應(yīng)用時(shí)間序列分析第4章答案

1、河南大學(xué):姓名：汪寶班級(jí):七班學(xué)號(hào)：51班級(jí)序號(hào)：685：我國(guó)1949年一2008年年末人口總數(shù)（單位：萬(wàn)人）序列如表4一8所示（行數(shù)據(jù)）.選擇適當(dāng)?shù)哪Ｐ蛿M合該序列的長(zhǎng) 期數(shù)據(jù)，并作5期預(yù)測(cè)。解：具體解題過(guò)程如下：（本題代碼我是做一問(wèn)寫(xiě)一問(wèn)的）1：觀察時(shí)序圖：data wangbao4_5；input x；time 二1949+_n_T；cards；5416755196563005748258796602666146562828646536599467207662076585967295691727049972538745427636878534806718299285229871771000

2、721016541030081043571058511075071093001110261127041143331158231171711185171198501211211223891236261247611257861267431276271284531292271299881307561314481321291328028921!90859924209371794974962599754298705proc gplot data=wangbao4_5； plot x*time=l；symbol 1 c=black v=star i=join；分析:通過(guò)時(shí)序圖我可以發(fā)現(xiàn)我國(guó)1949年一20

3、08年年末人口總數(shù)（隨時(shí)間的變化呈現(xiàn)出線性變化故此時(shí)我可以 用線性模型擬合序列的發(fā)展.f Xt=a+bt+It t=l,2.3. ，60lE(It)=0.var(Il) = o2其中，h為隨機(jī)波動(dòng)；Xt=a+b就是消除隨機(jī)波動(dòng)的影響之后該序列的長(zhǎng)期趨勢(shì)。2：進(jìn)行線性模型擬合：proc autoreg data=wangbao4_5；model x二time； output out=out p=wangbao4_5_cup；run;proc gplot data=out；plot x*time=l wangbao4_5_cup*time=2/overlay ； symbol2 c=red v=n

4、one i=join w=2 1=3;run;The SAS Systern15:28 Wednesday, December 7, 2013The AUTOREG ProcedureDependent VariablexOrdinary Least Squares Est imatesSSE262296607DFE58MSE4522355Root MSE2127SBC1095.89983AIC1091.71114Regress R-Square0.9931Tota1 R-Square0.9931Durbi rr Watson0.0724VariableDFEstimateStandardEr

5、rort ValueApproxPr |t|Intercept1-277082831366-88.340001time1144915.$52891.38 FModel22.4608E81.2304E838875.9 0001Error1253956243165.0Corrected Total1272.4648E8得到的擬合模型為：“ =6048 + 1122xl0307+（5）參數(shù)信息摘要ParameterEst imateApproxStd ErrorApproximate 95X Conf idenee Limitsa604.813.0152579.0630.5b112.24.09991

6、04.1120.3c1.03070.0002881.03011.0312t=h 2,，128（6）近似相關(guān)矩陣Approxirnate Correlation Ms.trizabca1.0000000-0.87589790.8427539b-0.87589791.0000000 0.9851736c0.8427538-0.89517361.00000003、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=l xhat*t=2/overlay； symbol 1 c=black v=star i=join； symbol

7、2 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:兀=604.8 + 112.2xl.0307z來(lái)擬合該序列的長(zhǎng)期趨勢(shì)。擬合效果很不錯(cuò)。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）如表411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(cè)1995年9月至1997年9月該城市的生豬屠宰量。解：具體解題過(guò)程如下：（本題代碼我是做一問(wèn)寫(xiě)一問(wèn)的）ata wangbao4_8；input x；time=_n_；cards；76378 71947 33873 96428 1050

8、84 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 96479 97580 109490 110191 90974 98981107188 94177 1

9、15097 113696 114532 120110 93607 110925 103312 120184103069 103351 111331 106161 111590 99447 101987 85333 86970 1005618954389265827197949874846738197702978446869787587869571757226418277357632925938078332723815597169750854727013379125858058177886852690697955688174666987225873445761318608275443739697

10、813978646662697377680034706948182375640755408222975345770347858979769759827807477588841009796689051935038474774531919008163589797810227826577271850439541879568103283 9577091297 101244 114525 101139 93866 95171 100183 103926 102643 10838797077 90901 90336 88732 83759 99267 73292 78943 94399 929379013

11、0 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 data=wangbao4_8；plot x*t ime=l；symbol 1 c=red i=join v=star；run；proc arima dat a=wangbao4_8；identify var=x； run;1

12、：時(shí)序圖與平穩(wěn)性判別分析：上圖是數(shù)據(jù)對(duì)應(yīng)的時(shí)序圖，從圖上曲線分析來(lái)看，數(shù)據(jù)并沒(méi)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(dòng)。所以由該序列圖我可以認(rèn)為它是個(gè)平穩(wěn)的數(shù)列。即可以用第三章的AR模型或血模型 或ARMA模型進(jìn)行擬合。但是為了穩(wěn)妥起見(jiàn)，我還需要利用自相關(guān)圖進(jìn)一步輔助識(shí)別。具體如下：自相關(guān)圖：0Covari enceIhe SystemThe ARIMA ProcedureName of Variable = xMean of WorkiSeriesStandard Dev i at i onNumbor of Obsorvat ionsCor re I at

