應(yīng)用時(shí)間序列分析第章答案

1、河南大學(xué)：姓名：汪寶班級(jí):七班學(xué)號(hào):1122314451 班級(jí)序號(hào):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(zhǎng)期數(shù)據(jù)，并作 5 期預(yù)測(cè)。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(shí)序圖：datawangbao4_5;inputx;time=1949+_n_-1;cards;5416755196563005748258796602666146562828646536599467207662076585967295691727049972538745427636878534806718299285

2、229871778921190859924209371794974962599754298705100072101654103008104357105851107507109300111026112704114333115823117171118517119850121121122389123626124761125786126743127627128453129227129988130756131448132129132802;procgplotdata=wangbao4_5;plotx*time=1;symbol1c=blackv=stari=join;run;分析:通過時(shí)序圖，我可以發(fā)現(xiàn)

3、我國 1949 年2008 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.Xt=a+bt+Itt=1,2,3,-,60E(It)=0,var(It尸2其中，It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：procautoregdata=wangbao4_5;modelx=time;outputout=outp=wangbao4_5_cup;run;procgplotdata=out;plotx*time=1wangbao4_5_cup*time=2/overlaysymbol2c=redv=nonei=join

4、w=2l=3;run15：Wednesday,DeceinMr7T20131TheAUTOREGProcedureDependentVariableOrdinaryLeastSquaresEstinatesSSE262286607DFt58MSE4522356RootMSE2127SBC35冊(cè)383AIC1091.71114R Re eg gr re es ss sR R- -S Sq qL Li ia ar re e0.9921Tola1R-Square0.99S1Durbin-Watson0.07245:結(jié)論所以本題擬合的模型為:Xt=-2770828+1449t+Itt=1,2,3,-,

5、60E(It)=0,var(It)=2TheSASSystemVariableDFEstimateIntercept1-2770828time11449StsirdardApprcxErrortValuePr|t|S13S-88.8440001凡852$E 面心。刈分析：由上面輸出結(jié)果可知：兩個(gè)參數(shù)的p值明顯小于0.05，即這兩個(gè)參數(shù)都是具有顯著非零,4:模型檢驗(yàn)又因?yàn)镽egressR-square=totalR-square=0.9931,即擬合度達(dá)到99.31%所以用這個(gè)模型擬合的非常好。6:作 5 期預(yù)測(cè)procforecastdata=wangbao4_5method=stepartr

6、end=2lead=5out=outoutfulloutest=est;idt;varx;procgplotdata=out;plotx*time=_type_/href=2008;symbol1symbol2i=nonei=joinv=starv=nonec=black;c=red;symbol3i=joinv=nonec=blackl=2;symbol4i=joinv=nonec=blackl=2;run;X XI I5 5I IM MD DC CI I4 4M MD DC CISDONI I2 2M MD DI IO OM MD DC C9 9W WD D（S SM MD DI I7 7

7、MME EM MD DC CIMM1 1腌U U）1 13 30 0I IW WO OH HO OD D劉M M2 20 01 10 0司2 21 16:愛荷華州 1948-1979 年非農(nóng)產(chǎn)品季度收入數(shù)據(jù)如表 49 所示（行數(shù)據(jù)），選擇適當(dāng)?shù)哪Ｐ蛿M合該序列的長(zhǎng)期趨勢(shì)。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(shí)序圖datawangbao4_6;inputx;time=_n_;cards;60160462062664164264565568267869270773675376377577578379481382382682983183083885487288290391993

8、792796297599510011013102110281027104810701095111311431154117311781183120512081209122312381245125812781294131413231336135513771416143014551480151415451589163416691715176018121809182818711892194619832013204520482097214021712208227223112349236224422479252825712634268427902890296430853159323733583489358

9、836243719382139344028412942054349446345984725482749395067523154085492565358285965procgplotdata=wangbao4_6;plotx*time;symbolc=blackv=stari=join;run;分析;可知時(shí)序圖顯示該序列有明顯的曲線遞增趨勢(shì)。嘗試使用修正指數(shù)型模型進(jìn)行迭代擬合:xtabct+?t,t=1,2,，1282、擬合模型procnlinmethod=gauss;modelx=a+b*c*time;parametersa=0.1b=0.1c=1.1;outputpredicted=xhat

