Tietokoneharjoitus 2

Tehtävä 5

Simuloi AR(1) mallia.

a<-0.5
x0<-0
T<-1001
seed<-2
set.seed(seed)

# normaalijakauma
e<-rnorm(T)
x<-matrix(x0,T,1)
for (t in 2:T) x[t]<-a*x[t-1]+e[t]
plot(x,type="l")


# t-jakauma
df<-10
kh<-sqrt(df/(df-2))
e<-rt(T,df=df)/kh
x<-matrix(x0,T,1)
for (t in 2:T) x[t]<-a*x[t-1]+e[t]
plot(x,type="l")

Simuloi MA(1) mallia.

# MA(1)-malli
a1<-0.8
T<-1001
seed<-2
set.seed(seed)
e<-rnorm(T)
x<-matrix(0,T-1,1)
for (t in 2:T) x[t]<-e[t]+a1*e[t-1]
plot(x,type="l")

cor<-a1/(1+a1^2)
cor

x0<-x[1:(length(x)-1)]
x1<-x[2:length(x)]
plot(x0,x1)

aa<-seq(-3,3,0.01)
bb<-aa/(1+aa^2)
plot(aa,bb)

mak<-max(bb)
ind<-(bb==mak)
mak
aa[ind]

#[1] 0.5
#[1] 1

# MA(2)-malli
a1<--1
a2<--1
T<-1001
seed<-2
set.seed(seed)
e<-rnorm(T)
x<-matrix(0,T-2,1)
for (t in 3:T) x[t]<-e[t]+a1*e[t-1]+a2*e[t-2]
plot(x,type="l")