# Code for doing Exercises #1 and #2 in Chapter 5.

 graphics.off()
 
 ##############
 # No. 1
 ##############
 
 # please read data first
 
 data1=read.csv(file="c:/zcai/res-teach/econ6219/Bank-of-America.csv",header=T)
 data2=read.csv(file="c:/zcai/res-teach/econ6219/sp100.csv",header=T)
 rt=data1[,5]                # returns for the individual stock
 rt=rev(rt)
 rt=diff(log(rt))
 rmt=data2[,5]               # returns for the market index
 rmt=rev(rmt)
 rmt=diff(log(rmt))
 rt=rt[abs(rmt)<=0.1]        # delect outliers
 rmt=rmt[abs(rmt)<=0.1]          
 rmt=rmt[abs(rt)<=0.1]
 rt=rt[abs(rt)<=0.1]
 n=length(rt)                # sample size
 
 fit1=lm(rt~rmt)             # fit the market model
 print(summary(fit1))
 
 beta=fit1$coefficients      # obtain the estimated coefficients
 res_f=fit1$residuals        # obtain the residuals
 std=sqrt(diag(vcov(fit1)))  # obtain the standard errors
 t1=(beta[2]-1)/std[2]       # t-test statistics for testing H_0: beta=1
 p_value1=2*(1-pt(abs(t1),n-2))   # p-value for H_1: beta\=1
 print(c("The p-value for (c) is", p_value1))

 sse_f=sum(res_f^2)          # SSE for the full model
 sse_r=sum((rt-rmt)^2)       # SSE for the reduced model
 f1=(sse_r-sse_f)*(n-2)/(sse_f*2) 
                             # F-test statistic for testing H_0: alpha=0 & beta=1
 p_value2=1-pf(f1,2,n-2)
 print(c("The p-value for (e) is", p_value2))

 #################
 #  No. 2
 #################

 L=252                       # set the window length
 beta1=rep(0,2*(n-L+1))
 dim(beta1)=c(n-L+1,2)
 for(i in 1:(n-L+1)){
 y=rt[i:(i+L-1)]
 x=rmt[i:(i+L-1)]
 fit2=lm(y~x)
 beta1[i,]=fit2$coefficients
 }
 
 win.graph()
 par(mfrow=c(2,2),mex=0.4,bg="light blue")
 plot(rmt,rt,xlab="S&P100",ylab="BoA")
 ts.plot(beta1[,1],main="Time series plot for alpha")
 abline(beta[1],0)
 ts.plot(beta1[,2],main="Time series plot for beta")
 abline(beta[2],0)