13、i on1 Wednesday, December 匚 ZU13 190640.3413888.89188Autocorre Iat i ons冰if!冰冰1!冰SfS冰昭SfS冰冰-fj冰5冰冰:f!nT*PsTep EC你山 wStd Error22456?890123456781923011961146229861031677511128090188299461493898788887353938157039679781236806326686665197775911189 93635921 57138875 57204007 51274826 37118950 52085763 343

14、414931.00000 0.59421 0.53482 0.58480 0.43024 0.48573 0.46000 0.42286 0.41359 0.41800 0.94552 0.39352 0.48541 0.29621 0.29655 0.26581 0.19242 0.27001 0.17803w 山 vi*cjiijif Ji fjir jifjiiTifp |pTp nT*PsTep仔nTvT*sTep仔nT*z*tr zr*rT*溶出冰水nChiSq Autocorrelations6311.936.00010.5940-5350.5850-4300.4860.46012

15、519.0612.00010.4230.4140.4180-3480.3940.48518599.1818.00010.2380.29?0.2680-1920.2700.17824634.1624r w n* n mm20.28093ib illiln di T, 3U318H*4-0.06324,He050.1829360.03697* .?0.086898-0.0155690.10226腳.10-0.09136:卿110.1376?*120.2016013-0.2033314-0.09154.w15-0.11645160.00449170.0573718-0.09712190.007892

16、0-0.03669:卅210.01754220.04719出230.05890240.03542$ .分析：觀察自相關(guān)圖和偏自相關(guān)圖，從這兩圖來(lái)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ARMA模型進(jìn)行擬合。但是為了穩(wěn)妥起見(jiàn)，我還需要利用計(jì)算機(jī)進(jìn)行相對(duì)最優(yōu)定階。2:相對(duì)最優(yōu)定階：identify var=x nlag=18 minic p=（0：5） q=（0：5）;run;17： 4-2 WrjcJmcwdiwv r- 7 .20 1 31 6Mini mumI nf o rmo. t 1 on C r 1 E er- 1 on0K0MA OMA 1MA 2MA 3MA A

17、THc- SAS Svwt -mThe? AR TMA 戶 LGc=E?zh_i 廠dMA 6RRRRRRO123AD7700289BBO833729B4 -1 -1 -8 -8 . BB1B1818-89HH118.3704 18-37BE8 18.17E77 18.1 773/1 8 1 8E 1 6987B986800780181 BTelzB321 8 8 8 8 nB9BB7DO3BB8978B337OO3D173211 - 8 HBBesl1 B _ 786HO18-28AOB1 8.22S 1 718.1 BOBS18.176D 8 S S 8038888188B12D9 eeE

18、sl 37100VEE7137221 -1 -8 -E- ro r aar I oa modal :ARMini muirrt Tab I a Wa. I ua 二 BIC=分析：從上圖可以看出，在眾多模型中，八RMA模型的BIC信息量是最小的是ARMA （4, 5）,因而我們接下來(lái)會(huì)采用 ARMA模型來(lái)進(jìn)行擬合分析，這和我們?nèi)斯ゎA(yù)測(cè)的相吻合。3：參數(shù)估計(jì)：estimate p=4 q=5；run；具體輸出結(jié)果如下圖：The ARIMA ProcedureConditicml Least Squares Est irnat ionParameterEst irftateStandardErro

19、rt Va.lueApproxPr |t|LagMU76426.57064.410.82.00010NA1,10.844110.239053.530.00051MAI, 2-0.480980.23838-2.020.04512MAI, 3-0.424420.18931-2.130.03463MAI, 40.663130.095616.94.00014NA1,5-0.204930.11109-1.840.06675AR1,11.214570.237495.11ChiSq_ 丄 _ -Hui.uuur r e iau i ui80.000.0001-0.0090.0080.033a.0290.01

20、7-0.0341217.8130.00050.105-0.031-0.0260.02G0.2G41823.979a.0044-0.0730.0280.020-a.0840.053-0.1082431.14150.0084-0.0270.028-0.0630.0050.0600.1543040.3521a.0067-0.0290.014-0.043-0.0960.037-0.16G3651.1927a.00330.0840.062-0.136a.0970.0410.080Mode I for variable xEstimated Mean 76428.4?Autoregressive Fa.c

21、torsFactor 1：1 - 1.21457 B榊（1） + 0.70228 B榊（2） - 0.04985 B榊（3） - 0.41243 B刪（4）該輸出形式等價(jià)于XL+故該模型為：“+（）（B）/e（B）e t=（3）序列預(yù)測(cè)（1995年9月至1997年9月） forecast lead=24 id=time out=wangbaoyc； run；The SAS System 18:43 Wednesday, December 7, 2013 17The ARIMA ProcedureObsForecastStd Error95X Conf idenee Limits18996315

22、.90349958.143376798.3013115833.505618086460.148210618.50975646.2341117274.004319196995.951810860.84975709.0789118282.824713287636.985411813.87874286.0282120987.962519396736.895912086.80573047.1929120426.598813495486.902012386.88071208.0631118764.740819594853.762512755.49369853.454?119854.07021369518

23、2.133413342.99163030.3507121333.916219795592.065013818.288608.7189122675.411013895312.250414115.92167645.5530122978.947813994439.755414323.48066366.2512122513.259620093732.426114579.44685157.2384122307.615720193641.183314931.42564376.1274122906.239120283868.209415294.90063890.7559123845.862920393812.923815567.40263301.3760124324.471620493290.0690157G3