擬合garch模型及autoreg模型-預(yù)測

#第五章SAS作業(yè)學(xué)號：200930980106姓名：何斌年級專業(yè)：10級統(tǒng)計(jì)1班指導(dǎo)老師：肖莉問題1:試選擇恰當(dāng)模型擬合某種股票的價(jià)格數(shù)據(jù)，數(shù)據(jù)如下:10.510.449.9410.25119.8810.51213.9412.2512.6113.513.4412.4413.515.3915.7513.8814.515.516.1314.7511.7515.2517.1320.51921.520.2525.6326.8827.6323.8826.382424.38U利用擬合模型預(yù)測未來二期該股票的價(jià)格；2、按照書本相應(yīng)例題的格式完成問題，并附上SAS程序。解:1.1建立數(shù)據(jù)集，繪制時(shí)序圖datagupiao;inputvaluetim令二n;MMFcards;10.510.449.9410.25119.8810.51213.9412.2512.6113.513.4412.4413.515.3915.7513.8814.515.516.1314.7511.7515.2517.1320.51921.520.2525.6326.8827.6323.8826.382424.38procgplotdata=gupiao;plotvalue*time;symboli=joinv=starh=lci=redcv=blackw=2;run;L2輸出時(shí)序圖顯示該序列非平穩(wěn)。如圖1-1所示。

圖1-1股票價(jià)格序列的時(shí)序圖3對該序列進(jìn)行一階差分運(yùn)算，程序修改如下：datagupiao;inputvaluedifv=dif(value);cards;10510.449.9410.25119.881051213.9412.2512.6113.5134412.4413.515.3915.7513.8814515.516.1314.7511.7515.25171320.51921.520.2525.63268827.6323.8826.382424.38procgplotdata=gupiao;plotdifv*time;symboli=joinv=starh=lci=redcv=blackw=2;procarima;identifyvar=value(l)minicp=(0:5)q=(0:5);run;1.4考査一階差分后序列的平穩(wěn)性。所得時(shí)序圖如圖1-2所示。圖1-2序列difv的時(shí)序圖時(shí)序圖顯示差分后序列difv沒有明顯的非平穩(wěn)特征。1.5序列d辻v的識別，如下圖所示。CovarianceCorrelation-1987654321C)1234567891StdError3.5212571.00000床床床床床床床床床床床床床床******0-0.85681924333.*****0.1690310.2948010.08372?*0.178759?1.476456?.41930********0.1798761.4684670.41703******林0.205917-0.57304716274***0.2287780.5835960.16574?**0.232062-1.092783?.310340.2354200.0788680.022400.246832Autocorrelationsm^rkstwostandarderrorsIg012345678LInverseAutocorrelationsLagCorraction-1987654321012345678911-0.0088720.11143**30.26772*****?4-0.28641?**c*c*c*c*c50.1944560.04433*70.07494*S0.20365圖1-3序列cHfv的自相關(guān)圖.偏自相關(guān)圖AutocorrelationCheckforWhiteNoise6ChL-ChiSqSquareDFAutocorrelations'19.2860.0037-0.2436ChL-ChiSqSquareDFAutocorrelations'19.2860.0037-0.2430.084-0.4190.417-0.1630.166圖1-4殘差圖MA0FflA1MA2MA3MX4MA51230471.3251891.4143071.376S021.2328361.2&3827126874712838811.3256551.193191.2245111.325804135642713445541.4148541.287151.3110521.410&321204878110616S1.1933031.291SS81.3&1TT81.3917331.0948111672311.2686741.3884221.3&12011.42721T116411912654611.345S931.3143541.3931.4&5095riknLinujnIntormatLonCntenongs012345LaARARARARARARErrorseriesmodel：AR(5)MinimumTableValue：BIC(4,0)=1.09431圖1-5最優(yōu)模型選擇識別部分的輸出結(jié)果顯示，1階差分后，序列difv為平穩(wěn)非白噪聲序列，最優(yōu)擬合模型為AR(4)模型。

