SAS時間序列分析

1、試驗六時間序列分析一、 實(shí)驗?zāi)康模簩W(xué)習(xí)時間序列數(shù)據(jù)分析技巧，了解ARIMA模型。二、實(shí)驗內(nèi)容：47年1季度到96年3季度美國國民生產(chǎn)總值的季度數(shù)據(jù)。三、實(shí)驗要求：寫出分析報告。四、實(shí)驗軟件：SAS系統(tǒng)。一般實(shí)驗流程：1）平穩(wěn)性檢驗方法：時序圖、自相關(guān)系數(shù)和自相關(guān)圖檢驗、單位根檢驗2）模型識別方法：利用自相關(guān)系數(shù)、偏相關(guān)系數(shù)圖進(jìn)行模型識別；計算擴(kuò)展的樣本自相關(guān)函數(shù)并利用其估計值進(jìn)行模型識別;利用最小信息準(zhǔn)則進(jìn)行模型識別；利用典型相關(guān)系數(shù)平方估計值進(jìn)行模型識別；注：ACF圖和PACE®的模型識別自相關(guān)系數(shù)圖（ACF圖）偏相關(guān)系數(shù)圖（PACES）模型識別結(jié)果q階截尾拖尾F MA(q)拖尾P

2、階截尾AR(p)拖尾拖尾ARMA3）模型的參數(shù)估計及檢驗檢驗擬合性、參數(shù)估計顯著性、殘差項無自相關(guān)性（殘差項白噪聲檢驗）4）模型的預(yù)測例題實(shí)驗步驟：1）建立數(shù)據(jù)集data exp3;input gnp;date=intnx（ 'qtr' , '1jan47'd,_n_- 1）;format date yyqc.;cards ;227.8 231.7 236.1 246.3 252.6 259.9 266.8 268.1 263.0259.5261.2258.9269.6279.3296.9308.4323.2331.1337.9342.3345.3345.935

3、1.7364.2371.0374.5373.7368.7417.8368.4368.7373.4381.9394.8403.1411.4420.5426.0430.8439.2448.1450.1457.2451.7444.4448.6461.8475.0499.0512.0512.5516.9530.3529.2532.2 527.3 531.8 542.4 553.2 566.3 579.0 586.9594.1597.7606.8615.3628.2637.5654.5663.4674.3679.9701.2713.9730.4752.6775.6785.2798.6812.5822.2

4、828.2844.7861.2886.5910.8926.0943.6966.3979.9999.3 1008.0 1020.3 1035.7 1053.8 1058.4 1104.2 1124.91144.41158.8 1198.5 1231.8 1256.7 1297.0 1347.9 1379.4 1404.41449.71463.9 1496.8 1526.4 1563.2 1571.3 1608.3 1670.6 1725.31783.51814.0 1847.9 1899.0 1954.5 2026.4 2088.7 2120.4 2166.82293.72356.2 2437.

5、0 2491.4 2552.9 2629.7 2687.5 2761.7 2756.12818.82941.5 3076.6 3105.4 3197.7 3222.8 3221.0 3270.3 3287.83323.83388.2 3501.0 3596.8 3700.3 3824.4 3911.3 3975.6 4022.74100.44158.7 4238.8 4306.2 4376.6 4399.4 4455.8 4508.5 4573.14655.54731.4 4845.2 4914.5 5013.7 5105.3 5217.1 5329.2 5423.95501.35557.0

6、5681.4 5767.8 5796.8 5813.6 5849.0 5904.5 5959.46016.66138.3 6212.2 6281.1 6390.5 6458.4 6512.3 6584.8 6684.56773.66876.3 6977.6 7062.2 7140.5 7202.4 7293.4 7344.3 7426.67537.57593.6；run ;注：Intnx函數(shù)按間隔遞增日期，Intnx函數(shù)計算某個區(qū)間經(jīng)過若干區(qū)間間 隔之后的間隔的開始日期或日期時間值，其中開始間隔內(nèi)的一個日期或 日期時間值給出。Intnx函數(shù)的格式如下：Intnx(interval,from,n

7、)2、2）繪序列圖，輸入如下程序:proc gplot data=exp3;symbol1 i=spline;plot gnp*date=1;run;-laJj曹 GBAPHI T0HX.弟EG. GPU1Tdata lexp;set exp3;lgnp=log(gnp);run;4、繪變換后序列圖，輸入如下程序:proc gplot data=lexp;symbol2 i=spline c=red;plot lgnp*date=2;run;2000:11945:11950:11956:119S0:119GB:11970:1197&:11980:11986:11930:11995:1d

