計(jì)量經(jīng)濟(jì)學(xué)的各種檢驗(yàn)

經(jīng)濟(jì)計(jì)量學(xué)的幾種檢驗(yàn)1精選ppt多重共線性.Multicollinearityarisesbecausewehaveputintoomanyvariablesthatmeasurethesamething.Asthedegreeofmulticollinearityincreases,theregressionmodelestimatesofthecoefficientsbecomeunstableandthestandarderrorsforthecoefficientscangetwildlyinflated.Measure:vif,tol=1/vif,conditionindex;etc.2精選ppt多重共線性的后果1.存在完全多重共線性時(shí),參數(shù)的估計(jì)值無法確定,而且估計(jì)值的方差變?yōu)闊o窮大.2.存在不完全多重共線性時(shí),可以估計(jì)參數(shù)值,但是數(shù)值不穩(wěn)定,而且方差很大.3.多重共線性會(huì)降低預(yù)測的精度,甚至失效,增大零假設(shè)接受的可能性(t值變小).3精選ppt多重共線性的檢測方法

(1)樣本可決系數(shù)法如果樣本的可決系數(shù)R-square比較大，且回歸系數(shù)幾乎沒有統(tǒng)計(jì)上的顯著性，則可認(rèn)為存在多重共線性。Theil提出了一個(gè)指標(biāo)：多重共線性效應(yīng)系數(shù)4精選pptTheiltestresultsSas結(jié)果：結(jié)果表明有多重共線性。5精選ppt多重共線性檢測方法

（2）輔助回歸檢驗(yàn)法若存在多重共線性，則至少有一個(gè)解釋變量可精確或近似地表示為其余皆是變量的線性組合。相應(yīng)的檢驗(yàn)統(tǒng)計(jì)量為：6精選ppt輔助回歸檢驗(yàn)結(jié)果Sas結(jié)果：Klein經(jīng)驗(yàn)法則：若存在一個(gè)i,使得R(i)-square>R-square,則認(rèn)為多重共線性嚴(yán)重；本例中x1,x3有多重共線性。7精選ppt多重共線性檢驗(yàn)方法

（3）樣本相關(guān)系數(shù)檢驗(yàn)法8精選pptFGtestresultsfg=20.488013401p=0.0001344625；拒絕零假設(shè)，認(rèn)為存在多重共線性。具體那些變量之間存在多重共線性，除了上面提到的輔助回歸的方法外，還有以下提到的條件數(shù)檢驗(yàn)和方差膨脹因子法。9精選ppt

多重共線性檢驗(yàn)方法：

（4）特征值分析法所用的檢驗(yàn)統(tǒng)計(jì)指標(biāo);為第k各自變量和其余自變量回歸的可決系數(shù).

VIF>10,有多重共線性;TOL=1/VIF;條件指數(shù):

條件數(shù):;C>20,共線性嚴(yán)重.10精選ppt多重共線性的檢驗(yàn)和補(bǔ)救例一:進(jìn)口總額和三個(gè)自變量之間回歸;Sas結(jié)果如下:PearsonCorrelationCoefficients,N=11Prob>|r|underH0:Rho=0x1x2x3x11.000000.025850.99726GDP0.9399<.0001x20.025851.000000.03567存蓄量0.93990.9171x30.997260.035671.00000總消費(fèi)<.00010.9171從上面可以看出x1和x3線性相關(guān)嚴(yán)重.11精選ppt多重共線性的檢驗(yàn)和補(bǔ)救(2)回歸結(jié)果:

