1、金融時(shí)間序列的線性模型自回歸R實(shí)例例2.3> setwd("C:/Users/Mr.Cheng/Desktop/課件/金融數(shù)據(jù)分析導(dǎo)論基于R/DataSets/ch2data")%設(shè)置工作目錄> da=read.table("q-gnp4710.txt",header=T)> head(da) Year Mon Dat VALUE1 1947 1 1 238.12 1947 4 1 241.53 1947 7 1 245.64 1947 10 1 255.65 1948 1 1 261.76 1948 4 1 268.7> G=d

2、a$VALUE> LG=log(G)> gnp=diff(LG)> dim(da)1 253 4> tdx=c(1:253)/4+1947 %創(chuàng)建一個(gè)時(shí)間序列指數(shù)，從1947開始，每次增加一個(gè)季度，一共253個(gè)季度。> par(mfcol=c(2,1)畫兩行一列的小圖> plot(tdx,LG,xlab='year',ylab='GNP',type="l> plot(tdx2:253,gnp,type='l',xlab='year',ylab='growth')&

3、gt; acf(gnp,lag=12)%畫滯后12階的對(duì)數(shù)增長(zhǎng)率的自相關(guān)圖> pacf(gnp,lag=12)%畫滯后12階的對(duì)數(shù)增長(zhǎng)率的偏自相關(guān)圖> m1=arima(gnp,order=c(3,0,0)%計(jì)算AR(3)> m1Call:arima(x = gnp, order = c(3, 0, 0)Coefficients: ar1 ar2 ar3 intercept 0.4386 0.2063 -0.1559 0.0163s.e. 0.0620 0.0666 0.0626 0.0012sigma2 estimated as 9.549e-05: log likelih

4、ood = 808.56, aic = -1607.12> tsdiag(m1,gof=12)%模型檢驗(yàn)> p1=c(1,-m1$coef1:3)%設(shè)置多項(xiàng)式方程的系數(shù)：1-0.438z-0.206z2+0.156z3=0> r1=polyroot(p1)%解多項(xiàng)式方程得到特征根> r1> Mod(r1)%計(jì)算特征根的模1 1.832674 1.909216 1.832674> k=2*pi/acos(1.616116/1.832674)%計(jì)算周期> k1 12.79523> mm1=ar(gnp,method='mle')%用A

5、IC準(zhǔn)則自動(dòng)為AR（P）定階，方法為極大似然估計(jì)> mm1$order%查看階數(shù)1 9> names(mm1)%得到mm1的名字 1 "order" "ar" "var.pred" "x.mean" "aic" 6 "n.used" "order.max" "partialacf" "resid" "method" 11 "series" "frequen

6、cy" "call" "asy.var.coef"> print(mm1$aic,digits = 3)%查看mm1中的aic值，保留三位小數(shù) 0 1 2 3 4 5 6 7 8 9 10 11 77.767 11.915 8.792 4.669 6.265 5.950 5.101 4.596 6.541 0.000 0.509 2.504 12 2.057 > aic=mm1$aic> length(aic)1 13> plot(c(0:12),aic,type='h',xlab='order&

7、#39;,ylab='aic')%畫aic豎線圖> lines(0:12,aic,lty=2)%畫aic連線圖（虛線）> vw=read.table('m-ibm3dx2608.txt',header=T),3%讀取第3列數(shù)據(jù)> t1=prod(vw+1)%計(jì)算35年后的終值> t11 1592.953> head(vw)1 0.000724 -0.033374 -0.064341 0.038358 0.012172 0.056888> t1(12/996)-1%折算回平均每年的回報(bào)1 0.09290084l 模型的檢驗(yàn)>

