第五章非平穩(wěn)時間序列地隨機(jī)分析報(bào)告報(bào)告材料實(shí)驗(yàn)報(bào)告材料

1、第五章非平穩(wěn)時間序列隨機(jī)性分析實(shí)驗(yàn)報(bào)告下表為1948-1981年美國女性大于20歲月度失業(yè)率數(shù)據(jù)表5-11948-1981年美國女性月度失業(yè)率1月2月3月4月5月6月7月8月9月10月11月12月1948446650592561491592604635580510553554194962870862972482086510071025955889965878195011031092978823827928838720756658838684195177975479468165864462258872067074661619526466785525605785145415765225305644

2、421953520484538454404424432458556506633708195410131031110110611048100598710061075854100877719559828947957997817767618398428118437531956848756848828857838986847801739865767195794184676870979883183379880677195179919581156133212761373132513261314134312251133107510231959126612371180104610101010104698597

3、110371026947196010971018105497895510671132109210191110126211741961139115331479141113701486145113091316131912331113196213631245120510841048113111381271124411391205103019631300131911981147114012161200127112541203127210731964137514001322121410961198113211931163112011649661965115413061123103394011511013

4、110510119631040838196610129638888408809398681001956966896843196711801103104497289711031056105512871231107692919681105112798890384510209941036105097795681819691031106196496786710589871119120210979948401970108612381264117112061303139314631601149515611404197117051739166715991516162516291809183116651659

5、145719721707160716161522158516571717178918141698148113301973164615961496138613021524154716321668142114751396197417061715158614771500164817451856206718562104206119752809278327482642262827142699277627952673255823941976278427512521237222022469268628152831266125902383197726702771262823812224255625122690

6、27262493254422321978249423152217210021162319249124322470219122412117197923702392225520772047225522332539239423412231217119802487244923002387247426672791290427372849272326131981295028252717259327032836293829753064309230632991數(shù)據(jù)來源:Andrews&Herzberg(1985)。根據(jù)以上數(shù)據(jù)，下面用Eviewis6.0對1948-1981年美國女性大于20歲月度失業(yè)率數(shù)據(jù)進(jìn)

7、展隨機(jī)性分析。1.繪制時序圖S圖5-11948-1981年美國女性月度失業(yè)率序列時序圖從時序圖可以看出序列中既有長期趨勢又有周期性，因此進(jìn)展1階-12步差分。在數(shù)據(jù)窗口中選擇“ Quick/Graph ,出現(xiàn)以下對話框，在空白窗口中輸入D(S,1 , 12)，如圖 5-2 所示。圖5-3圖 5-21階-12步差分D(St1,12)5D04003002001000-100- -2D0- -3D0- D0-D(S,1, 12)時序圖從時序圖看，D S,1,12丨均值穩(wěn)定，沒有明顯測周期性，方差有界；生成序列D1=D(S,1,12)，通過相關(guān)分析，具體分析序列的平穩(wěn)性。如如下圖所示View| Pro

8、c.| iTlii iJbl:it| PwiofpErties | Print | hlarne | Freeze | Sample91 faEnr | SieErt| GrapK | Starts 11 dErrt fCorrelQQrinii or DiI_| Series: D Worktile： UMTlTLED:UntrtledVDOtCT4 I ime 0913sarnv 14.1C81M12Includ ed a ba en,ratic ns BS 5Aulocour lotionFirtl.1 Ccri elationACPACaSlalProbI匚li-D 13 0-O 1

9、387 &S51 DCI&i=V=2. isg0.1 7321 .SFS .0 3i11IJl3 02-2QU22 U /id.cuit4.00 10.0 4123. S 450.00 0II150a01 10.0 0723.5-93aoooIO1II6 D3P -.E2fl 0 36?4 *5 9? DCn-Cc17-C.CB427 O1 .DO1JI1180.04 30.0032S. 133o oo a11l9-0 013o ij ie28 1 9S0 00 1cu|i100.1230.14034.6 S2 .0 01111n DBS -好4Cl門船？36 77口 OGt1a1112-Cl