ParameterEstimatesParameterStandardVarianceVariableDFEstimateErrortValuePr>|t|InflationIntercept1-10.127991.21216-8.36<.00010x11-0.051400.07028-0.730.4883185.99747x210.586950.094626.200.00041.01891x310.286850.102212.810.0263186.11002發(fā)現(xiàn)x1的系數(shù)為負(fù),和現(xiàn)實(shí)經(jīng)濟(jì)意義不符,出現(xiàn)原因就是x1和x3之間的線性相關(guān).12精選ppt補(bǔ)救措施增加樣本;嶺回歸或主分量回歸;至少去掉一個(gè)具有多重共線性的變量;對(duì)具有多重共線性的變量進(jìn)行變換.對(duì)所有變量做滯后差分變換(一般是一階差分),問題是損失觀測值,可能有自相關(guān).采用人均形式的變量（例如在生產(chǎn)函數(shù)估計(jì)中）在缺乏有效信息時(shí),對(duì)系數(shù)關(guān)系進(jìn)行限制,變?yōu)橛屑s束回歸(Klein,Goldberger,1955),可以降低樣本方差和估計(jì)系數(shù)的標(biāo)準(zhǔn)差,但不一定是無偏的(除非這種限制是正確的).對(duì)具有多重共線性的變量,設(shè)法找出其因果關(guān)系,并建立模型和原方程構(gòu)成聯(lián)立方程組.13精選ppt嶺回歸嶺回歸估計(jì):K=0,b(k)=b即為OLSE;K的選取:即使b(k)的均方誤差比b的均方誤差小.14精選ppt嶺跡圖15精選ppt嶺回歸結(jié)果Obs_MODEL__TYPE__DEPVAR__RIDGE_k_PCOMIT__RMSE_Interceptx1x2x3y1MODEL1PARMSy0.48887-10.1280-0.0510.586950.287-12MODEL1RIDGEVIFy0.00方差膨脹因子

185.9971.01891186.110–13MODEL1RIDGEy0.000.48887-10.1280-0.0510.586950.287–14MODEL1RIDGEVIFy0.018.5990.981928.604-15MODEL1RIDGEy0.010.55323-9.18050.0460.598860.144–16MODEL1RIDGEVIFy0.022.8580.962192.859-1

7MODEL1RIDGEy0.020.57016-8.92770.0570.595420.127-18MODEL1RIDGEVIFy0.031.5020.943451.502-19MODEL1RIDGEy0.030.57959-8.73370.0610.590800.120-110MODEL1RIDGEVIFy0.040.9790.925320.979-111MODEL1RIDGEy0.040.58745-8.55830.0640.585910.116-1

16精選ppt主分量回歸主分量回歸是將具有多重相關(guān)的變量集綜合得出少數(shù)幾個(gè)互不相關(guān)的主分量.兩步:(1)找出自變量集的主分量,建立y與互不相關(guān)的前幾個(gè)主分量的回歸式.(2)將回歸式還原為原自變量結(jié)果.詳見,<<實(shí)用多元統(tǒng)計(jì)分析>>,方開泰;17精選ppt主分量回歸結(jié)果Obs_MODEL__TYPE__DEPVAR__PCOMIT__RMSE_Interceptx1x2x3y1MODEL1PARMSy0.48887-10.1280-0.051400.586950.28685–12MODEL1IPCVIFy10.250831.000850.25038–13MODEL1IPCy10.55001-9.13010.072780.609220.10626–14MODEL1IPCVIFy20.249560.000950.24971-15MODEL1IPCy21.05206-7.74580.073810.082690.10735-118精選ppt主分量回歸結(jié)果由輸出結(jié)果看到在刪去第三個(gè)主分量（pcomit=1)后的主分量回歸方程：Y=-9.1301+0.07278x1+0.60922x2+0.10626x3;該方程的系數(shù)都有意義，且回歸系數(shù)的方差膨脹因子均小于1.1；主分量回歸方程的均方根誤差（_RMSE=0.55)比普通OLS方程的均方根誤差（_RMSE=0.48887)有所增大但不多。19精選pptSas程序dataex01;inputx1x2x3y@@;labelx1="國內(nèi)生產(chǎn)總值";labelx2="存儲(chǔ)量";;labelx3="消費(fèi)量";labely="進(jìn)口總額";cards;149.34.2108.115.9161.24.1114.816.4171.53.1123.219.0175.53.1126.919.1180.81.1132.118.8190.72.2137.720.4202.12.114622.7212.45.6154.126.5226.15.0162.328.1231.95.1164.327.6239.00.7167.626.3;run;proc

corr

data=ex01;varx1-x3;run;*嶺回歸*;proc

reg

data=ex01outest=ex012graphicsoutvif;modely=x1-x3/ridge=0.0to0.1by0.01;plot/ridgeplot;run;proc

