广义异方差模型例题

广义异方差模型例题：例：1969年1月至1994年9月澳大利亚储备银行2年期有价证券月度利率数据如表所示（行数据）4.9955.035.035.255.265.35.455.495.525.75.685.655.86.56.456.486.456.356.46.436.436.446.456.486.46.356.46.36.326.356.135.75.585.185.185.175.155.215.235.054.654.654.64.674.694.684.624.634.95.445.566.046.066.068.078.078.18.058.068.078.068.118.610.811119.489.188.628.38.478.448.448.468.498.548.548.58.448.498.48.468.58.58.478.478.478.488.488.548.568.398.899.919.899.919.919.99.889.869.869.749.429.279.268.998.838.838.838.828.838.838.798.798.698.668.678.728.7799.619.79.949.949.949.959.949.969.9710.8310.7511.211.411.5411.511.3411.511.511.5812.4212.8513.113.1213.113.1513.113.214.214.7514.614.614.4514.514.815.8516.216.516.416.416.3516.113.713.51412.31214.3514.612.512.7513.713.4513.5512.61111.612.0512.3512.712.4512.5512.212.111.1512.112.512.912.513.213.6513.6513.513.4513.3514.4514.315.0515.5515.6514.6514.1513.312.6512.712.814.515.115.1514.314.2514.0514.715.0514.0513.813.2512.8512.611.81312.3511.4511.3511.5510.8510.912.311.712.0512.312.913.0513.313.8514.6515.0515.1515.715.415.114.815.815.81514.413.814.314.1514.4514.114.0513.7513.31312.5512.2511.8511.511.111.1510.710.2510.5510.2510.39.68.48.27.258.358.258.37.47.156.355.657.47.27.057.16.56.255.955.655.855.455.35.25.555.155.45.355.15.86.356.56.958.057.857.758.6(1)考察该序列的方差齐性。(2)选择适当的模型拟合该序列的发展解答：（1）1、时序图:时序图显示序列存在曲线趋势，我们对原序列进行差分得到残差序列的图。

差分后的残差图整均值平稳，但伴随大小不等的随机波动。我们对残差序列进行自回归，再考察自回归残差序列的方差齐性。2、用AUTOREG过程建立序列｛Xt｝关于一阶滞后项lagx的回归模型，并检验残差序列的自相关性和异方差性。Th-e ProceduirseOep-endentVariableOrdlinaryLccistSc]|warcsEs-tTnfuatu;SSE53,DTE3疣;MSEO,2T322RocrtVJ5E0,522?^SBCATCwR-Sq|Uimir右<a_qtssTTotmlR-Squiaire色-C756OurhitiihiPr>lii<0.ClB-13检验显示Dh统计量为1.8550,Dh统计量的P值为0.0318小于0.05,结果显示残差序列具有显著的自相关性。

12 hb.Z+yy<»tjyyi 35J.3/15 <.(dtJUlVariableDFEs"timciteStandardErrortValkieAppiroxPr>|t|Intercept10.17000.09471.踱0.07B6la脊10»98430.003916110.33<.0001显示回归模型常数截距项不显著(0.0736>0.05)。IUU1IIUJ'XI1 11JL»□ IF1>■ 11 七■.D-J-1oQsrid!_•' for'ARCHDistur'bdncesOrder艮Pr:QPr>Lv10,132~0.6697皿SS31217.4-6550,OC02IN3g，.00023IS.弭混Ci.砌犯10.4015由.0SO2423.7006<.000121.14LE：更.&3妃533.4612<.000123.5677<.0001E<.000123.3(513<.0001—49.。兆9<.000135.13F9<.000149.1315<.00013E.13914.0001分55.3120<.000135.3257<.@0011055.3713<.00013^.5387<.@0011155.9551<.00013S.13L7<.00011256.2409<.00013■9.3713<.0001显示残差序列具有显著的异方差性。3、arch的定阶procautoregdata=hh;modelx=lagx/lagdep=lagxarchtest;modelx=lagx/nlag=4backstepgarch=(p=1,q=1);outputout=rescev=v;run;

