傳遞函數(shù)模型的建模

1、傳遞函數(shù)模型的建模、實(shí)驗(yàn)?zāi)康氖煜鬟f函數(shù)模型的建模方法二、預(yù)備知識(shí)熟練掌握互相關(guān)函數(shù)特征三、實(shí)驗(yàn)內(nèi)容對(duì)數(shù)據(jù)集Lydia Pinkham進(jìn)行傳遞函數(shù)模型的建模 四、實(shí)驗(yàn)儀器與材料（或軟硬件環(huán)境）SAS/ETS 軟件五、實(shí)驗(yàn)程序或步驟傳遞函數(shù)模型的建模1、 開機(jī)進(jìn)入SAS系統(tǒng)。2、 建立名為exp6的SAS數(shù)據(jù)集，輸入如下程序：data sales;in put x y; t=_n_；cards ;輸入廣告支出及銷售數(shù)據(jù)run ;3、保存上述程序，繪序列圖，輸入如下程序：proc gplot data =sales;symbolli =spli nec=red;symbol2 i =spli ne

2、c=gree n;plot x*t= 1 y*t= 2;run ;4、提交程序，輸出圖像見圖1、圖2.仔細(xì)觀察兩序列圖形，發(fā)現(xiàn)x,y發(fā)展趨勢(shì)大 致相同，x與y均為非平穩(wěn)時(shí)間序列，且x為領(lǐng)先指標(biāo)。145、先觀察x,和y1的相關(guān)情況，看是否要做差分，輸入如下程序:proc arima data =sales;identify var =y crosscorr =(x) nlag =12;run ;proc arima data =sales;identify var =x nlag =12 ;6、提父程序，觀察Xt的yt自相關(guān)和互相關(guān)系數(shù)，如圖3為y的自相關(guān)圖，圖4為x的自相關(guān)圖，發(fā)現(xiàn)它們的自相關(guān)

3、圖都衰減得很慢，表明它們均為非平穩(wěn)時(shí)間序列，對(duì)它們進(jìn)行差分運(yùn)算Autacorrslftt ionsLag CovarianceCarre I at ion-198765432101Std Error0458.3011.000001450.5400.9832B2442.1500.964763432.9780.844754422.8400.922635411.9100.6987664DQJ1G0.874577889.3400.S4953S37SJB5 帛0.6251433G7.0660.30D9810356.0600.7768111344.9000.7525C12333.4800.72764dbO

4、rHrkLdHUli'H、一111,11”川11燈”1|11«11配用"|1值|1電電也遇售卜心山:H 山山山 :iih diMMPd glillnaa- HlilTlII 111 I I I "I Ip Ip Ip WL”加M耨,1曲圳k中!li*i 4imvrrmn toiia.isxbix* m* 2l> 111111 ip 11 f I r I f tf i I ra 11 O sp qs qi Tiir.i- , X i X ,ii la B1<H與 ®inirs 傕 hi 申中 n«|» P* wsmi

5、rwp 刑mrx-X'x山山：山AmnHuipipnBnRn'ipqh.T"n,n*i#4n4p吩Wy¥一網(wǎng)鄧鼎華”的2dg由。制叫IM填嚇Ji > fl 41 中。2»« LM d« Ur Jrdfdi MrIMTk 削WWi/FBrT* 用 hill rtjTi dl)IJUIikihlid1 diH!dmnMniRiraMNinrpMiari”, i uiiimyptlMIUIUyAIhlMUdjUII ILdLr4.ru LbjiT«TtT>i»T rT'TTIlhJjJlUUjd

6、.(iL/. JL.川3" l»T«-T« 11'T M r f0.081650 1.139350 0.1787961.2094490.2349861.2563840.2760210.2929340.3090390,3?1B23 0.333900 0.345028Covar I anceCarrel at ion0L4632251.00000110.96264.3939330.9336021 .溫艮0.909693L0.998153310790.96131410.84168.2995650.81629510.78478,2602940.76050

7、E 1.2315710.73254710.71525,1944 1 80.6888181.16294?$1.112777101圖3Autacdrrelat ions-1 9 8 7 6 5 4 3 20123456789土共涔 llliiNhliliTlTVrtrTrtkinrirtrtrimn'*illl JI mil 41 4111 Ila Bl all ill III BUM J IlilHIEmmin X 牛也力 mil MPfaPt 倬體帶 KN Jill 111 II 41 UI jUtllilllililaaaB'M'sll B 電 11 p 4 0 ”