print

data=ex012;run;*主分量回歸法*;proc

reg

data=ex01outest=ex103;modely=x1-x3/pcomit=1,2

outvif;*pcomit表示刪去最后面的1或2個(gè)主分量,用前面m-1或m-2各主分量進(jìn)行回歸*;run;proc

print

data=ex103;run;20精選pptSas程序/*theiltest*/;proc

reg

data=ex01;equation3:modely=x1x2;equation2:modely=x1x3;equation1:modely=x2x3;run;/*r-.9473;r3s=0.9828*/;datatheil;rsq=0.9919;r1s=0.9913;r2s=0.9473;r3s=0.9828;theil=rsq-(3*rsq-(r1s+r2s+r3s));puttheil=;run;/*輔助回歸檢驗(yàn)法*/;proc

reg

data=ex01;equation3:modelx3=x1x2;equation2:modelx2=x1x3;equation1:modelx1=x2x3;run;/*FGtest*/;proc

corr

data=ex01outp=corrnosimple;varx1-x3;run;proc

print

data=corr;run;title

"計(jì)算相關(guān)矩陣的行列式";proc

iml;R={1.000

0.026

0.997,0.026

1

0.036,0.9152

0.6306

1};d=det(R);printd;run;/*d=0.081371*/;title

"計(jì)算檢驗(yàn)統(tǒng)計(jì)量及其p值";datafg;n=11;p=3;d=0.081371;fg=-(n-1-1/6*(2*p+5))*log(d);df=p(p-1)/2;p=1-probchi(fg,df);putfg=p=;run;/*fg=20.488013401p=0.0001344625,拒絕零假設(shè)*/;21精選ppt異方差的檢驗(yàn)和補(bǔ)救

OLSEunbiased,inefficient;t,Ftestinvalid;forecastaccuracydecreased.Ifthemodeliswell-fitted,thereshouldbenopatterntotheresidualsplottedagainstthefittedvalues.Ifthevarianceoftheresidualsisnon-constant,thentheresidualvarianceissaidtobe"heteroscedastic."

22精選ppt異方差的檢測Therearegraphicalandnon-graphicalmethodsfordetectingheteroscedasticity.Acommonlyusedgraphicalmethodistoplottheresidualsversusfitted(predicted)values.

Example:grade:educatedyears;potexp:workingyears;exp2=potexp^2;union:dummyvariable.23精選ppt收入方程回歸的結(jié)果

DependentVariable:LNWAGEAnalysisofVarianceSumofMeanSourceDFSquaresSquareFValuePr>FModel412.422363.1055914.06<.0001Error9520.989380.22094CorrectedTotal9933.41174RootMSE0.47004R-Square0.3718DependentMean2.35921AdjR-Sq0.3453CoeffVar19.92374ParameterEstimatesParameterStandardVariableDFEstimateErrortValuePr>|t|Intercept10.595110.283492.100.0384GRADE10.083540.020094.16<.0001POTEXP10.050270.014143.560.0006EXP21-0.000561720.00028785-1.950.0540UNION10.165930.124451.330.185624精選ppt圖示法檢測利用殘差平和對(duì)因變量的預(yù)測值做散點(diǎn)圖如右圖所示:殘差變化不大,因此認(rèn)為沒有異方差存在.25精選ppt懷特檢驗(yàn)Sas程序結(jié)果:AnalysisofVariancSumofMeanSourceDFSquaresSquareFValuePr>FModel121.188810.099070.880.5731Error879.830780.11300CorrectedTotal9911.01958RootMSE0.33615R-Square0.1079DependentMean0.20989AdjR-Sq-0.0152CoeffVar160.15281ParameterStandardVariableDFEstimateErrortValuePr>|t|Intercept1-0.077670.98580-0.080.9374GRADE1-0.012200.12502-0.100.9225POTEXP10.077840.071881.080.2819EXP21-0.003990.00409-0.970.3325UNION10.648790.861600.750.4535grade210.002200.004250.520.6065exp41-3.34378E-70.00000151-0.220.8256exp310.000061700.000141920.430.6648gx210.000116830.000111021.050.2955gp1-0.003750.00494-0.760.4498gu1-0.051370.04430-1.160.2494pu10.001930.060610.030.9746eu1-0.000221850.00126-0.180.8605殘差項(xiàng)平方對(duì)所有一階,二階及交叉項(xiàng)回歸.1.由左邊的結(jié)果可知:故同方差的假設(shè)未被拒絕.2.Procregdata=aa;Modely=x/spec;Run;可得到相同的結(jié)果。26精選ppt布羅施-帕甘/戈弗雷檢驗(yàn)

