應(yīng)用時間序列分析答案

1、河南大學(xué):姓名:汪寶班級:七班學(xué)號:51班級序號:685:我國1949年2008年年末人口總數(shù)（單位：萬人）序列如表4 8所示（行數(shù)據(jù)）.選擇適當(dāng)?shù)哪Ｐ蛿M合該序列的長 期數(shù)據(jù)，并作5期預(yù)測。解：具體解題過程如下：（本題代碼我是做一問寫一問的）1:觀察時序圖：data wangbao4_5;in put x;time= 1949+n- 1;cards ;54167 55196 56300 57482 58796 60266 61465 6282864653 65994 67207 66207 65859 67295 69172 7049972538 74542 76368 78534 80671

2、 82992 85229 8717789211 90859 92420 93717 94974 96259 97542 98705100072 101654 103008 104357 105851 107507 109300 111026112704 114333 115823 117171 118517 119850 121121 122389123626 124761 125786 126743 127627 128453 129227 129988130756 131448 132129 132802;proc gplot data =wangbao4_5;plot x*time= 1

3、;symbol1 c=black v=star i =joi n;run ;分析：通過時序圖，我可以發(fā)現(xiàn)我國1949年一2008年年末人口總數(shù)(隨時間的變化呈現(xiàn)出線性變化.故此時我可以用線性模型擬合序列的發(fā)展.X t=a+bt+It t=1,2,3,60E(I t)=0,var(I t)= /其中，It為隨機(jī)波動；X=a+b就是消除隨機(jī)波動的影響之后該序列的長期趨勢。2:進(jìn)行線性模型擬合：proc mutoreg dmtm =wangbao4_5;model x=time;output out =out p=wangbao4_5_cup;run ;proc gplot data =out;pl

4、ot x*time= 1 wangbao4_5_cup*time= 2/ overlay ;symbol2 c=red v=none i =join w=2 l =3;run ;The SAS Systeiii15:28 lednesda Cecember 7, 2013 IThe AUTOREG F rocedursdependent Variable xOrdinary Lea&t Squares Est 血心遊262236607DFE6BMSE4522355Root MSE2127SBC1495.89983AID1031.71114Regress R-Square0.9931T

5、ot=a 1 R-Squia re0,9931Durb in-'tfatson0.0724VariableDFE吐 imateStandardErrort ValueApproxPr > IIIletercept12770828818BK-88.84<.0001tine1144&<.00(11分析：由上面輸岀結(jié)果可知：兩個參數(shù)的p值明顯小于，即這兩個參數(shù)都是具有顯著非零，4:模型檢驗(yàn)又因?yàn)镽egress R-square=total R-square=,即擬合度達(dá)到所以用這個模型擬合的非常好。5：結(jié)論所以本題擬合的模型為:X t=-2770828+1449t+

6、l t t=1,2,3,E(I t)=0,var(I t)= d,6026 :作5期預(yù)測procforecastdata=wa ngbao4_5 method=stepar trend=2 lead= 5out=out outfull outest=est;id t;var x;proc gplot data =out;plot x*time=_type_/ href =2008;symbolli=nonev=starc=black;symbol2i=joinv=nonec=red;symbol3i=joinv=nonec=blackl=2;symbol4i=joinv=nonec=black

7、l=2;run ;I5MDC4IM0CI2MD0HMDQ8KD07MKKM 00IR4U1QE -|I 就I19/1101010勿 M2010前 J6 :愛荷華州1948-1979年非農(nóng)產(chǎn)品季度收入數(shù)據(jù)如表4 9所示（行數(shù)據(jù)），選擇適當(dāng)?shù)哪Ｐ蛿M合該序列的長期趨勢。解：具體做題過程如下：（本題代碼我是做一問寫一問的）1、繪制時序圖data wangbao4 6;in put x;time=_n_;cards ;601 604 620 626 641 642645655682678692 707736 753 763 775 775 783794813823826829 831830 838 85

8、4 872 882 903919937927962975 9951001 1013 1021 1028 10271048107010951113 1143 1154 11731178 1183 1205 1208 12091223123812451258 1278 1294 13141323 1336 1355 1377 14161430145514801514 1545 1589 16341669 1715 1760 1812 18091828187118921946 1983 2013 20452048 2097 2140 2171 22082272231123492362 2442 24

9、79 25282571 2634 2684 2790 28902964308531593237 3358 3489 35883624 3719 3821 3934 40284129420543494463 4598 4725 4827 4939 5067 5231 5408 5492 5653 5828 5965proc gplot data =wangbao4_6;plot x*time;symbol c=black v=star i =join;run ;分析；可知時序圖顯示該序列有明顯的曲線遞增趨勢。嘗試使用修正指數(shù)型模型進(jìn)行迭代擬合:xta bct +? t， t=1 ，2，1282、