8、91哪M賺小則,iY 1 W*+Oliiiiilflfllrfirlimrlimniinmqpnnpnp齊力dlIIIiR IlinIIIIIM v UJJI.(1 >xm (| pis 9 (1!kj in 111JJU OGIXnXIH I小金 J u'l piapia ；l a 9 is I)|cli |11 E ir*H'*l7#娜攵y分網(wǎng)做差分運(yùn)算并查看它們的自相關(guān)系數(shù)及互相關(guān)系數(shù),.Q46572（輸出"x自相關(guān)圖見圖5、圖6;圖7x的偏相關(guān)系數(shù)圖；數(shù)圖見圖七rima data =sales;iden tify var =y( 1) crosscorr

9、run ;proc arima data =sales;identify var =x( 1) nlag =12 ;=(x( 1) nlag =12 ;std Error0*0816500.1369930.1743230*2035250.2279030.2466590.288S760A2031280.2976900.3103150.3216970.992071輸入如下互相關(guān)系runAutocorrelat ionsLae Cgvari ance-19 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1Std Error07.071198L000001n.6457730.

10、8118020.5761790,2781930.4G88S50.2263940.5221430.2521050.809832OJ4960E0.2767280J336170J302310.0628Se0 2742030.13239s-0.039048-.oiessid-u.0077359-,00374 II0.Z2O27GOJ06951?0.027219,01314Correlat i an卅出刑翻咄山軸|i常刪口 KHi察出神0.0819A30.095159 0.098707 0.1029360.1048370.10662S 0.105780 OJO鈾朋 0.106906O.I0G8O 9 0

11、.107617Autocorrelat ions二二0123456789101112Ccr/ariance0.100173-0.0453S90.01 M70-0.0116400-015285-0,0108630.0091697-0*00798020.012886-0.0064823-0,0116700.017A81<0,0061770Corrs I at ion1.00000A45320 0J2448-J1S20 0J5259-J0944 Q.08144-.079660JZ816-JB471-.11650 0J7361-.061 EG仙Ip體邛幣可tram軸.Sid Error0.081

12、923 0.087305 0.088368 0.099317DJ00878 0J01672 0.102222 0.102638 0.103625 0J 03896OJ04769 0 10AAR9La23 4587 a91011讓Correlat ion-0.45320-0.10152-0.1293511.08367-U.D09920.04725-0.011740,036510.05122-U.176830.0B0710.082B8Part ial Autocorrelat ions-1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1.xtI * *水札 $ WU

13、MI. 帕及觀察Xt的自相關(guān)和偏相關(guān)系數(shù)，可以看到自相關(guān)系數(shù)是一步截尾的，偏相關(guān)系數(shù)是三步截尾的。輸入如下程序:9、對(duì)Xt擬合AR(3)模型及模型MA(1),看是否充分,estimatep=3 plot 汀run ； 1estimateq=1 plot;11、提交程序,觀察輸出AR(3)模型擬合結(jié)果見圖8、圖9.MA( 1)模型擬合說明擬合效果不錯(cuò)，但結(jié)果見圖10、圖11.可看到模型均通過了白噪聲檢驗(yàn),是MA(1)模型的AIC與BSC值更小，說明MA( 1)模型的擬合效果更好。把擬合的方程式寫出來。= 0.02354 at-0.46910a(A11 it? nn ihih r ruLt?dur

14、tsConditional Le&?t Squares EstimationStandard ErrorParameter Emt im&t 亡t Value0.023640.01275L8&-0.517570.08262-6.28-0.167950.09208-L8?-0.13133D.08277-L59M AAAuP1R1P1ApproxPr > |t|La<<0.0657o:.UUUI10.070220.11343Constant Estl mate 0.0429S2 Variance Estimate 0,07$339 Std Error Es

15、t iirate 0.2S1672 AIC 49.21992 SBC 61.23571 Number of Residuals 149w AIC and SBC do not include luA det erm inflint.Autocorrelation Check of ResidualsChi-Pr>SquareDFSipi力LOG3D.7B1Or8.S93D.43S3kii,e?160.7036215JG21D.78210.0090.0060.037-0.0140.C91-0.068-0.017-0.042-0,0740.0GBDJ22-D.D21riutocorrelft

16、t ions0.053-0.0050.052-0.1000.1 SO-0.0080.0090,012-0.089D,023-0.001-O.OG7Conditional Least SquaresEst imat ionParameterMU MAI JEst i mate0.023540.46910StandardError0.012960.072901 L ValueE90 6.44ApproxPr> |t|0.0589<.0001Lgo1Const ant Est imate 0A023542 Variance Estimate 0.06CD97 Std Error Esti

