擬合garch模型及autoreg模型預測

1、 第五章SAS作業(yè)學號：200930980106姓名：何斌年級專業(yè)：10級統(tǒng)計1班指導老師：肖莉問題1:試選擇恰當模型擬合某種股票的價格數(shù)據(jù)，數(shù)據(jù)如下:10.510.449.9410.25119.8810.51213.9412.2512.6113.513.4412.4413.515.3915.7513.8814.515.516.1314.7511.7515.2517.1320.51921.520.2525.6326.8827.6323.882&382424.381利用擬合模型預測未來二期該股票的價格；2、按照書本相應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，繪制時序圖data

2、gupiao;inputvaluetime二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;plotvalue*time;symboli=joinv=starh=lci=redcv=blackw=2;run;L2輸出時序圖顯示該序列非平穩(wěn)。如圖1-1所示。圖1-1股票價格序

3、列的時序圖3對該序列進行一階差分運算，程序修改如下：datagupiao;inputvaluedifv=dif(value);time=_n_;cards;10510.449.9410.25119.881051213.9412.2512.6113.5134412.4413.515.3915.7513.8814515.516.1314.7511.7515.25171320.51921.520.2525.63268827.6323.882&382424.38procgplotdata=gupiao;plotdifv*time;symboli=joinv=starh=lci=redcv=blackw

4、=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。所得時序圖如圖1-2所示。圖1-2序列difv的時序圖時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)1234567891StdError3.5212571.000000-0.85681924333.*0.1690310.2948010.08372*0.1787591.476456.41930*0.1798761.4684670.41703

5、*0.205917-0.57304716274*0.2287780.5835960.16574*0.232062-1.092783.310340.2354200.0788680.022400.246832AutocorrelationsmrkstwostandarderrorsIg012345678LInverseAutocorrelationsLagCorraction-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

6、自相關圖.偏自相關圖AutocorrelationCheckforWhiteNoise6ChL-ChiSqSquareDFAutocorrelations19.2860.0037-0.2430.084-0.4190.417-0.1630.166圖1-4殘差圖MA0FflA1MA2MA3MX4MA51230471.3251891.4143071.376S021.2328361.2&3827126874712838811.3256551.193191.2245111.325804135642713445541.4148541.287151.3110521.410&321204878110616S1

7、.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。L6estimatep=4;對

8、序列Hfv擬合AR(4)模型。輸出結果顯示mu.ARI,RARI,2均不顯著，修改估計命令如下：estimatep=(3,4)noint;擬合結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.VarianceEstimate2.44562StAErrorEstimate1.563848AIC132.5667

9、SBC135.6774ffujnberofResiAu.als35*AICandSBCAonotin.clu.AelogAeiermiitajit.AutocorrelationCheckofResidualsToChi-PrLagSquareDFChiSqAutocorrelat1ons61.4840.83010.1180.0140.0460.090-0.1060.026125.20100.8773-0.034-0.199-0.1230.050-0.0840.095186.43160.98280.0240.0240.1010.0490.0540.0412412.35220.94960.118

10、-0.042-0.0420.1450.1100.096ModelforvariablevalueFeriod(s)ofDifferencing1Nomeanterminthismodel.AutoregressiveFactorsFactor1：1+0.35423B*(3)-0.54281B*(4)圖1-6序列difv模型擬合結果輸出結果顯示,序列value的擬合模型為ARIMA(3,4),1,0)模型，模型口徑為:Vvt-tt1+0.35423B3-0.5428IB4或等價記為：Vt=Vt-035423叫_3+089704Ft_4-0.54281Ft_5+st(7表示股價價格)L7forec

11、astlead=2id=time;,利用擬合模型對序列乞作2期預測。如圖1-7所示。圖1-737期、38期股票價格預測(Forecast值)Fcrcstsf-orvri=iblv=aluOBsForecastSidError95%ConfidexterLimits3721.45891.563818.393824.52403823.85902.211619.324327.99371.8擬合圖:vaIue40-3020100010203040timePLOT*vaIueForecastforvaIueLower95HConfideneeLimiAUpper95%ConfidenceLimitSAS

12、程序：datagupiao;inputvalue00;difv=dif(value);time二n;MBFcards;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

13、;identifyvar=value(l)minicp=(0:5)q=(0:5);estimatep=(3,4)noint;forecastlead=2id二timeout=resuIts;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

14、下所示:2203236022542165202420782214229222072119211921372132195517851747181819091958189219191853186819912111211919911859185619241892191619681928189818501841182418231843188019682029199619331805171317261752179517171648151213381383134413841484159716861707164016111632177518501809165316481665162717911選擇恰當模型，