GARCHEstiRiat«eE55E32.336&44^5Observations?0T■SE0.*务UncoridVur□.2(5393711LagLikelihoad-2?4,62414TortslR-^qucire0.9976SBC4^,423324r.IC4~5,243Z3-FJor'iria1£±yTest20S.531£Pr>Cliiiq<.SSSlfJOTE:fiointercepttermisuised.R-5q|uiares-areredefiredV?rislile□FStandardErr'or"tVslLie二pppa>Pr〉|t|10,址了0,0^224944+.4S-<.0001KR510,12720,04243.000.0027rtRCM®10.0,^12421,<.0001*电1电w醐E-nS.©四1.朋醐6AR<H118.EE-236.85E-150.031.000^参数检验显示除AR5参数不显著外，其它参数显著。GnRCHEstiirii^tesSSE82.3860446Obser'vsticins307WED.况维UncondV'ar0.265S8711LagLikelih-ood-234.G2414TotalR-Squar-e。,99765BC4^.4233-24AIC475.243ZS-[JormslityTest2B8.9316Pr>ChiSq<.0001[JQTE:[Jqinterceptt^r'inM r'edefin^d综合考虑残差序列自相关性和异方差性检验结果尝试拟合无回归常数项的广义异方差模型，nlag=4,garch=(p=1,q=1)。4、异方差模型:拟合效果很理想。尤=0.9997尤+£；=0.1272：5+U"广再Th=0.2700+6.173E-23.〔(其中eAt~n(0,0.26999))附程序:datahh;inputx@@;difx=dif(x);lagx=lag(x);year=intnx("month",”01jan1969"d,_n_-1);formatyearmonyy7.;cards;4.9955.035.035.255.265.35.455.495.525.76.446.456.486.46.356.46.36.326.356.135.75.585.185.185.175.155.215.235.054.654.654.64.674.694.684.624.634.95.445.566.046.066.068.078.078.18.058.068.078.068.118.610.811119.489.188.628.38.478.448.448.468.498.548.548.58.448.498.48.468.58.58.478.478.478.488.488.548.568.398.899.919.899.919.919.99.889.869.869.749.429.279.268.998.838.838.838.828.838.838.798.798.698.668.678.728.7799.619.79.949.949.949.959.949.969.9710.8310.7511.211.411.5411.511.3411.511.511.5812.4212.8513.113.1213.113.1513.113.214.214.7514.614.614.4514.514.815.8516.216.516.416.416.3516.113.713.51412.31214.3514.612.512.7513.713.4513.5512.61111.612.0512.3512.712.4512.5512.212.111.1512.112.512.912.513.213.6513.6513.513.4513.3514.4514.315.0515.5515.6514.6514.1513.312.6512.712.814.515.115.1514.314.2514.0514.715.0514.0513.813.2512.8512.611.81312.3511.4511.3511.5510.8510.912.311.712.0512.312.913.0513.313.8514.6515.0515.1515.715.415.114.815.815.81514.413.814.311.111.1510.710.2510.5510.2510.39.68.48.27.258.358.258.37.47.156.355.657.47.27.057.16.56.255.955.655.855.455.35.25.555.155.45.355.15.86.356.56.958.057.857.758.6；run;procgplotdata=hh;plot(xdifx)*year;symboli=line;run;procautoregdata=hh;modelx=lagx/lagdep=lagxarchtest;modelx=lagx/nlag=4backstepgarch=(p=1,q=1)noint;outputout=outp=ppm=pmr=rrm=rmucl=ucllcl=lclcev=cev;run;dataout;setout;uclr=1.96*sqrt(0.26747);lclr=-1.96*sqrt(0・26747);cuclr=1.96*sqrt(cev);clclr=-1.96*sqrt(cev);cuclp=p+1.96*sqrt(cev);clclp=p-1.96*sqrt(cev);run;procgplotdata=out;plotx*year=1p*year=2cuclp*year=3clclp*year=3lcl*year=4ucl*year=4/overlay;symbollc=blacki=nonev=star;symbol2c=redi=linev=none;