時間序列平穩(wěn)性檢驗及ARIMA模型的應(yīng)用

1、時間序列模型的應(yīng)用以2000年第一季度-2016年第四季度中國國內(nèi)生產(chǎn)總值統(tǒng)計數(shù)據(jù)為例，建立ARIMA 模型。所有數(shù)據(jù)按當(dāng)年價格計算，共有68個觀測值。年份季度GDP （億元）年份季度GDP （億元）2000121329.92009174053.1224043.4283981.3325712.5390014.1429194.34101032.82001124086.42010187616.7226726.6299532.4328333.33106238.7431716.84119642.5200212629520111104641.3229194.82119174.3331257.331269

2、81.6434970.34138503.32003129825.520121117593.9232537.32131682.5335291.93138622.2439767.44152468.92004134544.620131129747僂攵據(jù)來源： HYPERLINK /easyquery.htm?cn=B01 /easyquery.htm?cn=B01238700.821439673418553152905.3446739.84168625.12005140453.320141140618.3244793.12156461.3348047.83165711.9454024.8418118

3、2.52006147078.920151150986.7252673.32168503356064.73176710.4463621.64192851.9200715717720161161572.7264809.62180743.7369524.33190529.5478721.44211281.32008169410.4278769382541.9488794.31、利用ADF檢驗檢查序列的平穩(wěn)性PTCobjEc? :TChKrriPrint LManeFreessanp eGrm5tnr Sheet 匚 hEMtz der0 Series GDP Workfilr UN TITLEDil

4、JntrtledV-B xAugm*nt*d Dicke AFuller Unit Root Tsl on GQPAStatisticProb1Auarncnicd Dickcv Fuller test Giotstc1 6530420 0997Test c ntr fll valueslevel-3 E401985 怙 level2 909200ID% tevel2 582215JJJI Hypothesis: GEP has a unit rootIzKogenQus DonslartLength. 5 ； ALtu nalic -bdM on SIC. tridxlay-lO)l/acK

5、innor (1A9A) one-sided p-vNues.圖1-1.GDP單位根檢驗結(jié)果（有截距項無趨勢項）0Seifes:GDPWorkhle: UNTinED:Unlitled n xVlEWL Proc :ObjectPre pertie* Pnnt Nme Fr?p?e Samplr GenirSheet Graph Jit 北 IrkAugmented Diekty Fuller Unrt Root Test on GDPNull l-Aipcthesis: GDP has a unrt ractExDflenous: Constant Lrear TrendLag LerAti

6、. 5 (AutomAic - based on SIC. maxlagAW)t-Siatistic Prob *Aanenred dickcy Fuior test staiistc2.34 ?71U0/1027Tea critical va ues:1 % level虧 levtl 10% 創(chuàng)4.113017-3.A3970-m 171071AMxKinron (1S&5) sne-sided p-values圖1-2.GDP單位根檢驗結(jié)果（有截距項有趨勢項）Mull -lycoAesisMull -lycoAesis： GUP has a jnt raoiExogenous- NoneL

7、 自 g Length 5 lALitcmatic - tased ort SlQ rriaKlag=lO)t-SldiilicProb.Auamented Diclev Fuller lest statistc2202674.9929Test critical values:1% levelZ6027Q45% level1 0A6161 -1613396rh/j e- -es： COP VVrxkfi r LNTlTl FD :l)ntitirAl.1 1X包叫 Proc Object PropertiesPrim Name Fr&ez Samp e G&nrShAet Grapti=hdt

8、r1 J1,Augmented Dicky-Fuller Unrt Root Test on GDP*kgr Krunn (19 胎* nnp-sided p-v16Test critical values1 h level-23027945 利 levelA1.9A-16110% level1.613398MacKinnon (199氣 one-sided p-values圖1-4.GDP 一階差分單位根檢驗結(jié)果(無截距項無趨勢項)可以看出一階差分后，d (GDP)序列是不平穩(wěn)的。階差分結(jié)果如下：它 Series： GDP Wtorkfile： UhJTlTLE&： Untitled-nVe

9、w Proc Object 3roperties Pr nt Ndrre freeze Sairipk Genr Sheet GraphStatsAugmented Dlcky-Fullr Unit Root T&s( on D|GDP,2)Null Hypothesis: D(GDP,2) has a unit rootExogenous MarieLag Lsigtt) 3 (AiMomAtx - based on SIC, rrudag=1D) t-Statistic Prob Ajcmcntcd Dickqy Fuller test static斗 A&277 d 0900Test u

10、rgl values1 % level5 珂 level&416110% levelI 613398Tt-1ac Kj n non (19&6 ore-3 ice d p-values.圖1-5.GDP二階差分單位根檢驗結(jié)果(無截距項無趨勢項)因此，二階差分平穩(wěn)。2、確定模型形式檢查GDP二階差分序列的自相關(guān)函數(shù)和偏自相關(guān)函數(shù):Corr*kgrim of D(GDPDate： 01 D718 Time : 12：八5SdiTf) l 2C-MQ1 201 吧 4Inc udec ot seAvaiiori. -.6Auto correlationF*uai C orrelationACFACQ