8、ate5、提交程序，到 graph窗口中觀察變換后的序列圖，可以看出它成直線上升趨勢。對序列 做初步識別，輸入如下程序：proc arima data=lexp;identify var=lgnp nlag=12;run;運(yùn)行結(jié)果如下：The SAS System 21:51 Tuesday, December S, £011The ARINA ProcedureNus of Variable = ImpMean of Working Series7JS4182Standard Deviation*086036Number of Observations199Fig1.Descrip

9、tion statistics0 1 2 34 6 G 18 9 10 1112Autocorrelai ionsLagCovarlanceCorrelat i onStd Error1,173474 1.163735 LU735Q 1.1320E1 L116312 1J 00563 1.0S4SO?1,0681.0534731.0373041.0209141.004177C.SS72420.986710.973270.959790.946450.933100.919620.906560.893170.8794S0.865480.851380.83702JjiJj idj 山 ilfa i I

10、ji i Li Hi M i I»ill ill ill fall -|i 山 fh K 11 ! |i "p ij I| , r*rii I ! 'p ifLjisJi Ji-dj dj-iL-ilfHJijLiibjUjiihiJidi-iJi-Ji-dJ lL-iL i i p *i I I >r ! ii i 11 I I I i由 5 5 由訕山 dr dr 山 Q 血 心 山山山 土 山山 TE 用 甲 平， 中 中T« W W M 萍 E 叩 如 中：平5 普尊叩 平下 甲5 F F 叩 嚇T1平ill Il ill r I ill i

11、ll ill I a ill illdH I ill all il i i Iijiili li oli ill ill il tilii I|X*dllX|lX| 山山山rfiiTisTi Jn-rn rp 矩演rp-如 如 jJj ijj 一心心 i_|j 山 iJLi ilj Ji til 山 山 <!> <Li， i"n"i p-y« 平upirg'iiyiiYiiyiryii '"iills Ji .Ji I i .!« al. al. 11 1 L 'L1 L ,* *,!- J-*1 J-

12、V J 1ip I*1 I*BT* H* n*1 H1 'I3*1 1U 1 T'1 ,T, 1T11 I*1 I1 H1 "I* T*iTnTnTit |i ip i|11|11| jiTiifiijiiTiiinTiiTn |izi|i ip叩叩十a(chǎn)p ip：ija叩甲甲S F E綽f q*5F 邛 平 叩帝 平序甲 小項登叩十師IIII ill r 11 I ill ill 11 r I Ini I ii I nWnli ilii In I I/ 尊 F F 蘋?p架 甲甲覃 加 值| iji 5 F F 吁Jj Jj r I uli Hi Ha dll Hi

13、(IlH* iqi "Tirp Fi rjrl fp fjin|l nl rji ti0.070888 0.121眺 0.1559810J83272 0.20637& 0.22658?0,2446320.280969 0.275903 0.2696430.302364 0.314180marks two standard errorsInverse Autoccrrelat ionsL喝Correlation -1987654321 0123456789 1-0.50162ihHj Ji ill ik iKiHHiiNiiIi qi |i |i rp fp if ip ip

14、if if'2 -0.001593 O.OOG174 -0.0044660.0026660.00162?D.Q00628 -0.004259 -0.0018510 0.0052811 -0.0111412 0.00963P&rtial Autocorreht ionsLts Correlation -1987654, 210123&5678910.986712 -0.012023 -0.003534 -0.001735 0.007206 -0.0038b7 -0.005308 -0.012119 -0.018S210 -0.0174811 -0*0121312 -0.0

15、1723 H ilailjiJj ! ill ! Hi ! ill iHr ill ill illF if1* * l T* 伯帥叩師*T* n* *T , n*Fig 2. autocorrelations , inverse autocorrelations and partial autocorrelationsLacSquareIXDFChiSqftutocorre 1 at li61115.61 蠟6<,00010*9870.9730酬。0,9460.983122079.3312<.00010.9070.893LW9 0.9650.861Autocorrel&i

16、ion Check for White NoiseTo Chi-Pr >0*9200.037Fig 3. autocorrelation check for white noise6、提交程序，觀察樣本自相關(guān)系數(shù)，可看出有緩慢下降趨勢，結(jié)合我們觀察的圖形，我們 知道要對序列做差分運(yùn)算，作一階差分，輸入如下程序：identify var=lgnp(1) nlag=12;run;結(jié)果如下:Adtocorrelat ionsc0.0000101.00000Lii iiii ih li>X X1 ,Xa'X*'X*J.*Xr 'A1!Ji*'I* 山 ii|