8、; vw=read.table('m-ibm3dx2608.txt',header=T),3> m3=arima(vw,order=c(3,0,0)%用AR（3）擬合> m3Call:arima(x = vw, order = c(3, 0, 0)Coefficients: ar1 ar2 ar3 intercept 0.1158 -0.0187 -0.1042 0.0089s.e. 0.0315 0.0317 0.0317 0.0017sigma2 estimated as 0.002875: log likelihood = 1500.86, aic = -29

9、91.73> (1-.1158+.0187+.1042)*mean(vw)%計(jì)算phi(0)1 0.008967611> sqrt(m3$sigma2)%計(jì)算殘差標(biāo)準(zhǔn)誤1 0.0536189> Box.test(m3$residuals,lag=12,type="Ljung")%檢驗(yàn)殘差的自相關(guān)函數(shù)，如果顯示出額外的序列相關(guān)性，則應(yīng)該考慮到這些相關(guān)性并進(jìn)行擴(kuò)展Box-Ljung testdata: m3$residualsX-squared = 16.352, df = 12, p-value = 0.1756> pv=1-pchisq(16.35,

10、9)%由上一步算得Q（12）=16.352,并且基于它所漸進(jìn)服從的自由度為9(修正自由度12-2)的卡方分布，得到p值為0.06，因此在5%的顯著水平下無法拒絕原假設(shè)> pv1 0.05992276> m3=arima(vw,order=c(3,0,0),fixed=c(NA,0,NA,NA)%改進(jìn)模型：由于間隔為2的AR系數(shù)在5%的水平下不顯著，因此修改后的模型去除2階滯后項(xiàng)。（下面有補(bǔ)充計(jì)算）Warning message:In arima(vw, order = c(3, 0, 0), fixed = c(NA, 0, NA, NA) : 一些AR參數(shù)是固定的：把transf

11、orm.pars設(shè)成FALSE> m3Call:arima(x = vw, order = c(3, 0, 0), fixed = c(NA, 0, NA, NA)Coefficients: ar1 ar2 ar3 intercept 0.1136 0 -0.1063 0.0089s.e. 0.0313 0 0.0315 0.0017sigma2 estimated as 0.002876: log likelihood = 1500.69, aic = -2993.38> (1-.1136+.1063)*.0089 %計(jì)算phi(0)1 0.00883503> sqrt(m

12、3$sigma2)1 0.05362832> Box.test(m3$residuals,lag=12,type='Ljung')Box-Ljung testdata: m3$residualsX-squared = 16.828, df = 12, p-value = 0.1562> pv=1-pchisq(16.83,10)%修正自由度（12-2）> pv1 0.07821131%改進(jìn)后的模型對(duì)數(shù)據(jù)的動(dòng)態(tài)線性相依性的建模是充分的。關(guān)于系數(shù)顯著性的計(jì)算：> vw=read.table('m-ibm3dx2608.txt',header=

13、T),3> m3=arima(vw,order=c(3,0,0),fixed=c(NA,0,NA,NA)Warning message:In arima(vw, order = c(3, 0, 0), fixed = c(NA, 0, NA, NA) : 一些AR參數(shù)是固定的：把transform.pars設(shè)成FALSE> names(m3) 1 "coef" "sigma2" "var.coef" "mask" "loglik" "aic" 7 "ar

14、ma" "residuals" "call" "series" "code" "n.cond" 13 "nobs" "model" > tratio=m3$coef/sqrt(diag(m3$var.coef)%diag函數(shù)用于提取對(duì)角線上的元素。Warning message:In m3$coef/sqrt(diag(m3$var.coef) : longer object length is not a multiple of shorter object length> tratio ar1 ar2 ar3 intercept 3.6301072 0.0000000 -62.0713895 0.2859641 顯著性取0.05時(shí)就把|t|和1.96（查正態(tài)分布表的0.975對(duì)應(yīng)的值）比較，大于就顯著，小于就不顯著。顯著性取0.01時(shí)對(duì)比2.575，顯著性取0.1時(shí)對(duì)比1.645.畫自相關(guān)函數(shù)>