10、擬合模型proc nlinmethod=gauss;model x=a+b*c*time;parametersa= b= c=;output predicted =xhat out =out; run ;NLIN過程輸出以下六方面信息:(1 )迭代過程rte rat i ve Phase(2 )收斂狀況IteriSum oi c Squares00,10000.10001 112E.20.38562 1123.10.52483 1119.00.71484 11H.0O.SS5 1107.81.4112e1099.3£Q2 舲?100.3£.89918 1079.Q4.136

11、19 10C5.7E.0224101035.310.250711975.821.070?12733.661.5905IS694.0101-014614. 1107-015605.911L716604.8112.217SO.8112.2166W8112-21.1000NESISES1.06761,8«25EBLOGESI.BflDGEB1.062GL8803E81.05361.8401E41.06B6L 8773E81.0535i 幅的E$1.06D51.8469田1.04761.S15E81.0450E7ea4Ea1.04031.74E81.0947I.BTaZEB1.02B11.3

12、238E8L0S92228493271.03125430051.030739597S1.03073358241.03078956241.0907S35824l : ' _l'+'W(本次迭代收斂)(3)估計信息摘要匚 i mat ion Suri unaryMethodGauss-NevtonIt9rat ions18Slib it庁顯ticinsnOverate Subiterations1.222222RE.563E-7利R2-2G5E-7RPC(b)5-627E-8Object1J9E-10Object IveS86624Observations Read120O

13、bservationj Used129Observations Mi辟in*0(4)主要統(tǒng)計量SourceDFSuh afSquares：MeanSciureF ValueApproxPr > FModel22.1S08E8L2304E388875.9<.0001Error12&S858Z48165.1Corrected Tot«il1272.4648E6(5)參數(shù)信息摘要ApproxParautn&l&rEst itMteStd ErrorApproximate 95 X Cdrrf I (fence Limits(6)近似相關(guān)矩陣112.2L0

14、30718-01524.Q9990.000283579*C104J1.0301頌戈120.?1,0?12得到的擬合模型為:xt 604.8 112.2 1.0307tt t=1, 2,，128Approx Irate CorrelAtlon Matrixabc1.DODOOOO -0.S768S780.8427538-0.8759979I.ODODOOO-0.89617380,8127689 *0,8361736LDOOOOQO3、擬合效果為了直觀看出擬合效果，我們可以將原序列值和擬合值聯(lián)合作圖:proc gplot data =out;plot x*t= 1 xhat*t= 21 overl

15、ay ;symboll c=black v=star i =joi n;symbol2 c=red v=none i =join;分析：由上圖圖我們可以看出，原序列值和擬合值很接近，擬合效果較好。綜合以上的分析，我們可以選擇模型:Xt 604.8112.2 1.0307t t來擬合該序列的長期趨勢。擬合效果很不錯。8:某城市1980年1月至1995年8月每月屠宰生豬的數(shù)量（單位：頭卜）如表4 11所示（行數(shù)據(jù)），選擇適當(dāng)?shù)哪Ｐ蛿M合該序列的發(fā)展，并預(yù)測 1995年9月至1997年9月該城市的生豬屠宰量。解：具體解題過程如下：（本題代碼我是做一問寫一問的 ）ata wangbao4 8;in pu

16、t x;time=_n_;cards ;76378 71947 33873 96428 105084 95741 110647 100311 94133 10305590595 101457 76889 81291 91643 96228 102736 100264 103491 9702795240 91680 101259 109564 76892 85773 95210 93771 98202 97906100306 94089 102680 77919 93561 117062 81225 88357 106175 91922104114 109959 97880 105386 964

17、79 97580 109490 110191 90974 98981107188 94177 115097 113696 114532 120110 93607 110925 103312 120184103069 103351 111331 106161 111590 99447 101987 85333 86970 100561 89543 89265 82719 79498 74846 73819 77029 78446 86978 7587869571 75722 64182 77357 63292 59380 78332 72381 55971 6975085472 70133 79

18、125 85805 81778 86852 69069 79556 88174 6669872258 73445 76131 86082 75443 73969 78139 78646 66269 7377680034 70694 81823 75640 75540 82229 75345 77034 78589 7976975982 78074 77588 84100 97966 89051 93503 84747 74531 9190081635 89797 81022 78265 77271 85043 95418 79568 103283 9577091297 101244 11452

19、5 101139 93866 95171 100183 103926 102643 10838797077 90901 90336 88732 83759 99267 73292 78943 94399 9293790130 91055 106062 103560 104075 101783 93791 102313 82413 83534109011 96499 102430 103002 91815 99067 110067 101599 97646 10493088905 89936 106723 84307 114896 106749 87892 100506proc gplot da