17、i |iifiiyi qiif i|i |up i|i 111 i|i n| i|ii ii| i|i010.00007080.408201$出那岸*殊洋出*0.0710G720.000041120.27395n0.0S629436J817E-80.04085*0.0095704-0.0000115'.07661OJI0966450.00003S5-.22907辯率*0.083994e-0.00Q0132-.O87RF0.0927457-2.7533E-6-.018360.09316482.0931E-60.0133G0.0931829O.OOOQ24950.16825枷0.09319

18、3100.000031620.210650.09467911。0姬8480.169770.087017122.8S222E-60.019200.098874Las Covariance Correlat i or-19 3 7 6 5 3 2 1 012 3 4 5 6 7 3 81Std Er5marks two standard errors1-0.31989,2-0.1357830.03457* ,4-0.04973.:摧50.217336-0JB230,7-0.0Z682. *«80.13490g-0.05811:卅10-0.02689. *.ii-0.12141，.郵120

19、.10694Inverse AutocorrelatiorsL旺Correlat ior-I987654321C1234567891The ARIMA ProcedurePart ial Autoccrrelat ions10.48820榔州州出K神20.070103-0.14318»4-0.08416,ra5-o.ieese0.13702柵出9G70.06BBGS*0.04357.*»90.176471楠:M100.06921110.0397B1K 12-0.14363La« Correlation-19 6 7 6 6 4 3 2 10 12 3 4 5 6

20、7 6 3 1AutocorreKt ion Check for White NoiseToLasChiSquarePr >yr3 1 gnui-uuwr r E/i iwi昭«7?,57630010.46«0,2740.041-0.0?7-L223-0.0981295.5212<.0001-0.018。140.1跖L21IDJ900.0197、提交程序，觀察樣本自相關(guān)系數(shù)，可看出樣本自相關(guān)系數(shù) 5步后是截尾的，那么確定為MA(5) 模型，進(jìn)行參數(shù)估計，輸入如下程序： estimate q=5 plot;run;結(jié)果如圖:Condit i onal Least

21、Squares Est i mat i onParameterEst i mateStandardErrort ValueApproxPr > |t|LagMU0.017650.001225214.40<.ooai0MALI-0,487630.06943-7,02<-00011MA1,2*0.350130.07785-4J50<00012-O.OhSO0.06130-0.920.86B43MM3-0,021H60.07797-0,260.73334的，50.284410.089494.IQ<00015ConstantEst imate0L017647Varianc

22、eEst imHe0,00011Std ErrorEst inate0.010476AIC-1237.45SBC-1217.72Number ofFles i dua 1 s198* AIC and SBC donot i nc 1udelog determinant.參數(shù)估計及顯著性結(jié)果及擬合統(tǒng)計量To LetgChi- Squ&reDFPr >U H II 叫HUILUUUB r C 1 aL 1 Ul is60.6510.4193-0.0190.0040.0330.0030<u17-0,0371214.ZS70.04E5-0.008-0.0&50.1140.1

23、160.162-0.084IS23 J7130.03330.0010加-L0310.1330<05S0J142423, S3190,05610,008"147-0,011-0.019-0,0570.0853035.71250.0762o.ose0*022-0.0130.0480JO93$41 JO310.10600.0230.034-0.0400.1250<00?模型殘差項的白噪聲檢驗The ARIMA Procedure匾Autocorre 1 at i on Plot of R：es i dua 1 sLa 吞Coyoi ri anceCo rrclalion1876

24、6+32101 2 3 4 5 8 7 9 8 1Sid Error00.000109741.0000001-2.D957E-6-.0 1910D J07106724.G65e6L-?U.0U424U.0/109333.6GW1E-60.03336弟0.07109448.28014E-70.0Q7530J07117351.86S47E-60,016980,071177S-4-0327E-6-.03675g推0J0711981-8.892E-7-.008100 J0712938-6.01O3EZ-6-x0647?0.07I2SB90.00001264011490WB0.071610100,000

25、012680,11555W,0.0724271 10.000017770.1&1940,07395212-0.0000103-網(wǎng) 3邳3s*0,075138marks two standard errorsInverse Aulocorrelftt ionsLaCo rre 1 at il on-1 907654 3 2 I012 3 4567S3 110.04336咪.2-0.001783-0,09014，奉出4-0.01229S-Q.O24Q260.0S20570.0246280.061»C* .9*0,12008IQ-A.1JS7611-0.15675哪120*0904

26、2i1rPartial utocorrelatloosL蛤x Correction -1967654321012345678911 '-0.01810.2 o.oosee.3 0.03353出,4 o.ooeeo.5 0.01703.6 -0.03735*.1-0.01026.8-0.05620*.8、提交程序，觀察輸出結(jié)果，可看出模型通過了白噪聲檢驗，說明模型擬合充分。且MA1,3 ,MA1,4的T值較小，說明參數(shù)顯著為0,除掉這兩項重新進(jìn)行估計，輸入如下程序：estimate q=(1,2,5) plot;Condi Iional Least Squares Est imat io

