示。

R-squared 0.999074AdjustedR-squared 0.998965S.E.ofregression 0.053715R-squared 0.999074AdjustedR-squared 0.998965S.E.ofregression 0.053715Sumsquaredresid 0.049060Loglikelihood 3172772Durbin-Watsonstat 1.338164Meandependentvar B.380B24S.D.dependentvar 1.669792Akaikeinfocriterion -2.872772Schwarzcriterion -2.723412F-statistic 9171.844ProbfF-statistic) 0.000000VariableCoefficientStd.Errort-StatisticProb.C0.3754350.0682885.4978200.0000LNY(-1)0.9865380.007338134.44720.0000DLNX0.11278B0.4230290.2666200.7930圖5-23模型2的估計結(jié)果圖5-23表明了DW