自相關(guān)的檢驗(yàn)與修正

實(shí)驗(yàn)2自相關(guān)的檢驗(yàn)與修正一、實(shí)驗(yàn)?zāi)康模赫莆兆韵嚓P(guān)模型的檢驗(yàn)方法與處理方法.。二、實(shí)驗(yàn)內(nèi)容及要求：表1列出了1985－2007年中國(guó)農(nóng)村居民人均純收入與人均消費(fèi)性支出的統(tǒng)計(jì)數(shù)據(jù)（1）利用OLS法建立中國(guó)農(nóng)村居民人均消費(fèi)性支出與人均純收入的線性模型。（2）檢驗(yàn)?zāi)Ｐ褪欠翊嬖谧韵嚓P(guān)。（3）如果存在自相關(guān)，試采用適當(dāng)?shù)姆椒右韵?。?1985－2007年中國(guó)農(nóng)村居民人均純收入與人均消費(fèi)性支出（單位：元）年份全年人均純收入（現(xiàn)價(jià)）全年人均消費(fèi)性支出（現(xiàn)價(jià)）消費(fèi)價(jià)格指數(shù)（1985=100）1985397.6317.421001986423.8357106.11987462.6398.3112.71988544.9476.7132.41989601.5535.4157.91990686.3584.63165.11991708.6619.8168.91992784659.8176.81993921.6769.7201199412211016.8124819951577.71310.36291.419961923.11572.1314.419972090.11617.15322.3199821621590.33319.119992214.31577.42314.320002253.4167031420012366.41741316.520022475.61834315.220032622.241943.3320.220042936.42185335.620053254.932555343200635872829348.1200741403224366.9

實(shí)驗(yàn)如下:首先對(duì)數(shù)據(jù)進(jìn)行調(diào)整，將全年人均純收入和全年人均消費(fèi)性支出相應(yīng)調(diào)整為全年實(shí)際人均純收入和全年實(shí)際人均消費(fèi)性支出。年忖全年人內(nèi)純收人全年人均消費(fèi)性支出泊費(fèi)價(jià)格指斷空年人為實(shí)面純收/全年人自淇廚消費(fèi)性支牡（現(xiàn)價(jià)〉(BJlfft)(11185=190)IMSWL6317.42100117.42［臨HU35T1<KJ數(shù)斜J36L4S刑」1117410.17曲上刪知占476.7LiU411.36［瞬?ou34157乎珈函mcs1P9DS3WhfiS.1dlSJPMidi1^16J4J1礎(chǔ)曹41^.34SBJJmsW.441^3也或7^.72：H45151蹴.畀im112124A期J44IO.M［斷I577J1曲農(nóng)2914已1七44?.?8mu157*.1314JdH.fi?500.0520^.1KJU53MJ皿站ffll.K叭21H口肝肝315J$77員W382：11.31577J-23HJ7CMJ2501.B&嗎」］側(cè)3147IWS31.S5Wl1741aiirSW巔趣何10022-I75.J6im31SJ7S5.115?1辭她城也iw.3muaiaji606JOM3&.4?18S33S.G：0O53Z5'l.甜2555343礙附744JO2006際T2ES348.1lft.W.45張角頃7414D322436S.91UBJTB7S.711、用ols估計(jì)法估計(jì)參數(shù)爾EViev/sFileEditObjectViewProcQuickOptionsWindowHelpdataiy□Group；UNTITLEDWorklile:UNTTLED::Untillecl\[Hew||p『od|pbject〔Print|Nanm|FrEezE|Defadt 寸葩田|丁『莎心蚪ETit*■掃11^14川丁出己|Sample|397.BabsxY1985397.6000'317.42001986399.43DO33B.4BQ01997410.47DO353.420019904-1-1.56D0360.05001999380.9400339.08001990d1&.69D0351.110019914196400366.9600199244344QQ373.19001993458.51D0382.94001994492340041D.ODOO199554142M449.6000199661-1.67D050D.03Q01997649.50DO501.75001998677.53DO49B.3BOO199970452DD501.8800200D717.5400531.8500200174T.68W55D.OBOO2002735.41DO581.85002003B16.94D060B.9DOO20040T74.97DO651.07002005S48.96D0744.9DOO20061020.450'812.70002007112B.27DS7B.7100腐EViewsFileEditObjectViewProcQuirkOptionsWindowHelpdataIsyex□Equation:UNTITLEDWorkfile:UNTITLED::Untitled\YEwllPmdlciDject.Arint『lameIweeze]IEstimateForewsi||S；Bts||F^sclsIDependent'vana&le:￥Method:LeastSquaresDate:04/24M5^1710:12:32Sample19852007incluaeaoDsen/aiicns：23CoeffidentStd.Error tStatisticProb.C56.2187814.54858 3.3&421Q0.0009X0.6909200.021342 31.999730.0000R-squared0.979904dependentvar495.3013AdjustedR-squared0.978347s.D.dependsntvar158.35733.Eofregression22977D6Akaikeinfocrilerion9.189813Sumsquaredresid110B6.B7Schwarzcriterion9.2S9551Loglikelihood-1026828Hannan-Ouinncliter.9.214645F-slatlsUc10Z3.9B3DurtJin-V^aisonstatD.4D9903Prob(F-statistic)O.OOOODO