27、nParameterEstI mateSt&ndardErrort ValueApproxPr > |t|Laemu LQ.00109E41C.12<t00(1C郵1,1-0.467400.0BB19-7.07<.00011MAI,!-U.S07160.08692-4.66<*00012郵1,30.3Q0010.061654.87<.OQ015ConstantEst i mate0.01766VarianceEst i mat e0.000109Std ErrorEst imte0.010452AIC-1240.3SBC-1227.15Number ofF

28、tes i du 角 1 辱198# AIC and SBC donot includelog deteminant.參數(shù)估計及顯著性結(jié)果及擬合統(tǒng)計量Autocorre lat ion Chieck of F：esi duaI sToChi-KPr >LagSquaredDFChiSq -rutocofrelat ions1run;6 2 8 4 o G112 3 32J415.3328.8932.263S.1344.040.54470.08230.03150.05520.07580.09470.0040.0010.0200.0180.0640.0370.039 -0.026 0.099

29、 0.145 -0.0120.0380.0S9 0.104 -0.022QJ02 -Q JI? -0.043-0.008 0 J22 0 J43 -0.0110,060 0.12S0.0210.173C.076-0.047 0.05C C.007-C.023-C.08C0.123C.095-C.11CC.C58模型殘差項的白噪聲檢驗Autocorrelation Plat of ResidualsLasCovarianceCorrelet icrQ0.000109231,0000014J2091E-70.0037824.27371E-8D.0891239J3531E-G0.DBS 124-6J

30、872E-70062152.91551E-60.021208-2.5301E-6-.023167L94976E-70,001248-L85E-E-.02B0990.000011390J0376IQ0.000013280.1Z160110.000018880J72S712-3J03IE-6-.07967lLh yjlo ijuijjj業(yè)山*MUifiit1 'T1 'T1 T1 T'1 T1 u1 'T1 *71 'r1 'Ij it*00,071067* :0.0710660.0711770.0717360.0717410.0717720,071

31、810, *0.071010枇：0,071858瓣.0J726110*073632:帆l0*075654-19 8 7 6 5 4 3 2 10 12 3 4 5 5 7 8 9 1 Std Errormarks two standard errors殘差項的自相關(guān)系數(shù)圖9、提交程序，觀察輸出結(jié)果，可看出模型通過了白噪聲檢驗，說明模型擬合充分，且殘差標(biāo)準(zhǔn)誤與前一估計相差很小，故以此結(jié)果為我們所要的結(jié)果，依此結(jié)果寫出方程式。Novinc Average Hectorsgictor 1: 1 + 0.4674+ 0.30715 酗就2) - 0.3QD01所以可得模型方程式為：Z(t)+0.467

32、4Z(t-1)+0.30715Z(t-2)-0.30001Z(t-5)=0.01766+a(t)10、進(jìn)行預(yù)測，預(yù)測美國未來 2年的每季國民生產(chǎn)總值。輸入如下程序：forecast lead=6 interval=qtr id=date out=results;run;data results;set results;gnp=exp(lgnp);l95=exp(l95);u95=exp(u95);forecast=exp(forecast+std*std/2);run;proc print data=results;var date forcast;where date>= '

33、1jan96 ' d;run;11、提交程序，并把預(yù)測值記錄下來。Tht SA8 System 21:51 Tutsdav, Jecember 2011 26The 有RIMA ProcedureForecasts for variabIe IgnpQbs Forecast81 d Error95需 Conf idence LiKiils2006.94920.010582778.9687201B.3B500,01068.3灑9.00132020.02626.98229.03512039.00130.03218.93SS9.0C432049.0229D,O37I6.S4989.89502

34、053.08890.04028.96123.1107實(shí)驗練習(xí)：分析武漢市2002/01/01-2003/05/31日火車站旅客客流量數(shù)據(jù)（單位：千人） ，并預(yù)測6月份前10天的旅客流量。114 65 49 118 142 148 157 92 111 110 120 140 93 64 66 59 73 77 31 27 25 44 50 57 57 30 30 30 33 53 62 65 35 60 63 57 36 68 70 66 61 55 74 85 60 53 70 97 95 77 63 76 68 45 56 67 68 85 77 71 84 64 71 35 59 110 80 88 56 89 65 72 66 60 42 51 66 128 85 69 57 62 31 83 86 66 59 51 80 86 69 60 58 44 48 51 49 54 33 29 43 110 105 62 53 55 61 36 64 61 59 55 66 66 56 63 62 58 60 55 44 44 40 50 54 52 51 44 44 49 38 69 32 51 85 69 89 65 67 56 5