10、 -4-2*9121 OSj oo a131IE1130.04 1-C.073121.79o.oo aIEI114-0.0A10 1122 47o ooaiH115-D 0610|!190.04 7-0.0 3212 9.300.00 3i|iII120-0 D-*5-C 1)09130.65o oaa1 p1121 .Od 5O.C3513 0.7.ooi匸122-0.00 9-.122U U94T 3 0.30o ooai1JZ3 06 213.2 400 00 9-Eil2科0.070.3 0013 4 72m呂 ii0.00 0iIIli D*S7 - OSS力3誌a oonciIh2

11、6Cl COS2日30.co1JI1127.82-0.0 CM14 2 230.00 01(1lII2G-D.Dii-C1J-3 0G0 D0 011 i11 120D 012 35143 13a oao1iV1130 .02 40.063143.370.00 01ihn釦 oazO IJO613.97.oa1 |321-14.230.00 01rl33. 02 70.C41144 53a. ooo圖5-4D(S,1 ,12)的相關(guān)分析圖5-4中，自相關(guān)2階顯著，但是12階也是顯著的，因此在趨勢平穩(wěn)中又包含 了周期性因素。以下對其進(jìn)展ARM模型分析。對平穩(wěn)非白噪聲序列DS,1,12嘗試用ARM

12、模型擬合。1對序列進(jìn)展AR莫型擬合。在主窗口命令框中輸入LS D(S,1，12) AR(1)AR(12)，得到以下回歸結(jié)果，如圖5-5所示，并對其殘差相關(guān)性進(jìn)展檢驗(yàn)，如圖5-6。 Equation: UNTITLED Warkfiler UNTITLED:rUntitledVieProc Object Pmt Name Freeze Estimate Forecast Stats ResidsDependent Variable: D(S,1J2)Method: Least SquaresDate; 06/15U Time:0917Sample (adjusted). 1950M0219B1M

13、12Included obseivations: 383 3fler adjustmentsCon mergence achieved after 2 iterations圖5-5AR(1，12)模型擬合序列 D S, 1，12VaiabieCoefficientStd. ErrortstafcticProb.AR1)-0J 059660,045015-23540260.0191AR(12)0.4 602930.045286-10.164210.0000R-squared0220345Mean d e pendent var-0.253264Adjusted R-squared0226320S

14、.D.d ependento112.6560S.E. ot regression99,10001Akaike info criterion12.03534Sum squared resid3741729.Schwarz criterion1205596Log likelihood-2302.768Hannar-duinn enter.1204352Durbin-Wson stat2.030894Inverted AR Roots90-.24i90+241,65-66i.65+661.23,911.23+.91I-,25t90i25-.90i-,67+&6i*91+24)-.91-241殘差相關(guān)

15、性檢驗(yàn)結(jié)果如如下圖:圖5-6AR(1,12)模型擬合序列 D S, 1, 12的殘差相關(guān)圖從上圖看出模型殘差非白噪聲，模型提取信息不充分。2對序列進(jìn)展M/模型擬合。在主窗口命令框中輸入 LS D(S,1,12) MA(1)MA(12),得到以下回歸結(jié)果，如圖5-7所示，并對其殘差相關(guān)性進(jìn)展檢驗(yàn)，如圖5-8。LJNTTTI ED WnrIrRlffi UNTITLED:1 Jn+Ftl*dViewPl oc|ObjectFT in 11 NameFreezeEstlrnate Forecast| 5ts | Reslcis|Dp&ndnt Variable D(S 112)Meltiod Lea

16、st SquaresDate： 06/15/14 Time: 09:19Sainple (.adjusted. 1349M02 1931 L112 Included obseNations: 335 after adjustments Convergeroe acTilewd aft&r 8 iterations圖5-7MA(1,12)模型擬合序列 D S, 1 ,12圖5-8 AR(1 , 12)模型擬合序列 D S, 1 , 12的殘差相關(guān)圖MA UaCKCSSt 1948L102 1949MU1VariableCoetfic-iftnl3td. Errort-OtatlstlcProb.

