自相關(guān)性檢驗(yàn)

實(shí)驗(yàn)五自相關(guān)性【實(shí)驗(yàn)?zāi)康摹空莆兆韵嚓P(guān)性的檢驗(yàn)與處理方法?！緦?shí)驗(yàn)內(nèi)容】利用表5-1資料，試建立我國(guó)城鄉(xiāng)居民儲(chǔ)蓄存款模型，并檢驗(yàn)?zāi)Ｐ偷淖韵嚓P(guān)性。表5-1我國(guó)城鄉(xiāng)居民儲(chǔ)蓄存款與GDP統(tǒng)計(jì)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(shí)驗(yàn)步驟】一、回歸模型的篩選相關(guān)圖分析SCATXY相關(guān)圖表明，GDP指數(shù)與居民儲(chǔ)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(duì)數(shù)、對(duì)數(shù)、指數(shù)、二次多項(xiàng)式等不同形式，進(jìn)而加以比較分析。估計(jì)模型，利用LS命令分別建立以下模型⑴線性模型：LSYCX》=—14984.84+92.5075尤t=(-6.706)(13.862)R2=0.9100F=192.145S.E=5030.809⑵雙對(duì)數(shù)模型：GENRLNY=LOG(Y)GENRLNX=LOG(X)LSLNYCLNXInV=-8.0753+2.9588lnxt=(-31.604)(64.189)R2=0.9954F=4120.223S.E=0.1221⑶對(duì)數(shù)模型：LSYCLNXV=-118140.8+23605.82lnxt=(-6.501)(7.200)R2=0.7318F=51.8455S.E=8685.043⑷指數(shù)模型：LSLNYCXInV=5.3185+0.010005xt=(23.716)(14.939)R2=0.9215F=223.166S.E=0.5049⑸二次多項(xiàng)式模型：GENRX2=X"2LSYCXX2V=2944.56—44.5485x+0.1966x2t=(3.747)(-8.235)(25.886)R2=0.9976F=3814.274S.E=835.979選擇模型比較以上模型，可見(jiàn)各模型回歸系數(shù)的符號(hào)及數(shù)值較為合理。各解釋變量及常數(shù)項(xiàng)都通過(guò)了t檢驗(yàn)，模型都較為顯著。除了對(duì)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(duì)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(zhǎng)時(shí)期內(nèi)呈連續(xù)遞減趨勢(shì)而后又轉(zhuǎn)為連續(xù)遞增趨勢(shì)，指數(shù)模型則大體相反，殘差先呈連續(xù)遞增趨勢(shì)而后又轉(zhuǎn)為連續(xù)遞減趨勢(shì)，因此，可以初步判斷這兩種函數(shù)形式設(shè)置是不當(dāng)?shù)?。而且，這兩個(gè)模型的擬合優(yōu)度也較雙對(duì)數(shù)模型和二次多項(xiàng)式模型低，所以又可舍棄線性模型和指數(shù)模型。雙對(duì)數(shù)模型和二次多項(xiàng)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(gè)模型。二、自相關(guān)性檢驗(yàn)DW檢驗(yàn)；⑴雙對(duì)數(shù)模型因?yàn)閚=21，k=1，取顯著性水平a=0.05時(shí)，查表得d=1.22,d=1.42,而0<0.7062=DW<dL，所以存在(正)自相關(guān)。⑵二次多項(xiàng)式模型d=1.22，d=1.42，而d<1.2479=DW<d，所以通過(guò)DW檢驗(yàn)并不能判斷是會(huì)存在自相關(guān)。LU

偏相關(guān)系數(shù)檢驗(yàn)在方程窗口中點(diǎn)擊View/ResidualTest/Correlogram-Q-statistics，并輸入滯后期為10，則會(huì)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)，tt—1t—2t—10如圖5-11、5-12所示。AutocorrelationPartialCorrelationACPAGQ-StatProb111110.5370.5376.95430.00B111112-0.0B7-0.5277.14810.02B匚11113-0.3400.02710.2570.0171匚11匚14-0.300-0.15412.8170.0121匚11匚15-0.238-0.21214.5290.0131匚11匚16-0.206-0.14915.S940.0141匚11[17-0.106-0.0681E.2810.0231，111180.112O.OSO1E.7480.0331—11□190.3440.16521.5160.0111二>＞匚1W0.2B9-0.13125.1800.005圖5-1雙對(duì)數(shù)模型的偏相關(guān)系數(shù