自相關的檢驗與修正

實驗2自相關的檢驗與修正一、實驗目的：掌握自相關模型的檢驗方法與處理方法.。二、實驗內容及要求：表1列出了1985－2007年中國農(nóng)村居民人均純收入與人均消費性支出的統(tǒng)計數(shù)據(jù)（1）利用OLS法建立中國農(nóng)村居民人均消費性支出與人均純收入的線性模型。（2）檢驗模型是否存在自相關。（3）如果存在自相關，試采用適當?shù)姆椒右韵?。?1985－2007年中國農(nóng)村居民人均純收入與人均消費性支出（單位：元）年份全年人均純收入（現(xiàn)價）全年人均消費性支出（現(xiàn)價）消費價格指數(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

實驗如下:首先對數(shù)據(jù)進行調整，將全年人均純收入和全年人均消費性支出相應調整為全年實際人均純收入和全年實際人均消費性支出。年忖全年人內純收人全年人均消費性支出泊費價格指斷空年人為實面純收/全年人自淇廚消費性支牡（現(xiàn)價〉(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估計法估計參數(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時詁陌訓閔如H亡IpilalaxyI呂F"Gcal:^圖4從圖4中可以看出，中國農(nóng)村居民人均消費性支出與人均純收入存在著顯著的正相關關系。估計回歸方程:從圖3中可以得出，估計回歸方程為：Y=56.21878+0.698928X

t=(3.864210)(31.99973)R2=0.979904F=1023.983D.W.=0.4099032.自相關檢驗(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，表示殘差項存在階正自相關。DW檢驗從圖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OvD.W.v%，表明存在正自相關。B-G檢驗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,即存在自相關性。又因為，et-1，et-2的回歸系數(shù)均顯著地不為03?自相關的修正使用廣義差分法對自相關進行修正: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對原模型進行廣義差分，得到廣義差分方程:Yt-0.815Q24Yt,1=P1(1-0.815024)+B2(X,-0.815024人丿+ut對廣義差分方程進行回歸: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，此時不能確定是否存在自相關。在廣義差分法無法完成修正的情況下，現(xiàn)建立對對數(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對雙對數(shù)模型進行調整: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