17、UA-0 S2Q737D 02S951-2 0 77546 0000R*squared0 410415Liesn dependenlvar0.496203Adjusted RSquared0 408915S.D. dependent ar112.2025S.E. of regression85 26358Akaike info crile rion11 75774Sum squared cesid2924472.Scnwarzcnt non1177709Log HKeiiocd-2 320 154Hannan-Quinn enter117&572Oui曰tmon stal2.C74048Inv

18、erted MA Roots00.85 40t.6640150 9&i5t)+ a si01- )B*01+ Q8i- 4S- BSi-48+85i_5- 49i- 85+.49i-Qfi從圖5-8可以看出模型殘差也非白噪聲，模型提取信息仍然不充分經(jīng)過以上分析和ARM/模型擬合，效果不理想。序列中的長期趨勢，季節(jié)效 應(yīng)和隨機(jī)波動不能簡單分開，故以下對其運(yùn)用乘積季節(jié)模型擬合。圖 5-9 ARMA 1 , 1X 1, 0, 1仁擬合序列 D(S, 1, 12)圖 5-10 ARMA 1, 1X 1 , 0, 112擬合序列 D(S, 1, 12)模型參數(shù)可以看出SAR(12)的參數(shù)并不明顯，P值為

19、0.9608，因此刪除該項(xiàng)，并對序列重新進(jìn)展模型擬合I i EciUdti口n： LJ NT1T LE Dkfil c: U NTIT LE D; Ur i tii L=J IVieA | PocPrint| Freeze Estimat= | Forecas t Stats | Resiti-E |Dependent Vo ria bl a: DCS, 1,12 rielhod I .eas* 3cjuet*&sDate: 06/1571 Timor oa；2dSample (adjusted; 1949M03 1001-112indLidPd ot)sprvAlinns 3 94 atti

20、 adjusimentsConve rgen co achieved after 7 its rationsMA Backer st: 194BM02 l949bT02vanacioCoerrici*nt&Jtd. trrert yiatisiicFfObAR(1J- &8283 5O 1791B3-3 8111&0 00 02MA10 5651730 2033032.7 78720 .0057SMA-0 8272970 029014，-23.51400 .0000R-squaredO 41026 7Mean dependent varD.S12193Adjusled R-s qua red0

21、 J-15291S D dependeni112.10-91s.b. ot regressionZ 4 9Axaiimo criterion1 1. /4hJB4Gum squared resid2S7B403E5chv*an criterion11 77311i oo likelihood*231 1 521Hyn n a n-Q uin n Q 11r117ft083Durbin V*. alon ctst1 058387Ingn日口 ar Rocits 68Inserted MA RootsQ8,85-491.85491.40_85i斗 9-.3Si-0t)-.9Bi- 00- 99i-

22、49-.S Si-.57-.色幻+.HPI-E4削-.09圖 5-11 ARMA 1 , 1X 0, 0, 112擬合序列 D(S, 1, 12)圖 5-12 ARMA 1, 1X 0, 0, 112擬合序列 D(S, 1, 12)模型參數(shù)可以看出乘積模型的殘差為白噪聲序列，其P值顯著大于0.05，該模型提取序列的信息充分；參數(shù)都顯著，因此模型建立成立。 模型的具體形式為：1-B(1-B 12)S=1 0.5652B(1 0.8273B12)10.6829B將序列擬合值與序列觀察值聯(lián)合作圖，可以直觀地看出該乘積模型對原序列的擬合效果良好。2,500 -2DW-500-1&5519001975i

23、96019651&701950Forecast SFActual SForecast sample 1948M01 1981M12Adju$td sample: 1949M03 19A1M12 Included observations: 394Root Mean Squared Error 85 44433Mean Absolute Error 6471341Mean Abs. Percent Error 5.370171Theil Inequality Coefficient 0.027444Bias Proportion0.000290Variance Proportion 0 0007

24、35 Covariance Proportion 0 9&S975圖 5-13美國女性月度失業(yè)率序列擬合效果圖?2S E附表：以下是建立模型具體分析過程中產(chǎn)生的表格備表1D S, 1, 12的相關(guān)分析Date: 06/15/14 Time: 09:13Sample: 1948M01 1981M12Included observations: 395AutocorrelationPartial CorrelationACPACQ-StatProb*|. |*|. |1.|* |.|* |2.|. |.|. |3.|. |.|. |4.|. |.|. |5.|. |.|. |6*|. |*|. |

25、7.|. |.|. |8.|. |.|. |9*|. |*|. |10.|. |.|. |11*| |*| |12.|. |*|. |13.|. |.|* |14*|. |.|. |15.|. |.|. |16.|. |.|. |17*|. |.|. |18.|. |.|. |19.|. |.|. |20.|. |.|. |21.|. |*|. |22.|. |.|* |23*|. |*l.|24.|. |.|. |25*|. |.|. |26.|* |.|. |27.|. |.|. |28.|. |.|. |29.|. |.|. |30.|. |.|. |31.|. |.|. |32.|.