10、out=out;run;NLIN 過程輸出以下六方面信息：(1)迭代過程lieratIvePhaseR Re er r金bc cS Su um mo o S Sq qu ua ar re es s00.10080.10001.10009.521BEJB1112E-20.39581.06781L8825E821123.10.52481JG隔1.德口5E881119JI0.71481.06251L8S03E841114,0，麻145361L8S01EC511叱E1,41111.05661L8778E8610施81 Q53511,就就Efi71090.32.69911.050510489E8；810

11、79.04.13611,0476LS15E8910CE.75.6224I.Q4501L7E34E8101035.3110.25071.04031.7+E811975.821.07871.05471.67920812796.6El.5305l.0S11L3238E8ISG34.LI101.8I.0S922284992714614.1107.01.031254300516GOS.9111.71.030785597516604.8112.21.030783562J17G0FModel?2.46OSES1&04EB3BB7S.9 j ji i：MIDM;n no on n；* *1 10 00

12、 00 0- -s st to oo oa a: :一0 0w wm mS SO O如5 51 1即7 70 0B Bl l9 9D D1 11 10 0H HO O1 12 20 0情0 01 1 1 15 50 0H Hi iO O1 1? ?t t) )l lO OI IS SO O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(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 MA 莫型或 ARMA 莫型進(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(shí)別。具體如下：

13、自相關(guān)圖：IheSystem1工二42Wednesday,Decemberf*WUld7heARhlAPnocedureNameofVaribIs=xMeanofWorkins:Series30640.34StandardDeviation1380,69Nunhb&rofDteervatione169Autoccirnelations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(gè)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(shí)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 模型或 MA 莫型或 ARMA 莫型

14、進(jìn)行擬合Ihe占需Asternm加版由上Lecetiiber3TheARIMAProcedureAutoccrrelationCheckforWhiteNoise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(cè)未來月的生豬屠宰量。L.gCovarinceCorra1at.ion-1ssj7e01SE301186i.oocion11146223BE；0.5942121O31S77510.534022iisaoaoieO.Efid.Dri4S29848140.430E4S33C307000.4S5786E37353933.46000711.4228607970123BH,4135S

15、9eoGazBBe0.41S00106CC510770.94EE311759111893935212yatiauaziU.413bqi19571306750.29S22S9EE155127482E163711S9500.1924217520357630.2700I10343414S30.173031ft布瑞小小/市中幫案木滿/林1Vill1liIMHIHHihaillala幣不kiT15小那 E 燈0管開0.072982IIiiIii|BI1BB( (Br|iarini|tBrg0-095204_京強(qiáng)瓏血求肥求用米求出空0.11DOBS.球小邛世|3床跟片中0.126

16、525審刑邦中時(shí)1*|1柞中出0.1S3136.T1(111rTBTB1rH0.142252雷21附小巡指gU_149956出來濯M席海噩棒0,166170水踹邛制灰踹耀0.16139151陋串出9棚WQ.1C7504和H幅0-171282富*技和1：雅米木幫出U.1，叩26*來濯I*.0.193007季米邛和榴K.0,19654C事聘詠.0.1390440.190032端瞄呻世ts.0.1910660.193086ToLagChiSquareOFPr)ChiSqE311.386.o( (m0.53412519班12J0D10.42318599JG18M0.2能244.1624：.00010.

17、179。展0.58504300.4860.46D0.4UD.4180.U60.3841485O.?97。施0J320.2700.1780.182&J200J3fl0.1730.186分析：由上面數(shù)據(jù)可知：由于p 值顯著小于 0.05,故可以否定原假設(shè)（%）,接受備選假設(shè)（Hi）,即我可以認(rèn)為該AutocorrelaiiansPartialflutocornelBitions分析：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 ARMA 莫型進(jìn)行擬合。但是為了穩(wěn)妥起見，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：identifyv

18、ar=xnlag=18minicp=(0:5)q=(0:5);run;ThvnijmImfpr*naticnnrItori分析：從上圖可以看出，在眾多模型中，ARMA 莫型的 BIC 信息量是最小的是采用 ARMA 莫型來進(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)：estimatep=4q=5;run;具體輸出結(jié)果如下圖：-199765432I0IZ34567891LasCarrelion0.59421卅*用巾0.29098UJ曲-0.063U*帶*格爾iC.18283HtMdt0.03697申.0.08689出明0.01556D.1022C*-0.09136津出a0.1378?由耕