20、ta =wangbao4_8;plot x*time= 1;symbol1 c=red i =join v=star;run ;proc arima data =wangbao4_8;den tify var =x;run ;1:時序圖與平穩(wěn)性判別lanoa 片!IHfl1 il1101:1訕121 ODO :Hlooi: id(30i:BKOO :BKOO '7ID0Q :RfOOfl ;snnr -41 nor -3(000 -分析：上圖是數(shù)據(jù)對應(yīng)的時序圖，從圖上曲線分析來看，數(shù)據(jù)并沒有周期性或者趨向性規(guī)律，并且每月的生豬的屠宰量大約在80000上下波動。所以由該序列圖我可以認(rèn)為它

21、是個平穩(wěn)的數(shù)列。即可以用第三章的AR莫型或MA莫型或ARM模型進(jìn)行擬合。但是為了穩(wěn)妥起見，我還需要利用自相關(guān)圖進(jìn)一步輔助識別。具體如下: 自相關(guān)圖：I he 紜AsternThe 凸RlMfi Procedure2：蛀 edn&sday, December /, ZUia 1Name of Var l«ib I e = xMean of Workine Series *0640.34St&ndard Dev i ai ion1 SOSO,89AutocorreIftt i onsI he 沖 AsternNumbter* of ObeervAl ii>ns190

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24、bijj-UaMj-T!T"s l| 1" Bl|! 1 (Bl I"0. 15G1709808323660.41800*"町!"申 qi "iffc ffii pD18198110CCC610770.346B2陽屮屮屮卅0. 1C75341 1759111890.33352丄la i 11 11ill !i 11 TT u 11 >Kl|» l«l |»0.171282IE33«aS3zI.48S4IiiIiihIbi di ajla ill"XilLb1 11 | ii 11

25、11!( nTB 1 r1 n > r«0. l?60Z29621.ij|.Bk.j|i, iLcdUiL ''T"'! '1 " !' IB0.13300714572040070.28866illliBlBi jls|丄0.18554015B127432810.1960416371189500.19242#fliSK常禎0- 190032I ?520857630.2 ZOO 1土 BIB'TS'ip 'T''TTS0.191066IS943414830

26、.173030. 193085Cova r i ftnceCo rreI at I onSI：d Error分析：由上圖可知：樣本自相關(guān)圖中的自相關(guān)系數(shù)在延遲4階之后幾乎全部落入2個標(biāo)準(zhǔn)差范圍之內(nèi)，并且向零衰減的速度還是比較快的。所以我認(rèn)為該序列是平穩(wěn)的序列。由時序圖與自相關(guān)圖可知其是平穩(wěn)序列。故可以用第三章的AR莫型或MA模型或ARM模型進(jìn)行擬合V：4Z Tecin&iclay, Deceiriber 匚口 3The 右RIMA ProcedureAutocorrelition Check for White? NoiseTqChi-Fir >LagSquareDFChiSq一

27、Autocorre 1 at ions-6311.88E<.00010,5340.53 &0.5850.4300J8S12519.OE1125010.4230.4U0,4100J4G0.394ie699.1016COOOI0.2S6O.?S70J660J920.27024634.IE24COftOI0.1790.1S20.1200.138h.1730.- -ku oo ph- 46黑 M分析：由上面數(shù)據(jù)可知：由于p值顯著小于，故可以否定原假設(shè)(H),接受備選假設(shè)(Hi)，即我可以認(rèn)為該序列是平穩(wěn)的非純隨機(jī)性序列。這樣就說明了我們可以根據(jù)歷史信息預(yù)測未來月的生豬屠宰量。Partia

28、l AutocorrelationsCorrelati on23456789012345878901234mlmm222220.53121iBi I fc.iajj. JjiXL1= J.hLpL1 <1juiiR"n nio.isvsa融k*張船|c(J.31778船K來裁耕|C-0.0e»248 »0.18293O.08B371* .O.0QB09-0.015660.1022Bmt.-0.091380.13767Ci.20160-Ci.20533-U.09154-li. I1S45軸O.OD4490.06737-9.097120.00703-0.0SSe

29、9-0.017641* ;o.OEaso串O.09E42:觀察自相關(guān)圖和偏自相關(guān)圖，從這兩圖來看，偏自相關(guān)圖是拖尾，而自相關(guān)系數(shù)是拖尾的。因而我們可以用ARM模型進(jìn)行擬合。但是為了穩(wěn)妥起見，我還需要利用計算機(jī)進(jìn)行相對最優(yōu)定階。 2 :相對最優(yōu)定階：_|identify var =x nlag =18 minic p=(0:5) q=(0:5);run ;37-lniLl理 -R S71a 7P21 -1 一 8 Bn SHIS曰H7日nm Hn1H Bn B<HDts BH EB41 了 AN ;snlrHnMR1B冃曰FFn 常ism 7nM4-茗3 了lilmJS2T1 -n - -