11、 SuitPTcb11 =1:120688 3390568JU19230 77336 032Q.05Q o ODau11q忖-oft) t H勺122 970000 o.ooa 011140八890.03_160 17SHQ 13O&i11160 302 -0.0301S5 95oooa111110 w訃(KBfTTUSoon1B 77B-0J30224 aaoooa11iry訃a. 2/o-0 031?710 001l1w-0 0042b2.b30_ODO1=1l11-0 4購0Q24270 50OOQO|12130 J/2J.D420 4554)0183d IJ 3?5 55O.OOQ O

12、OdQ111 1 l11OI1140 238o.oor33。450 00011iII15-04104)010145 25 ODOHi14 173 582甜40.J100.0193齷0Q.QOO DODO111i1I10 206 41(X3333 760 0tf=1l15 -0 屈0.027405 360 000IIlfl20 0 4EM01)0242921QOOO二11 :210 341 4)056地的oooa1 112?0 177 -0(八+ 14 000 000匚11123-0 293-0.IM245299O.ODOhm1i240 42C-00414M 840 00ftO112S4J.28

13、G0 027O.ODO1 11%0 H7D0184&3 33OOQO111270 002490 230 00011=111種0 354oomfiG4 船0 ODO匚11- 243-Q.0Q9&12舊DOOT1:11ma i23E1406DOMII11131-0.19八ll.U/EJSIL 080.0001二1320 2B90042530 OSOQDOc11330 20f.00106M 920 00ft1D |1340 100 -0 03753722oooaI-111 360 If0.1X13WO站00001n1孫0 235-0.063卻13o.oao1111370 166-0 003563 4

14、0ODDO1111比0.0790.014564.400_ODOid11390 12S002955? 150 0(W1圖2.1二階差分自相關(guān)、偏自相關(guān)函數(shù)從上圖可以看出自相關(guān)函數(shù)呈振蕩型衰減(拖尾)，而偏自相關(guān)函數(shù)在 3階后截尾，可初步判斷適合的模型為AR(1)、AR(2)、AR(3)。對GDP二階差分分別做AR(1)、AR(2)、AR(3)模型分析，結(jié)果如下:M Equahcjn, EQO V/uTle : O7AJnUtled-3k|vww|pr&c Ob|cl Orintj Nam# Freen j rtrwltFo/e(nod. Lea st Squares0 眥！ 0I/07/1S 八

15、ime 1307Sample (adjusted)： 200QQ4 2016Q4Incii.ded obsArvmticr* r.r mfer atJ.usfnTentsCorib-ieTgen ize ac hieved aflw rteralionsVariableCocffkicflftStd Zrror t-Stafusoc陌-0 67M990093130-7 200503OODDOR-squanedAdjusted R-sqiored 合 匚 offogrcssian Sum reAK：Log lihHihcnd DurtHn- Wstson stat0 4 斗 M3C亡 eti d

16、ependent var S-0.A47430 D- dtpendtifit var AKDi mfo 14715 06 erterxin Schwarz cntei ion 1.39E + 10 HaniiflriAQuinri Liz.71H 祐 79 2.2547102&35SOO 1&?ftS.0O 22 04640 2207965 r ninveled AR Kost?r7圖2.2 GDP二階差分AR(1)模型回歸結(jié)果jQQQOJlOQSQQQQyQEUntitled-3 X-bitct print電”w韭Forwaasta：s 恥、fidMrpeiifirnl Vaiiabt! D

17、D(GDP) t/ethod Least Squares Date Q1； 0TH8 Time 13:10 Sample (adjust) 2001Q1 20 伯 Q4 Inr hided nhseniAlAns fi4 sfter AdjiiAmFTits Convergers e achieved after 2 re ratio nsVariableCoefficientStd Eitmt-5utis : icProfc.AR03419550.1189412e?A&as0 0055R-sqJ ared0.115詣Mean deoendenl 尸尸26&S437Adjusted R-Aqu

18、dreiJ0115S1BS D cepen Jent13951 15S E of regression1B760 2GAkaike irfn erttenor22 53237Sum squared resid222E+10Schwara cnt&nonZ2.=CbWLog lAeliAood-720.0359Hannan - nn enter.22.54566Durbri-Watson slat2606279IrA-crtcd AH Root358*50圖2.3 GDP二階差分AR(2)模型回歸結(jié)果i Equsiion- JNTTTLED Wokfle： 07 : UntitledW- n x卜血 Proc j Obji&ct 曲“ Fr mlNam x八freeze隹Far so itStaUFZDtepffideni Varidbk O(D(G