圖形分析:FileEdlH:DkjuctWlwPmrQuick0時(shí)詁陌訓(xùn)閔如H亡IpilalaxyI呂F"Gcal:^圖4從圖4中可以看出，中國(guó)農(nóng)村居民人均消費(fèi)性支出與人均純收入存在著顯著的正相關(guān)關(guān)系。估計(jì)回歸方程:從圖3中可以得出，估計(jì)回歸方程為：Y=56.21878+0.698928X

t=(3.864210)(31.99973)R2=0.979904F=1023.983D.W.=0.4099032.自相關(guān)檢驗(yàn)(1)圖示法?EVie^s?EVie^sFileEditObjectViciwProcQuickQpticrnsWindowHelpdataxyisyexscat!y□Equation:UNTITLEDWorHife:UNlTTLED::Untitled\'JieviR"oc||ODject||PrhtNane-reeiEEadmateForecastSiafa:Reaids圖5從圖5中，可以看出殘差的變化有系統(tǒng)模式，連續(xù)為正或連續(xù)為負(fù)，表示殘差項(xiàng)存在階正自相關(guān)。DW檢驗(yàn)從圖3中可以得到D.W.=0.409903，在顯著水平去5%,n=23,k=2,dL=1.26,dU=1.44o此時(shí)OvD.W.v%，表明存在正自相關(guān)。B-G檢驗(yàn)FileEditObjectViewProcQuickOptionBWindowHelpdataKyIsyexscatty□Equation:UNTITLEDW&rkfile:UNTI7LED::Urtitled\|vif.IIFrac|Ctajrd]Friiit||Nunir||尸2"匚Estimate||Ftjrumt]siaX|RleizhBreuscti-GodfreySerialCorrelationLMTestF-statistic 17.49437FrcbF(2,19) O.OODOObs^R-squared 14.90587PrcbChi-Squarefi) O.OOD6TestEquation:CeptndentVariablo:RESIDMeinod.LeastsquaresDale:04^24/15Tine:1245Sample:199&2007Includedobservatlcnb.23Presamplerriasinovaluelacoedresidualssettozero.Goemcientstd.ErrorvstatisticF"wu.C-1.3190739.704225 -0.1359260.0933X0.0028590.015044 0.1900590.8513RESI0(-1)1.0691660.22022" 4.35496&D.0DD1RESID(-2)-0.3500610.254050 -1.4081250.1752R-squared0.649081He甘ndependentvar2.35E-14AdljuatedlR-squared0.59251ES.D.dependentrar22.+40BOS.t.otegression1433009AKaiKeinfocriterion￡319371Sumsquaredrssid2901677Schwarzcriterion8.51&S4SLoglikelihood-91.67276Hannan-Quinncriter.0.369036l--staiistic11.66324DurDin-lrtalsDnstai2020025Prob(F-￡tati￡lic)0.00014S圖6從圖6中可得到，nR2=14.90587,臨界概率P=0.0006，因此輔助回歸模型是顯著的,即存在自相關(guān)性。又因?yàn)椋琫t-1，et-2的回歸系數(shù)均顯著地不為03?自相關(guān)的修正使用廣義差分法對(duì)自相關(guān)進(jìn)行修正:SEViewsFileEditObjectViewPrcxQuickOptionsWindowHelpIsyexscatxyIsee(-1)□Equation:UNTITLEDWorkfile:UNTITLED::Untitled\|View||Frac||Object||Printflame||Freeze||EstiniatE|ForecastStats||Resids|ependent畑佰ble:EMethod:LeastSquaresate:O4J24J15Time:13:20sample(adjusted):19862007Includedobsewations:22afteradjustmentsCoefficientStd.Error t-StatisticProb.E(-1)0.8150240141910 5.743240J.0000R-squared0.610545Meandependentvar0.758751AdjustedR-squared0.610545S.D.dependentvar22.67321S.E.orregression14.14951Akaikeinfocriterion8.131626Sumsquaredresid4204.383Schwarzcriterion8.231219Loglikelihood-00.99709Hannan-Quinncriter.0.193309□urbin-Watsonstat1.251316對(duì)原模型進(jìn)行廣義差分，得到廣義差分方程:Yt-0.815Q24Yt,1=P1(1-0.815024)+B2(X,-0.815024人丿+ut對(duì)廣義差分方程進(jìn)行回歸:亶E#品sFileEditObjectViewProcQuickOptionsWindowHelpscatxyIsee(-1}lsy-0.3150247(-1)c1-0.815D24*K(-1}□Equation!UNTITLEDWorkfile:UNTITLED：；Untitled\［View|Prx||Object||訊社|恤罔葉亡￡￡亡］|EstimatEForneast〔Stats||瓦諭旳］ependentVariable:Y-0.615024*Y(-1}Method:LeastSquaresate:04/24/15Time:13:29Sample(adju3ted>19962007Includedobservations:22afteradjustmentsCoefficientStd.Errort-StatisticProb.7.7517337.8135560.99209403330X-0.815024*X(-1)0.7309860.0斗955814.750220.0000R-squared0J915814MeandepsndEnti/mr114.0050AdjustedR-squared0.9116053.D.dependentvar斗7.75003S.E.ofregression14.19673AkaikeinfocriterionS.230400Sumsquaredresid4030.942SchwarzcriterionS.329594Loglikelihood-88.53449Hannan-auinnenter.S.253773F-statistic217.5691□urbin-Watsoislat1.324681Prob(F-statistic}0.000000圖8從圖8中可以得出此時(shí)的D.W.=1.324681，在取顯著水平為5%,n=23,k=2,dL=1.26,du=1.44，模型中dL<DW<dU，此時(shí)不能確定是否存在自相關(guān)。在廣義差分法無法完成修正的情況下，現(xiàn)建立對(duì)對(duì)數(shù)模型:岳￡ViewsFileEditObjectViewProcQuickOption弓WindowHelpqbnrlny=loa(y)isinycini□Equation;UNTITLEDWorkfib;UNTITLED;;UntitlKl\ |1=1]回l|￡3I[vicw][Proc]Object]|Print][Name][Fr亡亡疋Estimate]|Fore!：Est|Stats|Reads|□即endentvariaEie:lnyMethoctLeastSquaresDate:04723i!15Tme:22:52sample:198E2007Includedohsenjalions:23coefllaent3ta.Errort-3tatisticHroft.c0.2654670.D92207 2J765310.0090LNX0.93-23220.D12699 73.41545O.QODOR-squaredl0.996119Mesandependentva.r7.005657AcjustedR-squared0.995934SLD.dependentvarD.7D5712S.Ecfregression0.0J4B99Akaikeinfccriterion-3.281Sumsquaredresidl0.042524Schwarzcriterion-3.102653Loglikelihood39.73600Hannan-Quinncriter.-3.256559F-stalistic5289.629Durbin-Watsonstat0.4796B4Prob(F-statistic；o.oqodoo對(duì)雙對(duì)數(shù)模型進(jìn)行調(diào)整:船EViewsFileEditObjectViewProcQuickOptionsWindowHelpgenrlnx=log(x)IsInycIrwIsInycInsar(1)ar(2)OEquation:UNTITLEDWorkfile:UNTULED::Untitled\ [■=■||回||S3][view||Proc||Object]Print||NamE|-reezej|Estimate||zorecast||Stats||Resi±IcorrelogramorResiduals□ate:04J23；15Time:23:5DSample:19372007Includedobservalions:21Q-statisticprobabilitiesadjustedforSARMAterm(s)AutocorrelatiorPartialCorrelationACFACQ-StatProb匚II111-0.099-0.0990.2343□I1□120.1900.1321.1525匚I1113-0.124-0.095156540.211匚I1匚14-0.163-0.2302.36950.306■I1□150.1540.1833.08930.378匚I1116-0.182-0.1104.15630.385圖10

岳EViewsFileEditObjectVieivProcQuickOptionsWindowHelpgenrlnx=log(s)ISI附CinxIsln^cInxar(1)ar(2)□Equation:UNTTlfDWorkfile:UNTTTLED::Untitled\ |□||B|yew][Prcc||Cibject||Print||Naine]|Freeze]Estimate|Forecast||Stats||Resids|Breusch-GodTrejSerialCornelatiDnLblTestF-statistic0.526522Prob.F(2,15)0.6D12Obs*R-squared1377552Prob.3hi-Square(2