)檢驗(yàn)AutocorrelationPartialCorrelationACPAGQ-StatProb1■11_1110.31B0.3162.44280.11B11112-0.572-0.74910.7540.005111■13-0.6B1-0.31623.1970.000|E11■14-0.080-0.25123.3780.00011■150.450-0.22129.4970.0001■11160.306-0.47532.5030.0001111■17-0.062-0.17432.5960.0001匚11匚18-0.180-0.24433.SOO0.0001111119-0.046-0.10933.8860.00011>>■1W0.046-0.15433.9700.000圖5-2二次多項(xiàng)式模型的偏相關(guān)系數(shù)檢驗(yàn)從5-11中可以看出，雙對(duì)數(shù)模型的第1期、第2期偏相關(guān)系數(shù)的直方塊超過(guò)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(xiàng)式模型僅存在二階自相關(guān)。BG檢驗(yàn)在方程窗口中點(diǎn)擊View/ResidualTest/SeriesCorrelationLMTest，并選擇滯后期為2,則會(huì)得到如圖5-13所示的信息。Breusch-GodfreySerialCorrelatioriLMTest:F-statistic9.931164Probability0.001390Ot>s*R-squar&d11.31531Prob北ility0.003491

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(duì)數(shù)模型的BG檢驗(yàn)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?yàn)椋?，匕2的回歸系數(shù)均顯著地不為。，說(shuō)明雙對(duì)數(shù)模型存在一階和二階自相關(guān)性。。*二次多項(xiàng)式BG檢驗(yàn)BG檢驗(yàn)與偏相關(guān)系數(shù)檢驗(yàn)結(jié)果不同三、自相關(guān)性的調(diào)整：加入AR項(xiàng)1.對(duì)雙對(duì)數(shù)模型進(jìn)行調(diào)整；在LS命令中加上AR(1)和AR(2)，使用迭代估計(jì)法估計(jì)模型。鍵入命令:LSLNYCLNXAR(1)AR(2)則估計(jì)結(jié)果如圖5-16所示。Convergenceachievedafter4iterationsVariableCoefficientStd.Errort-StatisticProb.C-7.B4452B0.310490-25.2649?0.0000LNX2.9192840.05541252.682910.0000AR⑴0.9450690.2040204.63G1070.0003AR(2)-0.5913530.194324-3.0431310.0002R-squared0.998158Meandependentvar8.525164AdjustedR-squared0.997790S.D.dependentvar1.582174S.E.ofregression0.074378Akaikeinfocriterion-2.174642Sumsquaredresid0.082982Schwarzcriterion-1.975813Loglikelihoad24.65910F-statistic2709.985Durbir-WMsonstat1.644516Prob(F-statistic)0.000000InvertedARRoois.47+.611.47-,61i圖5-16加入AR項(xiàng)的雙對(duì)數(shù)模型估計(jì)結(jié)果圖5-16表明，估計(jì)過(guò)程經(jīng)過(guò)4次迭代后收斂；p1，p2的估計(jì)值分別為0.9459和-0.5914,并且,檢驗(yàn)顯著，說(shuō)明雙對(duì)數(shù)模型確實(shí)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(shí)，查表得有=1.18,d=1.40,而d<1.6445=DW<4-d，說(shuō)明模型不存在一階自相關(guān)性；再進(jìn)行偏相關(guān)系數(shù)檢驗(yàn)(圖5-17)和BG檢驗(yàn)(圖5-18),也表明不存在高階自相關(guān)性，因此，中國(guó)城鄉(xiāng)居民儲(chǔ)蓄存款的雙對(duì)數(shù)模型為：lny=—7.8445+2.9193lnxt=(-25.263)(52.683)R2=0.9982F=2709.985S.E=0.0744DW=1.6445Q-statisticprobabilitiesadjustedfor2ARMAterm(s)AutcicorrelationPartialCorrelationACPACQ-StatProb1p11■110.1440.1440.4627■匚11匚