—懷特檢驗(yàn)的特例（1）OLS殘差額et和一個(gè)估計(jì)的干擾誤差

（2）用OLS將對(duì)選中的解釋變量進(jìn)行回歸，并計(jì)算解釋平方和(ESS);(3)在零假設(shè)下，有(4)一個(gè)更簡單且漸進(jìn)等價(jià)的做法是直接利用殘差平方對(duì)選中的解釋變量進(jìn)行回歸.在零假設(shè)(同方差)下,27精選ppt

DependentVariable:rsqSumofMeanSourceDFSquaresSquareFValuePr>FModel121.188810.099070.880.5731Error879.830780.11300CorrectedTotal9911.01958RootMSE0.33615R-Square0.1079DependentMean

0.20989AdjR-Sq-0.0152BPGtestresults(1)28精選pptBPGtestresults(2)DependentVariable:rsqadjustAnalysisofVarianceSumofMeanSourceDFSquaresSquareFValuePr>FModel310.704153.568051.430.2386Error96239.411162.49387CorrectedTotal99250.11531RootMSE1.57920R-Square0.0428DependentMean0.99997AdjR-Sq0.0129CoeffVar157.92443ESS=10.7041529精選pptBPGtestresults(3)?*ESS=5.35<因此,同方差的假設(shè)不能被拒絕.如果利用(4)直接回歸的結(jié)果:DependentVariable:rsqSumofMeanSourceDFSquaresSquareFValuePr>FModel30.471600.157201.430.2386Error9610.547980.10987RootMSE0.33147R-Square0.042830精選ppt戈德菲爾德-匡特(Goldfeld-Quandt)檢驗(yàn)按potexp的值將數(shù)據(jù)從小到大進(jìn)行排列.取前后個(gè)35個(gè)觀測值分別回歸.c=30;回歸的主要結(jié)果:RSS1=6.39573;RSS2=7.2517;RSS2/RSS1=1.13;而;該比值不顯著,不能拒絕同方差的原假設(shè);去掉的中間觀測值的個(gè)數(shù)要適中,否則會(huì)降低功效,一般取觀測值個(gè)數(shù)的1/3.31精選ppt補(bǔ)救措施---已知方差的形式1.廣義最小二乘法(GLS);請(qǐng)參考講義中的例子;2.模型變換法,適用于函數(shù)型異方差;已知方差的函數(shù)形式;3.加權(quán)最小二乘法(WLS);實(shí)質(zhì)上是一種模型變換法;具體參見講義中的例子;

采用面板數(shù)據(jù),增加信息量.32精選ppt未知方差的形式Furnival(1961)提出了一種擬合指數(shù)進(jìn)行不斷的修正,最后找出最佳的權(quán)重(使得該指數(shù)值最小).33精選ppt處理盲點(diǎn)---robustregression1.迭代加權(quán)最小二乘法(IRLS),Neter提出了2中加權(quán)函數(shù),HuberandBisquare,但是不易操作.SASv8中常使用ProcNLIN迭代.2.非參數(shù)回歸.ProcLoess.3.SASv9.0中有一個(gè)過程ProcrobustregStata中有一個(gè)比較好的命令:rreg直接進(jìn)行魯棒回歸(robust),采用迭代過程.34精選ppt序列相關(guān)性(serialcorrelation)

