廣義異方差模型例題

廣義異方差模型例題：例：1969年1月至1994年9月澳大利亞儲備銀行2年期有價證券月度利率數(shù)據(jù)如表所示（行數(shù)據(jù)）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)考察該序列的方差齊性。(2)選擇適當(dāng)?shù)哪Ｐ蛿M合該序列的發(fā)展解答：（1）1、時序圖:時序圖顯示序列存在曲線趨勢，我們對原序列進行差分得到殘差序列的圖。

差分后的殘差圖整均值平穩(wěn)，但伴隨大小不等的隨機波動。我們對殘差序列進行自回歸，再考察自回歸殘差序列的方差齊性。2、用AUTOREG過程建立序列｛Xt｝關(guān)于一階滯后項lagx的回歸模型，并檢驗殘差序列的自相關(guān)性和異方差性。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檢驗顯示Dh統(tǒng)計量為1.8550,Dh統(tǒng)計量的P值為0.0318小于0.05,結(jié)果顯示殘差序列具有顯著的自相關(guān)性。

12 hb.Z+yy<?tjyyi 35J.3/15 <.(dtJUlVariableDFEs"timciteStandardErrortValkieAppiroxPr>|t|Intercept10.17000.09471.踱0.07B6la脊10?98430.003916110.33<.0001顯示回歸模型常數(shù)截距項不顯著(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顯示殘差序列具有顯著的異方差性。3、arch的定階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.*務(wù)UncoridVur□.2(5393711LagLikelihoad-2?4,62414TortslR-^qucire0.9976SBC4^,423324r.IC4~5,243Z3-FJor'iria1￡±yTest20S.531￡P(guān)r>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*電1電w醐E-nS.?四1.朋醐6AR<H118.EE-236.85E-150.031.000^參數(shù)檢驗顯示除AR5參數(shù)不顯著外，其它參數(shù)顯著。GnRCHEstiirii^tesSSE82.3860446Obser'vsticins307WED.況維UncondV'ar0.265S8711LagLikelih-ood-234.G2414TotalR-Squar-e。,99765BC4^.4233-24AIC475.243ZS-[JormslityTest2B8.9316Pr>ChiSq<.0001[JQTE:[Jqinterceptt^r'inM r'edefin^d綜合考慮殘差序列自相關(guān)性和異方差性檢驗結(jié)果嘗試擬合無回歸常數(shù)項的廣義異方差模型，nlag=4,garch=(p=1,q=1)。4、異方差模型:擬合效果很理想。尤=0.9997尤+￡；=0.1272：5+U"廣再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;