L6“estimatep=4;"對序列<Hfv擬合AR(4)模型。輸出結(jié)果顯示mu.ARI,1>ARI,2均不顯著，修改估計(jì)命令如下：estimatep=(3,4)noint;擬合結(jié)果顯示模型顯著且參數(shù)顯著。如圖1-6所示。ParajneterEstimateStaxilarAErrortValueApproxPr>|t|LagARI,1-0.354230.14518-2.440.02023ARI,20.542810.154813.510.00134CoitiitionalLeastSquaresEstimation.VarianceEstimate2.44562StAErrorEstimate1.563848AIC132.5667SBC135.6774ffujnberofResiAu.als35*AICandSBCAonotin.clu.AelogAeiermiitajit.AutocorrelationCheckofResidualsToChi-Pr>LagSquareDFChiSqAutocorrelat1ons61.4840.83010.1180.0140.0460.090-0.1060.026125.20100.8773-0.034-0.199-0.1230.050-0.0840.095186.43160.9828■0.024■0.0240.1010.0490.054■0.0412412.35220.94960.118-0.042-0.0420.1450.110■0.096ModelforvariablevalueFeriod(s)ofDifferencing1Nomeanterminthismodel.AutoregressiveFactorsFactor1：1+0.35423B**(3)-0.54281B**(4)圖1-6序列difv模型擬合結(jié)果輸出結(jié)果顯示,序列value的擬合模型為ARIMA((3,4),1,0)模型，模型口徑為:一f1+0.35423B3-0.54281B4或等價(jià)記為：Vt=-0?35423叫_3+0?89704匕_4-0.54281Ft.5+st(7表示股價(jià)價(jià)格)1.7^forecastlead=2id=time;”，利用擬合模型對序列乞作2期預(yù)測。如圖1-7所示。1.7^forecastlead=2圖1-737圖1-737期、38期股票價(jià)格預(yù)測(Forecast值)Fcr^c^stsf-orv^ri=ibl^v=alu^OBsForecastSidError95%ConfidexterLimits3721.45891.563818.393824.52403823.85902.211619.324327.99371.8擬合圖:vaIue40-30?2030?20?10?0?010203040timePLOT**vaIueForecastforvaIue■—Lower95HConfidenceLimiF—Upper95%ConfidenceLimitSAS程序：datagupiao;inputvaluedifv=dif(value);time=n;cards;10.510.449.9410.25119.8810.51213.9412.2512.6113.513.4412.4413.515.3915.7513.8814.515.516.1314.7511.7515.2517.1320.51921.520.2525.6326.8827.6323.8826.382424.38procgplotdata=gupiao;plotdifv*time;symboli=joinv=starh=lci=redcv=blackw=2;procarima;identifyvar=value(l)minicp=(0:5)q=(0:5);estimatep=(3,4)noint;forecastlead=2id二timeout=results;run;procprint;run;procgplot;plotvalue*time=lforecast*time=2195*time=3u95*time=3/overlaylegend;symbol1c=blacki=nonev=star;symbol2c=redi=joinv=nonew=2;symbol3c=greeni=joinv=none1=32;run;問題2：1867-1938年英國綿羊數(shù)量如下所示:2203236022542165202420782214229222072119211921372132195517851747181819091958189219191853186819912111211919911859185619241892191619681928189818501841182418231843188019682029199619331805171317261752179517171648151213381383134413841484159716861707164016111632177518501809165316481665162717911＞選擇恰當(dāng)模型，擬合該序列的發(fā)展；2、利用擬合模型預(yù)測1938-1945年英國綿羊的數(shù)量；3、按照書本相應(yīng)例題的格式完成問題，并附上SAS程序。解.;建立數(shù)據(jù)集，繪制時(shí)序圖datamianyang;inputx輕；t=n;cards;220323602254216520242078221422922207211921192137213219551785174718181909195818921919185318681991211121191991185918561924189219161968192818981850184118241823184318801968202919961933180517131726175217951717164815121338138313441384148415971686170716401611163217751850180916531648166516271791procgplotdata=mianyang;plotx*t;