OLSEunbiased,butinefficientanditsstandarderrorestimatorsareinvalid;BLUEoftheGauss-MarkovTheoremnolongerholds.Thevarianceformulasfortheleastsquaresestimatorsareincorrect.AR,MA,orARMAformsofserialcorrelation.TaketheAR(1)forinstance:35精選pptDw檢驗(yàn)需要注意的地方假定了殘差是服從正態(tài)分布,而且是同方差;自變量是外生的,如果包含了內(nèi)生滯后變量,就需要用修正的dh檢驗(yàn)(procautoreg).只適用于一階自相關(guān),對(duì)高階或非線性自相關(guān)不適用.樣本容量至少為15.36精選ppt自相關(guān)檢驗(yàn)的標(biāo)準(zhǔn)德賓和沃森根據(jù)顯著水平,n,k,確定了二個(gè)臨界值du(上界),dl(下界);然后進(jìn)行比較;(1)d<dl,拒絕零假設(shè),認(rèn)為有正一階自相關(guān);(2)d>du,不拒絕零假設(shè);(3)dl<d<du,無結(jié)論;直觀:;d<2,正自相關(guān);d>2,負(fù)自相關(guān);d=2,無自相關(guān);37精選pptEg:Icecreamdemand(Hildreth,Lu(1960))Cons:consumptionoficecreamperhead(pints);Income:averagefamilyincomeperweek($);Price:priceoficecream(perpint);Temp:averagetemperature(inFahrenheit);Data:30four-weeklyobsfromMarch1951to11July1953;38精選ppt殘差的散點(diǎn)圖39精選ppt回歸結(jié)果

ParameterEstimatesParameterStandardVariableDFEstimateErrortValuePr>|t|Intercept10.197320.270220.730.4718price1-1.044410.83436-1.250.2218income10.003310.001172.820.0090temp10.003460.000445557.76<.0001

Durbin-WatsonD1.021NumberofObservations301stOrderAutocorrelation0.33040精選ppt1.DWtest查表可得:在0.05的顯著水平上,dl=1.21(N=30,k=3);du=1.65;直接在回歸的語句中加上一個(gè)dw選項(xiàng);Dw=1.021<dl=1.21;故有一階正的自相關(guān);41精選ppt2.當(dāng)回歸元嚴(yán)格外生時(shí)---AR(1)序列相關(guān)的檢驗(yàn)1.yt對(duì)做xt1,xt2,…,xtk回歸,得到殘差?t.2.進(jìn)行回歸:?t對(duì)?t-1,采用t檢驗(yàn).注意:采用t檢驗(yàn)時(shí),必須假定:?t=?t-1+et種的誤差項(xiàng)et服從同方差的假定,否則采用穩(wěn)健的檢驗(yàn)統(tǒng)計(jì)量(robust).42精選ppt3.當(dāng)回歸元非嚴(yán)格外生時(shí)

---AR(1)序列相關(guān)的檢驗(yàn)步驟當(dāng)解釋變量非嚴(yán)格外生時(shí),會(huì)有一個(gè)或多個(gè)解釋變量和ut-1相關(guān),t檢驗(yàn)和dw檢驗(yàn)失效.例如含滯后因變量一種解決辦法:dh檢驗(yàn)統(tǒng)計(jì)量(Durbin,1970).另一種更一般的方法,無論有多少個(gè)非嚴(yán)格外生變量都有效:1.yt對(duì)做xt1,xt2,…,xtk回歸,得到殘差?t.2.進(jìn)行回歸:?t對(duì)xt1,xt2,…,xtk,?t-1(包含截距項(xiàng)),采用t檢驗(yàn).(同樣可以采取穩(wěn)健性t檢驗(yàn))43精選ppt4.高階的BG(Breusch-Godfrey檢驗(yàn))

—AR(P)序列相關(guān)檢驗(yàn)假設(shè)干擾項(xiàng):零假設(shè):所有自回歸系數(shù)為零;檢驗(yàn)步驟:(拉格朗日乘數(shù)檢驗(yàn))(1)yt對(duì)做xt1,xt2,…,xtk回歸,得到殘差?t.(2)輔助回歸(3)44精選pptBreusch-Goldfrey(BG)testP=1;(一般從低階開始探測直到10左右,如果沒有什么顯著的結(jié)果,就認(rèn)為擾動(dòng)項(xiàng)不存在序列相關(guān)).e(t)—e(t-1),OLSN*R-square=29*0.15=4.35>;因此拒絕零假設(shè),認(rèn)為有自相關(guān);且顯著一階正相關(guān);ParameterEstimates