26、|.|. |33.|. |.|. |34*|. |.|. |35.|. |*l.|36備表2 AR 1 , 12模型擬合序列 D S, 1, 12Dependent Variable: D(S,1,12)Method: Least SquaresDate: 06/15/14 Time: 09:17Sample (adjusted): 1950M02 1981M12Included observations: 383 after adjustmentsConvergence achieved after 2 iterationsVariableCoefficientStd. Errort-Sta

27、tisticProb.AR(1)AR(12)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared resid3741729.Schwarz criterionLog likelihoodHannan-Quinn criter.Durbin-Watson stat.90+.24Inverted AR Rootsi.23+.91.65+.66i-.25+.90i-.67+.66i-.91+.24i備表3 AR 1, 12模型擬

28、合序列 D S, 1, 12的殘差分析Date: 06/15/14 Time: 09:18Sample: 1950M02 1981M12Included observations: 383Q-statistic probabilities adjusted for 2 ARMAterm(s)AutocorrelationPartial CorrelationACPAC Q-StatProb.|. |.|* |.|. |.|* |.|. |.|. |.|. |.|. |.|. |*|. |.|. |*|. |.|. |.|. |.|. |*|. |.|. |.|. |.|. |.|. |.|.

29、|.|. |.|. |*|. |.|. |*|. |.|. |*|. |.|. |.|. |.|. |.|. |.|. |.|. |.|. |.|* |.|. |.|. |.|. |12345.|.|6*|.|7.|.|8.|.|9*|.| 10.|.|11*|.|12.|.|13.|. |.|. |.|. |.|. |.|. |.|. |.|. |1415161718192021*|.|22.|.|23*|. |.|. |.|. |.|. |.|. |2425262728.|.|29.|*|30.|. |.|. |.|. |.|. |31323334*|. |*|. |36.|. |備表4

30、MA 1, 12模型擬合序列 D S, 1 , 12Dependent Variable: D(S,1,12)Method: Least SquaresDate: 06/15/14 Time: 09:19Sample (adjusted): 1949M02 1981M12Included observations: 395 after adjustmentsConvergence achieved after 8 iterationsMA Backcast: 1948M02 1949M01VariableCoefficientStd. Errort-StatisticProb.2924472.

31、Mean dependent varS.D. dependent varAkaike info criterionSchwarz criterionHannan-Quinn criter.MA(1)MA(12)R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihood Durbin-Watson statInverted MA Roots.99.86+.49i.50+.85i.01+.98i-.48+.85i-.85+.49i備表5 MA 1 ,12模型擬合序列 D S, 1, 12殘差相關(guān)圖Date

32、: 06/15/14 Time: 09:20Sample: 1949M02 1981M12Included observations: 395 Q-statistic probabilities adjusted for 2 ARMA term(s)AutocorrelationPartial CorrelationACPAC Q-Stat Prob12345678910111213141516171819202122232425262728293031323334.|. | .|* |.|. |.|. |.|. |.|. |.|. |.|. | .|. | *|. |.|. |.|. |.|

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34、36.|. |備表6ARM 1, 1X 1, 0, 112擬合序列D(S, 1 , 12)模型參數(shù)Dependent Variable: D(S,1,12)Method: Least SquaresDate: 06/15/14 Time: 09:22Sample (adjusted): 1950M03 1981M12Included observations: 382 after adjustmentsConvergence achieved after 12 iterationsMA Backcast: 1949M02 1950M02VariableCoefficientStd. Error

35、t-StatisticProb.AR(1)SAR(12)MA(1)SMA(12)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared resid2802717.Schwarz criterionLog likelihoodHannan-Quinn criter.Durbin-Watson statInverted AR Roots.62.54+.31i.31+.54i.00+.62i-.31+.54i-.54+.31i.85+.4Inverted MA Roots.98 9i.00+.9.49+.85i8i-.49+.85i-.85+.49i備表7 ARMA 1, 1X 0, 0, 112擬合序列D(S, 1, 12)模型參數(shù)Dependent Variab