#######################################################
# News Impact Curves for GACRCH ZOO MODELS
#
# 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
#######################################################

#First get get fits of the tgarch, pgarch, garch

module(finmetrics)

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

# We have done this before.
# Now the new part.
# We get and plot the News Impact Curves.

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)
##############################################################

# Addendum: If you have not explored plot() applied to a GARCH object
# this is a good time to try it.
# Just do plot(hp.garch) to look at the stuff we have associated with the hp fit.
# Go over each of these looking at the story first.