ParameterStandardVariableDFEstimateErrortValuePr>|t|resid10.384540.170292.260.031945精選ppt補(bǔ)救方法1.已知rho時(shí),采用廣義差分變換.2.未知rho時(shí),先求相關(guān)系數(shù),然后進(jìn)行廣義差分.求相關(guān)系數(shù)的方法有:(1)Cochrane-Orcutt迭代方法;(2)Hildreth-Lu.(3)Durbin2step.46精選ppt對(duì)嚴(yán)格外生回歸元的序列相關(guān)的校正

AR(1)模型----可行的廣義最小二乘法(FGLS)采用估計(jì)的相關(guān)系數(shù)值回歸方程:FGLS步驟:1..yt對(duì)做xt1,xt2,…,xtk回歸,得到殘差?t.2.?t=?t-1+et,求出相關(guān)系數(shù)的估計(jì)值3.對(duì)上面的方程進(jìn)行回歸.常見的標(biāo)準(zhǔn)誤,t統(tǒng)計(jì)量和F統(tǒng)計(jì)量都是漸進(jìn)正確的.采用相關(guān)系數(shù)估計(jì)值的代價(jià)是FGLS有限樣本性質(zhì)較差,可能不是無偏的(數(shù)據(jù)弱相關(guān)時(shí)),但仍然是一致的.盡管FGLS不是無偏的,不是BLUE,但是當(dāng)序列相關(guān)的AR(1)模型成立時(shí),比OLS更漸進(jìn)有效47精選ppt區(qū)分科克倫-奧克特(Cochrane-Orcutt)和普萊斯-溫斯登(Paris-Winsten)估計(jì)Co估計(jì)省略了第一次的觀測值,使用的是?t=?t-1+et滯后項(xiàng)系數(shù)估計(jì)值,而Pw估計(jì)方法使用了第一次的觀測值,見上面的回歸式.大體來說是否使用第一次的估計(jì)值并不會(huì)帶來很大的差別,但是時(shí)間序列的樣本很小,實(shí)際中還是有很大差別.注意下面的估計(jì)結(jié)果中沒有還原到原方程,還原時(shí)要寫正確.高階序列相關(guān)的校正,類似于一階的修正,廣義的差分方法.48精選pptSas程序dataice;inputconsincomepricetemptime@@;cards;…..;proc

reg

data=ice;modelcons=priceincometemp/dw;output

out=ice1p=conspr=resid;run;symbol1

i=nonev=dotc=blueh=.5;proc

gplot

data=ice1;plotresid*time=1/vref=0;run;/*BGtest*/datatt1;setice1;resid1=lag(resid);run;proc

reg

data=tt1;modelresid=resid1/noint;run;/*rh0=0.40063,R-square=0.1541*/;databgt;bg=29*0.1541;chisq=cinv(0.95,1);ifbg>chisqthent=1;elset=0;putt=;run;/*t=0*/;49精選pptSas程序高階的BG檢驗(yàn):/*高階BGtestp=3*/;datatt2;setice1;resid1=lag(resid);resid2=lag(resid1);resid3=lag(resid2);run;proc

reg

data=tt2;modelresid=resid1resid2resid3/noint;run;/*R-square=0.1792*/;databgt2;bg=(29-3)*0.1792;chisq=cinv(0.95,3);ifbg>chisqthent=1;elset=0;putt=chisq=bg=;run;/*t=0,無高階自相關(guān)*/;50精選pptSas程序/*yule-walkerestimates*/;proc

autoreg

data=ice;modelcons=priceincometemp/nlag=1

method=yw;run;*COCHRANE-ORCUTT;proc

reg

data=ice;modelcons=priceincometemp/dw;output

out=ttp=chatr=res;run;proc

print

data=tt;run;datatt;settt;relag=Lag(res);run;proc

print

data=tt;run;proc

reg

data=ttoutest=b1;modelres=relag/noint;run;/*可算出rh0=0.40063*/;datapp;settt;c1=lag(cons);t1=lag(temp);i1=lag(income);p1=lag(price);run;proc

