x = scan("roster.txt",what="CHAR",sep="\n")
sample(x)
n = length(x)
y = sample(x)
for(i in 1:n){
if(i == 1)  cat("\n\n  Tue Mar 7\n")
if(i == 8) cat("\n\n  Thu Mar 9 \n")
if(i == 15) cat("\n\n  Tue Mar 14 \n")
if(i == 22) cat("\n\n  Thu Mar 16 \n")
cat(i,y[i],".\n") 
}

  Tue Mar 7
1 HUANG, XIAOHONG .
2 XIE, MEIHUI .
3 ZHANG, FAN .
4 KICHAEV, GLEB .
5 NAVAR, DAVID ANTHONY .
6 XU, HAOTIAN .
7 KIM, WOONG BAE .

  Thu Mar 9 
8 KIM, LAURA .
9 SUH, YON SOO .
10 KREBS, ALEX JOSHUA .
11 YE, YE .
12 WANG, HUANCHEN .
13 WEN, LIWEN .
14 BRUMBAUGH, STEPHEN PAUL .

  Tue Mar 14 
15 YEUNG, FIONA CHEHONG .
16 LEE, HUNG-I .
17 CHOI, SOO WOO .
18 ZHANG, AILIN .
19 CHIBA, KAORI .
20 MURRAY, GALEN PATRICK .
21 SHAO, KANGHONG .

  Thu Mar 16 
22 WANG, HSIN-HUA .
23 CHAFFEE, ADAM WALTER .
24 LAI, PENG YUAN .
25 AMARAL PORSANI, RAFAEL .
26 DABAGH, SAFAA M .
27 HORNAK, ROBIN .

p91.
par(mfrow = c(1,2))
plot(arima.sim(list(order=c(0,0,1), ma=5), n=100, sd = 1), ylab="x",
     main=(expression(MA(1)~~~theta==5)))
mtext("sigma = 1",s=3,l=.5)
plot(arima.sim(list(order=c(0,0,1), ma=1/5), n=100, sd = 5), ylab="x",
     main=(expression(MA(1)~~~theta==0.2)))
mtext("sigma = 5",s=3,l=.5)

1. Xt − Xt−1 = Wt − 1/2 Wt−1 − 1/2 Wt−2. Identify the ARMA(p,q) model, and say if it is causal or invertible. 
The AR polynomial is φ(z) = 1 − z, which has root 1. 
The MA polynomial is θ(z) = 1 − z/2 − z^2/2, which has roots [-b+/-√(b^2-4ac)]/2a
= [1/2 +/- √(1/4 + 2)]/-1 = -1/2 +/- 1.5,
or −2 and 1. 
Since these polynomials share a common root, they have the common factor 1 − z. 
Factoring these out, the irredundant representation has AR polynomial φ(z) = 1, 
which has no roots, so it is causal, 
and MA polynomial θ(z) = 1 + z/2, which has root −2, so it is invertible. 
This is a causal and invertible ARMA(0, 1) process. 
The reduced process is Xt = Wt + 1/2 Wt-1. 
Xt - Xt-1 = Wt + 1/2 Wt-1 - Wt-1 - 1/2 Wt-2 = Wt - 1/2 Wt-1 - 1/2 Wt-2. 

2. Xt − 2Xt−1 + 2Xt−2 = Wt − 8/9 Wt−1.
The AR polynomial is φ(z)=1−2z+2z^2, which has roots [2+/-√(4-8)]/4, 
or 1/2 ± i/2. These roots are inside the unit circle because 1/2^2 + 1/2^2 = 1/2 < 1. 
The MA polynomial is θ(z) = 1 − 8z/9, which has root 9/8. 
So this is an ARMA(2, 1) process which is invertible but not causal.