金融時間序列得線性模型

1、金融時間序列的線性模型一一自回歸R實例例2.3> setwd("C:/Users/Mr.Cheng/Desktop/課件/ 金融數(shù)據(jù)分析導論基于 R/DataSets/ch2data") %設置工作目錄> da=read.table("q-gnp4710.txt",header二T)> head(da)Year Mon Dat VALUE1194711238.12194741241.53194771245.641947101255.65194811261.76194841268.7> G=da$VALUE> LG=log(G

2、)> gnp=diff(LG)> dim(da)1 2534> tdx=c(1:253)/4+1947%創(chuàng)建一個時間序列指數(shù)，從 1947開始，每次增加一個季度，一共253個季度。> 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,g np,type二T,xlab二'year',ylab二'growth')19501960197019S0199020002010ye

3、aryear> acf(gnp,lag=12) %畫滯后12階的對數(shù)增長率的自相關圖> pacf(gnp,lag=12) %畫滯后12階的對數(shù)增長率的偏自相關圖Series gnp12D9> m仁arima(gnp,order二c(3,0,0)%計算 AR(3)> mlCall: arima(x = gnp, order = c(3, 0, 0)Coefficie nts:ar1 ar2ar3in tercept0.43860.2063-0.15590.0163s.e. 0.06200.06660.06260.0012sigmaA2 estimated as 9.549

4、e-05: log likelihood = 808.56, aic = -1607.1> tsdiag(m1,gof=12)%模型檢驗.I.ll .IlliJ II 11II JI1 A L hlill lljlll IIIilll ll ill 1 ri i n 1 1 li 1 iii . 1 i ill ll l i 1 III .I191III1叫、I III 11P"M I" ''' '1 rr -|f|ir ri| Standairdizod kosiduaikHQirmp2W2MACF of Rusiidudlsp vs

5、luQcfoc Ljung Box ttatictic0an-nk.CL> p1=c(1,-m1$coef1:3)%設置多項式方程的系數(shù)：1-0.438z-0.206z 2+0.156z 3=0> r1=polyroot(p1)%解多項式方程得到特征根> r1> Mod(r1) %計算特征根的模1 1.8326741.9092161.832674> k=2*pi/acos(1.616116/1.832674)%計算周期> k1 12.79523AR (P)定階，方法為極大似> mm仁ar(gnp,method二'mle')%用 AIC

6、準則自動為然估計> mm1$order %查看階數(shù)1 9> names(mm1) %得到mm1的名字1 "order""ar""var.pred"6 "n.used""order.max""partialacf""x.mea n""aic""resid""method"11"series"frequency"call""asy.var.

7、coef"> print(mm1$aic,digits3)%查看mm1中的aic值,保留三位小數(shù)101177.767 11.9158.7924.6696.2655.9505.1014.5966.5410.0000.5092.504122.057 > aic=mm1$aic > length(aic)1 13> plot(c(0:12),aic,type二'h',xlab二'order',ylab二'aic')> lines(0:12,aic,lty=2)%畫 aic 連線圖(虛線)%畫aic豎線圖廠-一丁_

8、廠-一-T-1II0246order> vw二read.table('m-ibm3dx2608.txt',header二T),3> t1=prod(vw+1) %計算35年后的終值> t11 1592.953> head(vw)10.000724 -0.033374-0.0643410.038358> t1A(12/996)-1%折算回平均每年的回報1 0.0929008410 12%讀取第3列數(shù)據(jù)0.0121720.056888模型的檢驗> vw=read.table('m-ibm3dx2608.txt',header=T)

9、,3> m3=arima(vw,order=c(3,0,0)%用 AR ( 3)擬合> m3Call:arima(x = vw, order = c(3, 0, 0)Coefficie nts:ar1ar2ar3in tercept0.1158-0.0187-0.10420.0089s.e. 0.03150.03170.03170.00171500.86, aic = -2991.7sigmaA2estimated as 0.002875: log likelihood3> (1-.1158+.0187+.1042)*mean(vw)%計算 phi(0)1 0.0089676

10、11> sqrt(m3$sigma2) %計算殘差標準誤 1 0.0536189> Box.test(m3$residuals,lag=12,type二"Ljung")%檢驗殘差的自相關函數(shù)，如果顯示出額外的序列相關性，貝S應該考慮到這些相關性并進行擴展Box-Lj ung testdata: m3$residualsX-squared = 16.352, df = 12, p-value = 0.1756> pv=1-pchisq(16.35,9)%由上一步算得Q (12) =16.352,并且基于它所漸進服從的自由度為9(修正自由度12-2)的卡方分布

11、，得到p值為0.06，因此在5%的顯著水平 下無法拒絕原假設> pv1 0.05992276> m3二arima(vw,order二c(3,0,0),fixed二c(NA,O,NA,NA)%改進模型：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。(下面有補充 計算)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transform.pars設成FALSE> m3Call:arima(x = vw, order = c(3

12、, 0, 0), fixed = c(NA, 0, NA, NA)Coefficie nts:ar1ar2ar3in tercept0.11360-0.10630.0089s.e. 0.031300.03150.00171500.69, aic = -2993.3sigmaA2estimated as 0.002876: log likelihood8> (1-.1136+.1063)*0089%計算 phi(0)1 0.00883503> sqrt(m3$sigma2)1 0.05362832> Box.test(m3$residuals,lag=12,type二'

13、Ljung')Box-Lj ung 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%改進后的模型對數(shù)據(jù)的動態(tài)線性相依性的建模是充分的。關于系數(shù)顯著性的計算：> vw=read.table('m-ibm3dx2608.txt',header=T),3> m3二arima(vw,order=c(3,0,0),fixed=c(NA,0,NA,NA)Warning

14、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 設成FALSE> names(m3)"aic""n .c ond"1 "coef""sigma2" "var.coef" "mask""loglik"7 "arma""residuals" "call"&quo

15、t;series" "code"13 "nobs""model"> tratio二m3$coef/sqrt(diag(m3$var.coef)%diag函數(shù)用于提取對角線上的元素。Warning message:In m3$coef/sqrt(diag(m3$var.coef) :Ion ger object len gth is not a multiple of shorter object len gth> tratioar1ar2ar3 in tercept3.63010720.0000000-62.07138950.2859641顯著性取0.05時就把|t|和1.96(查正態(tài)分布表的0.975對應的值)比較，大于就顯著,小于就不顯著。顯著性取 0.01時對比2.575，顯著性取0.1時對比1.645.畫自相關函數(shù)> po=1> p1=0.