symboli=joinv=starci=redcv=blackw=2;run;1.2輸出時(shí)序圖顯示該序列非平穩(wěn)。如圖1-1所示。圖1-1綿羊數(shù)量序列X的時(shí)序圖1?3時(shí)序圖顯示序列具有顯著線性遞減的趨勢，且波動(dòng)幅度隨時(shí)間遞增，所以考慮使用AUT0REG過程建立序列｛俎｝關(guān)于時(shí)間t的線性回歸模型，并檢驗(yàn)殘差序列的自相關(guān)性和異方差性。執(zhí)行程序：procautoregdata=mianyang;modelx=t/nlag=5dwprobarchtest;run;得到結(jié)果如下：DW檢驗(yàn)結(jié)果顯示，殘差序列具有顯著的正自相關(guān)性，如圖1-2所示。Durbin.-Wa.tson.Sta.tisticsOrderDWFr<DWFr>DW10.3613<00011.0000圖1-2普通最小二乘估計(jì)DW檢驗(yàn)結(jié)果

殘差序列5階延遲自相關(guān)圖顯示殘差序列至少具有2階顯著自相關(guān)性，如圖1-3所示。EstimatesofAutocorrelationsLagCoxrarianceCorrelation-198765432101234567831LagCoxrariance019123.019123.11.000000115280.70.799068294&4.90.49494634&16.70.24141942722.2040.145449WWW圖1-3殘差序列5階延遲自相關(guān)圖參數(shù)估計(jì)結(jié)果顯示回歸模型參數(shù)顯著，如圖1-4所示。Varia*bleHFEstimateStandardErrortValueApproxFr>111Intercept1216433.404164.78<0001t1-8.38860.7953-10.56<0001圖1-4線性回歸模型參數(shù)估計(jì)結(jié)果異方差檢驗(yàn)結(jié)果顯示殘差序列具有顯著的異方差性，且具有顯著的長期相關(guān)性，如圖1-5所示。Ord^r123456789W1112QOrd^r123456789W1112QFr>QUliFr>Uil35.4104<.000134.9710<.000144.8342<.000138.1644<.000145.2763<.000138.4478<.000146.8955<.000139.3154<.000150.9033<.000139.3477<.000154.6288<.000139.3710<.000157.8390<.000139.6152<.000159.5575<.000139.6340<.000159.5628<.000140.4606<.000160.8433<.000140.6282<.000163.7334<.000140.6339<.000166.0093<.000140.7443<.0001Q^ndUilTestsforARCHDisturbances圖1-5異方差檢驗(yàn)結(jié)果1.4“modelx=t/nlag=2garch=(p=l,q=l)綜合考慮殘差序列自相關(guān)性和異方差性檢驗(yàn)結(jié)果，嘗試擬合AR(2)-GARCH(1,1)模型。模型最終擬合結(jié)果如圖1-6所示。

GAHCHEstimatesSSE344169.24901>servations72MSE4780UncondVar5316.72882LogLikelihood.-407.25362TotalR-Sq*uar€0.9036SBC840.167247AIC826.50725MAE52.735066AICC827.799558MAPE2.89335488formalityTest0.0876Pr>ChiSq0.9572VariableDFEstimateStandardErrortValueApproxFr>111Intercept1213047.912744.46<.0001t1-7.38651.2637-5.85<.0001ARI1-1.261701203-10.49<0001kR210.52140.12274.25<0001ARCKO15182127S4.05<0001ARCK110.02540.18480.140.8908GARCK11-S.26E-231.454E-15-0.001.0000圖1-6普通最小二乘估計(jì)輸出結(jié)果參數(shù)估計(jì)結(jié)果顯示該模型擬合較成功。最終模型口徑為：(xt=2130-7.3869(+utut=1.2617血“—0.5214uf_2+st￡t=密N(0?4780)/if=5182+0.0254^-!1.5最終輸出擬合效果圖如圖1-7所示。

圖1-7擬合效果圖2.1預(yù)測1939-1945年英國綿羊的數(shù)量，如下表2-1所示。表2-11939-1945年英國綿羊的數(shù)量19391820.2819401769.5919411688.3919421610.519431552.719441518.519451503.562.2預(yù)測效果圖，如圖2-2所示。