19、0.20160-C.20333-0.09154-0,I1B45榔0.004490.05737出.-0.097120.007891：-0.08069,H1-C.017D40.04719出：0.0&090出.0.0854?庫.1 1ntntUO45678UO4567890123456799012349012345679901234,1,11 1,1,1JIiJIiJIJI1 1JI1JI1,n/-22OL,n/-22OL后(舊舊HlHls s71lniu&71lniu&MINIMINI- -1 1二二君6BnBH1SBnBH1SBnIBRDB B4 4日口?3 3d日R R

20、SE4SE41 1日22111o22111o1 1BHBBSaBHBBSa. .illills sGnBR/HGnBR/HsBBHsBBHg g7003&17003&17 7H2H21111. .- -n n V V- -nAnAMlMlBR7B3SBR7B3SBn44bnBn44bn-B-B7-4-4I IS S工日HNl:-MsB_HBH11nilnil14S74614S746H了b后才fl日rlrly y丁FFSFFSB-HillB-Hill- -H H-BVBB83-BVBB8376197619-41-417丁口*UNnlm口SM-S72SM-S72S S日4 41 1

21、- -1-1-B-s-B-s-SHISHInlsnlsnlzssHRRnlzsIt|LaeMU7S42E.570G4.410.fi?G90D11MAIJ0.844110.238953.680.90D51仙1,2-0.480880J3638-2.C20.14512NAI,3-0.424?0J3831-M3( (1.13463MAIH0.G8313O.095G1C.54fl65LOO!-D.61?明，4-0.036-0.0970.366-0.61Z1.000Ml,5-0.021-0.791口5g-0.36-0.26?軀1J-o.oo?U.脂。-0.S750.7540,19?陽，2-0,016-0.

22、S950.934-0.8190.202NR14蚓.40,007-0.0240.7S6-0.87CQ.SS7-0.9(11OJ9-O.fi75-k4co0.3Q3CorrelationsofParameterEatimatesParameterL1AU5幅1,1ARL2AAUARL4MU-0.0210.002-0.018D.0?-0.024蜘-0.7910.350-0.895QJ86-OJ01MAU9.580-9760.934-0.S7EMR,3MAI,4-9J640e?54-U.8130.897-04875-0.1920.282-0.1000.393MAL6ARIJi.ooa-0.717Q.6

23、41-0.513-0,71?1.D0D-0,S510.84Q-Q,044ObsForecus-tStdError96315.90349958.143396460.148210619.SOS96995/51。1O0CO.G4987536.9S5411913.3783B796.995S12088.60536496.802C12386.88094868.762512765.4933S182.13341334Z.99195592,加19010.2009531?.2504U115.32194433.755414323.43。83732.42811457334693G41,1+531,42593868.2

24、094152S4.90083812.923816567.40293290.069(1157G9.22232567.53931E9G4.9B192889.50451B19B.22132386,84&516468.E2792390.469918698.06082093.336716878.68991615.72S417033.53531253.94531720B.S04golgol史2452456 678go123478go1234國啟7OO8U17OO8U1cc9-_9cc9-_9_9_933-firo-firoAvAvn-_u_u-uin-_u_u-ui4 411II1111111-2

25、11II1111111-22 2222221291133,3。死1740CJ1G95XConfidance7B790.3Q1375646.294175709.0769?420fi.O?8273047.192971209JG81E98b3.4S4763030.3507600.718867645.5530663祥.251265157,238464376.127463690.755963301.376062394.721361836.951960831.974460135.78S359B72,S72958021.S2?S58230.610557525,114057017.9419115033.5O5

26、117274.0043119202.8247120S87.9B2512042E.5986119764.7408119864.1702121333.3182122675.41101E2976.3476計(jì)2513.2596122307.8157122906.2591儂8菊用蹺124324.4716124186.41G7128388.7236124107.K94B124665.3247izb108,zees1E5166.0504125000.8423124982,777812524e.864G【he$福$k*巾5；43Wednesday,i,ZUS6TheARIMAProcedureCorrelationsofP社r。幀terEstin) )3iteaRarameterMAU5ARIJARH2ARlf4峭1J口.641-0.9511.000-0.334O.fi57同，9-0,5190.940-0.954L010-0.942期1,4U.56S-0.84-40.057-0.3421.000AutoccrrelaiIanChecl( (ofResiduaIsToChi-PrLacSiusreDFChiSqflutocorrelationsftutorepressliveFactorsFactor1：1-L21457+0.70228Q.04985B*(3)-