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#
# EGARCH, TGARCH, and PGARCH ... the ZOO DOORS ARE OPENED....
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module(finmetrics)

# First, Neslson(1991) EGARCH

hp.egarch = garch(hp.s~1, ~egarch(1,1), leverage=T, trace=F)
hp.egarch

# Just for fun calculate a t-statistic for the Leverage "by hand"...
coef(hp.egarch)[5]/sqrt(vcov(hp.egarch)[5,5])

#More to the point of understanding the return series,

summary(hp.garch)


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# Next the TGARCH of GJR(1993)

hp.tgarch = garch(hp.s~1, ~tgarch(1,1), trace=F)

summary(hp.tgarch)

#t-stat on coefficient
coef(hp.tgarch)[5]/sqrt(vcov(hp.tgarch)[5,5])


################################ 
# Next the  PGARCH of Ding, Granger, Engle (1993): Case of d=1.
#

hp.pgarch = garch(hp.s~1, ~pgarch(1,1,1), leverage=T, trace=F)

summary(hp.pgarch)

# t-stat on leverage effect
coef(hp.pgarch)[5]/sqrt(vcov(hp.pgarch)[5,5])


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# Now, the so-called news impact curves
# This is a theoretical object that one can view as the graph of sigma^2_t as a function of epsilon_{t-1}
# conditional on everything else...
# It shows the relative impact of the "news" in the various models
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a0 = hp.tgarch$coef[2]
a1 = hp.tgarch$coef[3]
b1 = hp.tgarch$coef[4]
g1 = hp.tgarch$coef[5]
A = a0 + b1*hp.tgarch$asymp.sd^2
epsilon = seq(-0.21,0.14, length=100)
sigma2.t.TGARCH = A+(a1+g1*(epsilon < 0))*(epsilon^2)

a0 = hp.pgarch$coef[2]
a1 = hp.pgarch$coef[3]
b1 = hp.pgarch$coef[4]
g1 = hp.pgarch$coef[5]
A = (a0 + b1*hp.pgarch$asymp.sd)^2
error = abs(epsilon) + g1*epsilon
sigma2.t.PGARCH = A + 2*sqrt(A)*a1*error + (a1*error)^2

hp.garch = garch(hp.s~1, ~garch(1,1), trace=F)
a0 = hp.garch$coef[2]
a1 = hp.garch$coef[3]
b1 = hp.garch$coef[4]
#g1 = hp.garch$coef[5] #BOGUS IN TEXT
A = a0 + b1*hp.garch$asymp.sd^2
error = abs(epsilon) + g1*epsilon
sigma2.t.GARCH = A + a1*(error^2)

matplot(cbind(epsilon, epsilon, epsilon),
cbind(sigma2.t.TGARCH,sigma2.t.PGARCH,sigma2.t.GARCH),
type="l")

key(-0.05, 0.0045, lines=list(type="l", lty=1:3),
text=list(c("TGARCH","PGARCH","GARCH")),border=1, adj=1)
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