圖2-21939-1945年英國綿羊的數(shù)量預(yù)測效果圖3.SAS程序：datamianyang;inputx@@;t=intnx(*year','ljanl867,d,_n_-l);formattyear4.;cards;22032360225421652024207822142292220721192119213721321955178517471818190919581892191918531868199121112119199118591856192418921916196819281898185018411824182318431880196820291996193318051713172617521795171716481512133813831344138414S415971686170716401611163217751850180916531648166516271791procgplotdata=mianyang;plotx*t;symboli=joinv=starci=redcv=blackw=2;run;procautoregdata=mianyang;modelx=t/nlag=5dwprobarchtest;modelx=t/nlag=2garch=(p=l,q=l);outputout=outp=xp;procgplotdata=out;plotx*t=2xp*t=3/ove:rlay;symbol2i=nonev=starc二black;symbol3i=joinv=nonec=redw=2;run;procprintdata=outnoobs;run;問題3,使用Auto-Regressive模型分析例5.9序列。（要求只對變量為延遲序列值進(jìn)行模型擬合，作業(yè)格式參照書“例5.6續(xù)”）1962-1991年德國工人季度失業(yè)率序列行數(shù)據(jù)（％）1.01.51.01.01.08.07.07.48.59.010.08.7&8&99.010.2&&7.6&6.86.06.26.2

解：1?1建立數(shù)據(jù)集，繪制時(shí)序圖datashiyelv;inputx輕；t=intnxfquarter，,'ljanl962,d>_n_-l);formattyear4.;cards;1.01.51.01.01.08.07.07.48.59.010.08.7&88.910.48.9&910.28.6&&4&28.87.67?57.68.1■6.86.06.26.2rprocgplotdata=shiyelv;plotx*t;symboli=joinv=starci=redcv=blackw=2;run;1?2輸出時(shí)序圖。如圖1-1所示。

圖1-1德國工人季度失業(yè)率時(shí)序圖1?2建立延遲因變量回歸模型執(zhí)行語句：procautoregdata=shiyelv;modelx=lagx/lagdep=lagx;run;輸出結(jié)果如下圖所示TheAUTOREGProcedureDependentVari^blexESESEBCAEAP63.ESESEBCAEAP63.788407DFE1170.54520RootNSE0.73836273.062927AIC267.504680.56825477AICC267.60812827.1498286RegressR-Squwr電0.3489TotalR-Sqaar電0.S483OrdinaryLeastSquaresEstimatesStatisticValuerrobLatelDurbinh-2.02450.0215Fr>hSt^nd^rdApproxVariableDFEstimateErrortV￡LnePr>ItlIntercept10.16560.11231.470.1430lagx10.97150.020846.62<.0001MiscellaneousStatistics圖1-2延遲因變量回歸分析結(jié)果檢驗(yàn)結(jié)果顯示,Durbinh統(tǒng)計(jì)量的值為-2.0245,P值為0.0215,故拒絕原假設(shè)，認(rèn)為殘差序列高度自相關(guān)。參數(shù)檢驗(yàn)結(jié)果顯示，截距項(xiàng)不顯著(P值大于0.1430)。1.3擬合無截距項(xiàng)，并檢驗(yàn)殘差的自相關(guān)性。執(zhí)行程序：procautoregdata=shiyelv;modelx=lagx/lagdep=lagxnlag=4noint;run;輸出結(jié)果如下圖所示VariableDFEstimateStandardErrortValueApproxPr>|t|lagx10.99600.012678.92<.0001CovarianeeEstimatesofAutocorrelationsCovarianee00.54601.000000******************林1■0.1019■0.1865802?0.1233■0.225901*****3■0.1172■0.21458540.47770.8748505?0.1334■0.244299*****Correlation-198765432101234567891圖1-3參數(shù)檢驗(yàn)及殘差的自相關(guān)性檢驗(yàn)檢驗(yàn)結(jié)果顯示,參數(shù)顯著，擬合殘差的AR檢驗(yàn)結(jié)果顯示,參數(shù)顯著，擬合殘差的AR(4)模型。1.4殘差的AR1.4殘差的AR(4)模型執(zhí)行程序：procautoregdata=shiyelv;modelx=lagx/1agdep=1agxn