15、擬合該序列的發(fā)展；2、利用擬合模型預測1938-1945年英國綿羊的數(shù)量；3、按照書本相應例題的格式完成問題，并附上SAS程序。解.1.;建立數(shù)據(jù)集，繪制時序圖datamianyang;inputx;t=n;cards;2203236022542165202420782214229222072119211921372132195517851747181819091958189219191853186819912111211919911859185619241892191619681928189818501841182418231843188019682029199619331805171317

16、26175217951717164815121338138313441384148415971686170716401611163217751850180916531648166516271791procgplotdata=mianyang;plotx*t;symboli=joinv=starci=redcv=blackw=2;run;1.2輸出時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的時序圖13時序圖顯示序列具有顯著線性遞減的趨勢，且波動幅度隨時間遞增，所以考慮使用AUT0REG過程建立序列X關于時間t的線性回歸模型，并檢驗殘差序列的自相關性和異方差性。執(zhí)行程序：pro

17、cautoregdata=mianyang;modelx=t/nlag=5dwprobarchtest;run;得到結果如下：DW檢驗結果顯示，殘差序列具有顯著的正自相關性，如圖1-2所示。Durbin.-Wa.tson.Sta.tisticsOrderDWFrDW10.3613111Intercept1216433.404164.780001t1-8.38860.7953-10.56QUliFrUil35.4104.000134.9710.000144.8342.000138.1644.000145.2763.000138.4478.000146.8955.000139.3154.00015

18、0.9033.000139.3477.000154.6288.000139.3710.000157.8390.000139.6152.000159.5575.000139.6340.000159.5628.000140.4606.000160.8433.000140.6282.000163.7334.000140.6339.000166.0093.000140.7443servations72MSE4780UncondVar5316.72882LogLikelihood.-407.25362TotalR-Sq*uar0.9036SBC840.167247AIC826.50725MAE52.73

19、5066AICC827.799558MAPE2.89335488formalityTest0.0876PrChiSq0.9572VariableDFEstimateStandardErrortValueApproxFr111Intercept1213047.912744.46.0001t1-7.38651.2637-5.85.0001ARI1-1.261701203-10.490001kR210.52140.12274.250001ARCKO15182127S4.05;cards;220323602254216520242078221422922207211921192137213219551

20、78517471818190919581892191918531868199121112119199118591856192418921916196819281898185018411824182318431880196820291996193318051713172617521795171716481512133813831344138414S415971686170716401611163217751850180916531648166516271791procgplotdata=mianyang;plotx*t;symboli=joinv=starci=redcv=blackw=2;ru

21、n;procautoregdata=mianyang;modelx=t/nlag=5dwprobarchtest;modelx=t/nlag=2garch=(p=l,q=l);outputout二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行模型擬合，作業(yè)格式參照書“例5.6續(xù)

22、”）1962-1991年德國工人季度失業(yè)率序列行數(shù)據(jù)（）1.10.50.40.71.60.60.50.71.30.60.50.71.20.50.40.60.90.50.51.12.92.11.72.02.71.30.91.01.60.60.50.71.10.50.50.61.20.70.71.01.51.00.91.11.51.01.01.62.62.12.33.65.04.54.54.95.74.34.04.45.24.34.24.55.24.13.94.14.83.53.43.54.23.43.64.35.54.85.46.58.07.07.48.510.18.98.89.010.0&7&

23、8&910.4&98.99.010.2&68.48.49.9&58.68.79.88.68.4&28.87.67.57.68.17.16.96.66.86.06.26.2解：11建立數(shù)據(jù)集，繪制時序圖datashiyelv;inputx輕；t=intnxfquarter,ljanl962,d,_n_T);formattyear4.;cards;1.10.50.40.71.60.60.50.71.30.60.50.71.20.50.40.60.90.50.51.12.92.11.72.02.71.30.91.01.60.60.50.71.10.50.50.61.20.70.71.01.51.00

24、.91.11.51.01.01.62.62.12.33.65.04.54.54.95.74.34.04.45.24.34.24.55.24.13.94.14.83.53.43.54.23.43.64.35.54.85.46.58.07.07.48.510.18.98.89.010.08.78.88.910.48.9&910.28.68.48.49.98.58.69.88.6&48.28.87.67.57.68.17.16.96.66.86.06.26.2rprocgplotdata=shiyelv;plotx*t;symboli=joinv=starci=redcv=blackw=2;run;

25、1.2輸出時序圖。如圖1-1所示。圖1-1德國工人季度失業(yè)率時序圖12建立延遲因變量回歸模型執(zhí)行語句：procautoregdata=shiyelv;modelx=lagx/lagdep=lagx;run;輸出結果如下圖所示 TheAUTOREGProcedureDependentVariblexESESEBCAEAP63.788407DFE1170.54520RootNSE0.73836273.062927AIC267.504680.56825477AICC267.60812827.1498286RegressR-Squwr電0.3489TotalR-Sqaar電0.S483OrdinaryLeastSquaresEstimates # StatisticValuerrobLatelDurbinh-2.02450.0215FrhS