V priklade su 3 na sebe nezavisle veci

1. GARCH z casoveho radu r.cref - ten je v ramci jedneho z packagov.

2. demonstracia, ako mozno GARCH nasimulovat.

3. odhad GARCH v ramci dow-jones indexu.


# kniznica

library("TSA")
library("tseries")
library("moments")
library("forecast")
win.graph(width=4.875,height=2.5,pointsize=8)
data(CREF)

# nadcitanie udajov o cenach fondu CREF

plot(CREF)

# logaritmicke vynosnosti

r.cref=diff(log(CREF))*100
plot(r.cref)
abline(h=0)

# autokorelacna funkcia a funkcia parcialnej autokorelacie (je potrebne
ARIMA?)

acf(r.cref)
pacf(r.cref)

# ACF a PACF z umocnenych vynosnosti (je potrebne ARIMA?)

acf(r.cref^2)
pacf(r.cref^2)

# McLeod a Li (1983) test na pritomnost ARCH efektu

win.graph(width=4.875,height=2.5,pointsize=8)
McLeod.Li.test(y=r.cref)

# test normality vynosnosti

win.graph(width=4.875,height=2.5,pointsize=8)
qqnorm(r.cref)
qqline(r.cref)

# test na normalitu , tiez na spicatost - pri pritomnosti garch su

vynosnosti spicate
jarque.bera.test(r.cref)
kurtosis(r.cref)
hist(r.cref)

# eacf

eacf(r.cref)

# odhad

model.11=garch(r.cref,order=c(1,1))
summary(model.11)

# diagnostika rezidui

plot(residuals(model.11),type="h",ylab="Standardizovane rezidua")
win.graph(width=4.875,height=2.5,pointsize=8)
qqnorm(residuals(model.11))
qqline(residuals(model.11))
acf(residuals(model.11)^2,na.action=na.omit)
McLeod.Li.test(y=model.11$residuals)


###############
# generovanie garch casovych radov
###############

set.seed(1234567)
garch01.sim=garch.sim(alpha=c(0.9,0),beta=.1,n=500)
plot(garch01.sim,type='l', main='',ylab=expression(r[t]),xlab='t')
plot(garch11.sim)
acf(garch01.sim^2)

###############
# komplexny pripad
###############

udaje=read.csv2("DowJones.csv")
DJ=ts(udaje)
plot(DJ)
dj=diff(log(DJ))
plot(dj)
win.graph(width=4.875,height=2.5,pointsize=8)
qqnorm(dj)
qqline(dj)
kurtosis(dj)
acf(dj)
pacf(dj)

###############

# package forecast
# prikaz auro.arima

auto.arima(dj)
ar.22=arima(dj,c(2,0,2))

# analyza rezidui

# Box.test(x, lag = 1, type = c("Box-Pierce", "Ljung-Box"), fitdf = 0)

plot(ar.22$residuals)
acf(ar.22$residuals)
pacf(ar.22$residuals)
win.graph(width=4.875,height=2.5,pointsize=8)
qqnorm(ar.22$residuals)
qqline(ar.22$residuals)
kurtosis(ar.22$residuals)
jarque.bera.test(ar.22$residuals)
Box.test(ar.22$residuals, lag = 20)

# analyza stvorcov rezidui

acf(ar.22$residuals^2,na.action=na.omit)
pacf(ar.22$residuals^2,na.action=na.omit)
Box.test(ar.22$residuals^2, lag = 20)
McLeod.Li.test(y=ar.22$residuals)
gmodel.21=garch(ar.22$residuals,order=c(2,1))
summary(gmodel.21)