print

data=pp;run;datapp1;setpp;if_n_=1

then

delete;c2=cons-0.40063*c1;t2=temp-0.40063*t1;i2=income-0.40063*i1;p2=price-0.40063*p1;run;proc

print

data=pp1;run;proc

reg

data=pp1;MODELc2=t2i2p2/dw;run;/*dw=1.54>1.65,因此不拒絕平穩(wěn)性假設(shè)*/;51精選pptSas程序上頁的科克倫-奧科特迭代只用了1次;對(duì)小樣本情況,迭代多次的仍然很難收斂,我做了三次迭代發(fā)現(xiàn)仍然不收斂;所以說多次迭代效果和一次的效果相差不大.從理論上來說兩者的漸進(jìn)性一樣.大樣本情況只需幾步就可收斂;/*下面采用fgls進(jìn)行估計(jì)校正*/;datafgls;settt1;if_n_=1

thenint=sqrt(1-0.40063*0.40063);elseint=1-0.40063;if_n_=1

thencons1=cons*sqrt(1-0.40063*0.40063);elsecons1=cons-0.40063*cons;if_n_=1

thenprice1=price*sqrt(1-0.40063*0.40063);elseprice1=price-0.40063*price;if_n_=1

thenincome1=income*sqrt(1-0.40063*0.40063);elseincome1=income-0.40063*income;if_n_=1

thentemp1=temp*sqrt(1-0.40063*0.40063);elsetemp1=temp-0.40063*temp;run;proc

reg

data=fgls;modelcons1=intprice1income1temp1/noint;run;52精選pptSas程序proc

autoreg

data=ice;modelcons=priceincometemp/nlag=1

dwprobarchtest;run;估計(jì)方法缺省為yule-walker估計(jì);又稱為兩步完全變換法;已知自回歸參數(shù)下的GLS估計(jì);其他方法:在model…/method=ML;ULS;ITYW;分別為極大似然估計(jì),無條件最小二乘估計(jì),以及迭代yule-walker估計(jì);自回歸參數(shù)較大時(shí)ml方法uls(又稱NLS)方法較好.詳見SAS/ETS中的autoreg過程.53精選pptYuler-walkerestimateTheAUTOREGProcedureDependentVariableconsOrdinaryLeastSquaresEstimatesSSE0.03527284DFE26MSE0.00136RootMSE0.03683SBC-103.63408AIC-109.23887RegressR-Square0.7190TotalR-Square0.7190Durbin-Watson1.0212Pr<DW0.0003Pr>DW0.9997NOTE:Pr<DWisthep-valuefortestingpositiveautocorrelation,andPr>DWisthep-valuefortestingnegativeautocorrelationStandardApproxVariableDFEstimateErrortValuePr>|t|Intercept10.19730.27020.730.4718price1-1.04440.8344-1.250.2218income10.0033080.0011712.820.0090temp10.0034580.0004467.76<.0001PreliminaryMSE0.00105EstimatesofAutoregressiveParametersStandardLagCoefficientErrortValue1-0.3297720.188812-1.7554精選pptEGLS(Cochrane-Orcutt兩步法)results

(一次迭代)DependentVariable:c2(generaldifferenced)

AnalysisofVarianceSumofMeanSourceDFSquaresSquareFValuePr>FModel30.047070.0156915.41<.0001Error250.025450.00102CorrectedTotal280.07252RootMSE0.03191R-Square0.6490DependentMean0.21712AdjR-Sq0.6069CoeffVar14.69553ParameterStandardVariableDFEstimateErrortValuePr>|t|Intercept10.094090.173580.540.5926t210.003560.000554546.42<.0001i210.003200.001552.070.0486p21-0.892270.81084-1.100.281655精選pptFGLS—包含第一次觀測的PW估計(jì)結(jié)果

AnalysisofVarianceSumofMeanSourceDFSquaresSquareFValuePr>FModel41.440320.36008836.01<.0001Error250.010770.00043071