自相关的检验与修正

实验2自相关的检验与修正一、实验目的：掌握自相关模型的检验方法与处理方法.。二、实验内容及要求：表1列出了1985－2007年中国农村居民人均纯收入与人均消费性支出的统计数据（1）利用OLS法建立中国农村居民人均消费性支出与人均纯收入的线性模型。（2）检验模型是否存在自相关。（3）如果存在自相关，试采用适当的方法加以消除。表11985－2007年中国农村居民人均纯收入与人均消费性支出（单位：元）年份全年人均纯收入（现价）全年人均消费性支出（现价）消费价格指数（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

实验如下:首先对数据进行调整，将全年人均纯收入和全年人均消费性支出相应调整为全年实际人均纯收入和全年实际人均消费性支出。年忖全年人内纯收人全年人均消费性支出泊费价格指斷空年人为实面纯收/全年人自淇厨消费性支牡（现价〉(BJlfft)(11185=190)IMSWL6317.42100117.42［临HU35T1<KJ數斜J36L4S刑」1117410.17曲上删知占476.7LiU411.36［瞬«ou34157乎珈函mcs1P9DS3WhfiS.1dlSJPMidi1^16J4J1础曹41^.34SBJJmsW.441^3也或7^.72：H45151蹴.畀im112124A期J44IO.M［断I577J1曲农2914已1七44?.«8mu157*.1314JdH.fi?500.0520^.1KJU53MJ皿站ffll.K叭21H口肝肝315J$77员W382：11.31577J-23HJ7CMJ2501.B&吗」］侧3147IWS31.S5Wl1741aiirSW巔趣何10022-I75.J6im31SJ7S5.115»1辭她城也iw.3muaiaji606JOM3&.4?18S33S.G：0O53Z5'l.甜2555343碍附744JO2006际T2ES348.1lft.W.45张角顷7414D322436S.91UBJTB7S.711、用ols估计法估计参数爾EViev/sFileEditObjectViewProcQuickOptionsWindowHelpdataiy□Group；UNTITLEDWorklile:UNTTLED::Untillecl\[Hew||p『od|pbject〔Print|Nanm|FrEezE|Defadt 寸葩田|丁『莎心蚪ETit*■扫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

图形分析:FileEdlH:DkjuctWlwPmrQuick0时詁陌训闵如H亡IpilalaxyI呂F"Gcal:^图4从图4中可以看出，中国农村居民人均消费性支出与人均纯收入存在着显著的正相关关系。估计回归方程:从图3中可以得出，估计回归方程为：Y=56.21878+0.698928X

t=(3.864210)(31.99973)R2=0.979904F=1023.983D.W.=0.4099032.自相关检验(1)图示法®EVie^s®EVie^sFileEditObjectViciwProcQuickQpticrnsWindowHelpdataxyisyexscat!y□Equation:UNTITLEDWorHife:UNlTTLED::Untitled\'JieviR"oc||ODject||PrhtNane-reeiEEadmateForecastSiafa:Reaids图5从图5中，可以看出残差的变化有系统模式，连续为正或连续为负，表示残差项存在阶正自相关。DW检验从图3中可以得到D.W.=0.409903，在显著水平去5%,n=23,k=2,dL=1.26,dU=1.44o此时OvD.W.v%，表明存在正自相关。B-G检验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图6从图6中可得到，nR2=14.90587,临界概率P=0.0006，因此辅助回归模型是显著的,即存在自相关性。又因为，et-1，et-2的回归系数均显著地不为03•自相关的修正使用广义差分法对自相关进行修正: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对原模型进行广义差分，得到广义差分方程:Yt-0.815Q24Yt,1=P1(1-0.815024)+B2(X,-0.815024人丿+ut对广义差分方程进行回归:亶E#品sFileEditObjectViewProcQuickOptionsWindowHelpscatxyIsee(-1}lsy-0.3150247(-1)c1-0.815D24*K(-1}□Equation!UNTITLEDWorkfile:UNTITLED：；Untitled\［View|Prx||Object||讯社|恤罔叶亡££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图8从图8中可以得出此时的D.W.=1.324681，在取显著水平为5%,n=23,k=2,dL=1.26,du=1.44，模型中dL<DW<dU，此时不能确定是否存在自相关。在广义差分法无法完成修正的情况下，现建立对对数模型: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对双对数模型进行调整: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图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