17、mate 0.283013 AIC 48.67635 SBC 54.68425Number of Residuals 149AIC and SBC do not include log determinant)圖10autocorrelation Check of ReAidualsChi- SauareDFPr>ChiSa Autocorrel ions15.8950.32300.0520.098-0 J35QJ33-0.0320J7312.69110.3140-0.021-0JS4-Q.0810.146-0.010U.86170.6050-0.00?-0.057-0.0510.004

18、0.012-0.031WJ1230.74620.0430.10S-0J110.0150.002-0,071圖11觀察預(yù)白噪聲化后的兩序列的互相關(guān)系數(shù)，輸入如下程序:identify var =y( 1) crosscorr =(x( 1) nlag =12 ;run11、提交程序，觀察樣本自相關(guān)系數(shù)和偏相關(guān)系數(shù)和互相關(guān)系數(shù)，我們可以初步識(shí)別傳遞函數(shù)模型為(1, 0, 3),即：(仁、iB)yt二必12、進(jìn)行參數(shù)估計(jì)，并查看殘差的相關(guān)情況，輸入如下程序：estimate in put =( 3$/( 1 )x)nocon sta nt plot; |run ;13、提交程序，觀察輸出結(jié)果，如圖1

19、2,13.模型通過白噪聲檢驗(yàn)，且各參數(shù)t檢驗(yàn) 通過。Autocorrelation Cheek at RetidualsTo Chi-Pr >1_醴Square)FChlSq wuiocoi re 1 bi 1&9.43E0J4790.225-0j刃-0.0560J闊0.0540tQ501210.35120.5353-0.04S-0JU4-0.0190.061-0.00®-0.0091814.58180.0902-0.020-0 0870.010-0.1050,0722420.24240.00900.0380.0310.083-0.0640J07圖12uondl 11

20、one I Least squares tst mt ionParameterEst imateStandard Errort ValueApprox Pr>HILagVariableShiftNUM14.806240.09G8446.08<.00010X3DENI,10.726380.006778082.74<.00011X3圖1314、觀察輸出結(jié)果如圖14,圖15,可以看到殘差的自相關(guān)系數(shù)與偏相關(guān)系數(shù)均是1 步截尾的。那么模型可識(shí)別為：或yt 0 A, -d-AB)a(1 -6b)15、進(jìn)行參數(shù)估計(jì)，輸入如下程序：estimate p = 1 in put =( 3$/(

21、 1 )x)noconstant plot;run ;estimate q=1 in put =( 3$/( 1 )x) nocon sta ntplot;run ;16、提交程序，觀察輸出結(jié)果如圖14、15,可看到模型均通過了白噪聲檢驗(yàn)，說明模型擬合充分，且各參數(shù)均通過t檢驗(yàn)，但是模型2的擬合效果更好（AIC與SBC的值更小）寫出方程:yt消黑(仁 0.28085B)atTa“心AMisre OF ChiSq6121024§H17拙O.-452D-01.023-0.118-0.0100-0350.079D.DGSID.9D74-山 0220.00?0,047o.m-Q.DI7Q.9

22、378-0,003C,08S-O-OIC0尸0.067O.S423U.O?BC.0B9DM4105-1.01950.0S4ParahelerE&linaLeVLWIIU1XIV .Error1 期 lueH-T.-l w a Pr>lllLutVari ah IsShiftARM-0.22B6S0.032332.730.4DG210NJM14.6403D0.0317750.57<J QQIi3KN1.10.72505O,OO?&95195,4<Af113Varlihce- EsLihatA(LI0SI94Eld Error EAinate，虢M豳AICSBCS

23、4.Z7BS5Wiiber of Resi(kills1 嶼t AIC and S8C dq ng( include IQC deterninaint.Cdrrelai. i ons of Parftft&ter Est imt&sWrlftbleP r+ncUry fiRhlKMUN|PEHUI/AR1J1 Iftl III-0.1130o血EXMDIM-DJ20LOGO-OuSB?XDEN1JD.0760.5671J DQAutiXQrrelal; ion Chcd< A F Kes i dualsPr>AM o&arr £3 I al I MIS-圖14Ksr&h&tertrtiK&tetnrorI ValueMrA|t|LM1VariabledillM41J0.2S0B&D.QS1I1?SUEO-QQO?1V0IWN14.S9I4H0.0893451 S4 10MI<0001jX.iCEN1.10J2834<00011X3¥ar i ancS Est I meite0.102103Sid Error Eat I hateD.31953BAIC83.60374SBC92 .S8 394Nmber aF Residuali145EC end S