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1日-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(duì)數(shù)模型調(diào)整后的偏相關(guān)系數(shù)檢驗(yàn)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)0.4170010.7030600.5931240.5789ARP)-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-squared0.4521SeMeandependentvar474E-11AdjustedR-squared-0.972124S.D.dependentvar0.06789BS.E.ofregression0.095350Akaikeinfocriterion-1723833Sumsquaredresid0.045459Schwarzcriterion-1.027931Loglikelihood30.37G41F-statistic0.31747BDurbin-Watsonstat2.005774Prob(F-statistic)0.955691圖5-18雙對(duì)數(shù)模型調(diào)整后的BG檢驗(yàn)結(jié)果對(duì)二次多項(xiàng)式模型進(jìn)行調(diào)整；鍵入命令：LSYCXX2AR(2)則估計(jì)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(xiàng)調(diào)整后用偏相關(guān)系數(shù)檢驗(yàn)仍然存在2階和6階自相關(guān)，且BG檢驗(yàn)結(jié)果與偏相關(guān)系數(shù)檢驗(yàn)結(jié)果不同，且BG檢驗(yàn)滯后期不同，結(jié)果不同。從雙對(duì)數(shù)模型和二次多項(xiàng)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(duì)數(shù)模型中的解釋變量：模型1：加入上期儲(chǔ)蓄LNY(-1)；模型2：解釋變量取成：上期儲(chǔ)蓄LNY(-1)、本期X的增長(zhǎng)DLOG(X)。檢驗(yàn)自相關(guān)性；⑴模型1鍵入命令：LSLNYCLNXLNY(-1)則模型1的估計(jì)結(jié)果如圖5-21所示。VariableCoefficientStd.Errort-StatisticProb.C-0.5240410.894277-0.5859940.5656LNX0.3199760.3144471.0175840.3231LNY(-1)0.B793570.105795B.311B970.0000R-squared0.999124MeandependentvarB.380B24AdjustedR-squared0.999021S.D.dependentvar1.669792S.E.ofregression0.052259Akaikeinfocriterion-2.927726Sumsquaredresid0.046427Schwarzcriterion-2.778366Loglikelihood32.2772GF-statistic9690.466Durbin-Watsonstat1.350468ProbfF-statistic)0.000000圖5-21模型1的估計(jì)結(jié)果圖5-21表明了DW=1.358,n=20,k=2,查表得dl=1.100,d=1.537,而dL<1.358=DW<dv,屬于無(wú)法判定區(qū)域。采用偏相關(guān)系數(shù)檢驗(yàn)的結(jié)果如圖5-22所示，圖中偏相關(guān)系數(shù)方塊均未超過(guò)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□I1匚1W0.168-0.1219.92000.448圖5-22模型1的偏相關(guān)系數(shù)檢驗(yàn)結(jié)果⑵模型2鍵入命令：GENRDLNX=D(LNX)LSLNYCLNY(-1)DLNX則模型2的估計(jì)結(jié)果如圖5-23所示。VariableCoefficientStd.Errort-StatisticProb.C0.3754350.0682885.4978200.0000LNY(-1)0.9865380.007338134.44720.0000DLNX0.11278B0.4230290.2666200.7930R-squared0.999074MeandependentvarB.380B24AdjustedR-squared0.998965S.D.dependentvar1.669792S.E.ofregression0.053715Akaikeinfocriterion-2.872772Sumsquaredresid0.049060Schwarzcriterion-2.723412Loglikelihood3172772F-statistic9171.844Durbin-Watsonstat1.330164ProbfF-stat