30、 s BRBHSHftTRM 召 ecc 斗斗ft口 7R 口 lai 517斗曰 12B H 21 - _ - :88 Hnun1le7<6 H7BB9B 曰旦b7s a -3II1 -a« w A BTBBSB?旦 Im卻 1 日nunuK 日斗 1 -1 -B -3 * SHIfils0123MBFtFrrFtMFt AAApAqMA 3MA 斗MH RKr I as- riJMZZiBZfla=i I I nii-Hii T Ab I u Vm Iar c n E ICE 川分析：從上圖可以看出，在眾多模型中，ARM模型的BIC信息量是最小的是 ARM(4, 5)，因而

31、我們接下來會采用ARM模型來進(jìn)行擬合分析，這和我們?nèi)斯ゎA(yù)測的相吻合。3 :參數(shù)估計：estimate p=4 q=5;run;具體輸出結(jié)果如下圖The ARIMA Procedures 0123451234ParameterEstimateStandardErrort V&lueApproxPr > ItlMU76426.57064.410.82<.0001MAI ,1D.844110.239053.530.0005MAI, 2-D.480980.23838-2.020.0451MAI, 3-D.42 4420.13931-2.130.0346MAU 4D.663130.0

32、95616.94<.0001MAI, 5-1.204930.11108-1.840.0667AR1J1.214570.237495.11<.0001ARI, 2-D.702280.35137-2.000.0472ARI, 3D.049850.308870.160.8720ARI, 4D.412430.189542.180.0308Const&nt 1Est in&te1944.097Variance 1Est inate89164617Std ErrorEstimate9958.143AIC4004.756SBC4037.12Number ofResiduals18

33、8* AIC and SBC donot i nclude1determ inant.-»ondi*t lonal Least Squares Est i mat i onDorre Iat ions of Parameter Est imatesParameterNUMA1,1NA1,2MAU3MAI, 4MU1.0000.033-0.0460.012-0.036NA1J0.0331.0000.9940.754-0.09?MAI, 2-0.046-0.8341.000-0.8651.0000.366MAI, 30.0120.754-0.865-0.812MAI, 4-0.036-0

34、.0970.366-0.6121.000MAh 5-0.021-0.7910.658-0.3C4-0.282陽1,1-0.0020.950-0.8750.754-0.182ARI, 2-0.016-0.8950.934-0.8190.282ARI, 30.0070.786-0.8760.897-0.400ARI, 4-0.024-0.8010.798-0.8750.383Correlations of Parameter EstimatesParameterMAI,5ARI JARI, 2ARI,3ARU4MU-0.021-0.0020.0160.007-0.024MAI ,1-0.7910.

35、950-0.9950.786-o.eoiMAI, 20.G58-0.8750.934-0.8760.798MAI, 3-0.3640.754-0.8130.887-0.875MA1,4-0.282-0.1920.282-0.4000.383MAI, 51.000-0.7170.541-0.5190.568AR1J>0.7171.000-0.9510.840-0.844巾冃站皤 和狀刖ltf：« Wednesday, UeGemLer匚典用 $The AFilMA Protedu reCorrcIotiuns of ParainetEstimatesE0.00C叩01-O.OU8

36、o.do?：0即-n+0230.0171217.813山汕如-0.1QS-0.Q31Q期-02&0.0251823.9790.0044-0.0730.0280,920-0.0840.0582431.U150.00640-0270,020-0.063O-OCS0X603040,3521O.OOC7-0-D25O.OU-0.143-a.09t0.0373651.13270.00330吐40.0620-13Ba.0870.041Model forvar ialbl eXEst imated4；ooooo-_o卩arameterMAL5AFl1ARI ,2ARb3ARI ,4ARI, 2).6

37、41-0.9511.000-0J540.857AR1J-(J.E1S0.940-0.344-0,9841.000-0.942ARI, 4(1.5 開0.057-0.9421.000Autocorrelalion Check of ResiduaIsToChi-Pr >La<Squa reDFChiSq-Autocorrel-Titions Ajtorressive FictorsFactor 1:-1.2M57 B>KiK(1) + 3.7C2I8 日刪(E) - 9.04365B*H3) - 0.41243 BM該輸出形式等價于Xt=+故該模型為：Xt=y +( 0( B)

38、 / $ (B) ? t = 序列預(yù)測(1995年9月至1997年9月)forecast lead =24 id =time out =wangbaoyc;run;The SflS Syste 18:43 Wednesday, December 7* 2013 17The ARINA ProcedureForecasts for variable 親1699631&.80849958,14337C79B.3018115833.5U5E13096460 J48210613.50875646.Z841117274.00431919355191065(.6497703.0749H帥$2 號4719297636.9954119137874286.0292120907.9C261S39678BJ8B91即86.8057