应用时间序列分析第章答案

1、河南大学：姓名：汪宝班级:七班学号:1122314451 班级序号:685:我国 1949 年2008 年年末人口总数（单位:万人）序列如表 4-8 所示（行数据）.选择适当的模型拟合该序列的长期数据，并作 5 期预测。解：具体解题过程如下：（本题代码我是做一问写一问的）1:观察时序图：datawangbao4_5;inputx;time=1949+_n_-1;cards;5416755196563005748258796602666146562828646536599467207662076585967295691727049972538745427636878534806718299285

2、229871778921190859924209371794974962599754298705100072101654103008104357105851107507109300111026112704114333115823117171118517119850121121122389123626124761125786126743127627128453129227129988130756131448132129132802;procgplotdata=wangbao4_5;plotx*time=1;symbol1c=blackv=stari=join;run;分析:通过时序图，我可以发现

3、我国 1949 年2008 年年末人口总数(随时间的变化呈现出线性变化.故此时我可以用线性模型拟合序列的发展.Xt=a+bt+Itt=1,2,3,-,60E(It)=0,var(It尸2其中，It为随机波动；Xt=a+b 就是消除随机波动的影响之后该序列的长期趋势。2:进行线性模型拟合：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册383AIC1091.71114R Re eg gr re es ss sR R- -S Sq qL Li ia ar re e0.9921Tola1R-Square0.99S1Durbin-Watson0.07245:结论所以本题拟合的模型为: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：由上面输出结果可知：两个参数的p值明显小于0.05，即这两个参数都是具有显著非零,4:模型检验又因为RegressR-square=totalR-square=0.9931,即拟合度达到99.31%所以用这个模型拟合的非常好。6:作 5 期预测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刘M M2 20 01 10 0司2 21 16:爱荷华州 1948-1979 年非农产品季度收入数据如表 49 所示（行数据），选择适当的模型拟合该序列的长期趋势。解：具体做题过程如下：（本题代码我是做一问写一问的）1、绘制时序图datawangbao4_6;inputx;time=_n_;cards;60160462062664164264565568267869270773675376377577578379481382382682983183083885487288290391993

8、792796297599510011013102110281027104810701095111311431154117311781183120512081209122312381245125812781294131413231336135513771416143014551480151415451589163416691715176018121809182818711892194619832013204520482097214021712208227223112349236224422479252825712634268427902890296430853159323733583489358

9、836243719382139344028412942054349446345984725482749395067523154085492565358285965procgplotdata=wangbao4_6;plotx*time;symbolc=blackv=stari=join;run;分析;可知时序图显示该序列有明显的曲线递增趋势。尝试使用修正指数型模型进行迭代拟合:xtabct+?t,t=1,2,，1282、拟合模型procnlinmethod=gauss;modelx=a+b*c*time;parametersa=0.1b=0.1c=1.1;outputpredicted=xhat

10、out=out;run;NLIN 过程输出以下六方面信息：(1)迭代过程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：上图是数据对应的时序图，从图上曲线分析来看，数据并没有周期性或者趋向性规律，并且每月的生猪的屠宰量大约在 80000 上下波动。所以由该序列图我可以认为它是个平稳的数列。即可以用第三章的 AR 模型或 MA 莫型或 ARMA 莫型进行拟合。但是为了稳妥起见，我还需要利用自相关图进一步辅助识别。具体如下：

13、自相关图：IheSystem1工二42Wednesday,Decemberf*WUld7heARhlAPnocedureNameofVaribIs=xMeanofWorkins:Series30640.34StandardDeviation1380,69Nunhb&rofDteervatione169Autoccirnelations分析：由上图可知：样本自相关图中的自相关系数在延迟 4 阶之后几乎全部落入 2 个标准差范围之内，并且向零衰减的速度还是比较快的。所以我认为该序列是平稳的序列。由时序图与自相关图可知其是平稳序列。故可以用第三章的 AR 模型或 MA 莫型或 ARMA 莫型

14、进行拟合Ihe占需Asternm加版由上Lecetiiber3TheARIMAProcedureAutoccrrelationCheckforWhiteNoise序列是平稳的非纯随机性序列。这样就说明了我们可以根据历史信息预测未来月的生猪屠宰量。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/市中帮案木满/林1Vill1liIMHIHHihaillala币不kiT15小那 E 灯0管开0.072982IIiiIii|BI1BB( (Br|iarini|tBrg0-095204_京强珑血求肥求用米求出空0.11DOBS.球小邛世|3床跟片中0.126

16、525审刑邦中时1*|1柞中出0.1S3136.T1(111rTBTB1rH0.142252雷21附小巡指gU_149956出来濯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：雅米木帮出U.1，叩26*来濯I*.0.193007季米邛和榴K.0,19654C事聘咏.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：由上面数据可知：由于p 值显著小于 0.05,故可以否定原假设（%）,接受备选假设（Hi）,即我可以认为该AutocorrelaiiansPartialflutocornelBitions分析：观察自相关图和偏自相关图，从这两图来看，偏自相关图是拖尾，而自相关系数是拖尾的。因而我们可以用 ARMA 莫型进行拟合。但是为了稳妥起见，我还需要利用计算机进行相对最优定阶。2:相对最优定阶：identifyv

18、ar=xnlag=18minicp=(0:5)q=(0:5);run;ThvnijmImfpr*naticnnrItori分析：从上图可以看出，在众多模型中，ARMA 莫型的 BIC 信息量是最小的是采用 ARMA 莫型来进行拟合分析，这和我们人工预测的相吻合。3:参数估计：estimatep=4q=5;run;具体输出结果如下图：-199765432I0IZ34567891LasCarrelion0.59421卅*用巾0.29098UJ曲-0.063U*带*格尔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?库.1 1ntntUO45678UO4567890123456799012349012345679901234,1,11 1,1,1JIiJIiJIJI1 1JI1JI1,n/-22OL,n/-22OL后(旧旧HlHls s71lniu&71lniu&MINIMINI- -1 1二二君6BnBH1SBnBH1SBnIBRDB B4 4日口?3 3d日R R

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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国启7OO8U17OO8U1cc9-_9cc9-_9_9_933-firo-firoAvAvn-_u_u-uin-_u_u-ui4 411II1111111-2

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26、117274.0043119202.8247120S87.9B2512042E.5986119764.7408119864.1702121333.3182122675.41101E2976.3476计2513.2596122307.8157122906.2591侬8菊用跷124324.4716124186.41G7128388.7236124107.K94B124665.3247izb108,zees1E5166.0504125000.8423124982,777812524e.864G【he$福$k*巾5；43Wednesday,i,ZUS6TheARIMAProcedureCorrelationsofP社r。帧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)-