#------------------------------------------------#
#                                                #
#   week12: Maximieren der Likelihood-Funktion   #
#              fuer das Beispiel 3               #
#                                                #
#------------------------------------------------#



# we have to calculate the log-Likelihood function:
# we use 'vectorized' calculation logic of R to make the code 
# a bit more performant -> code looks a bit less intuitive:


logL = function( d , d0 , ret )
{
  n = length(ret)

  cumsum_retsquared = cumsum(ret^2)
  
  # remove last d elements:
  cumsum_retsquared_shifted = cumsum_retsquared[-( (n-d+1):n )]

  # fill in d zeros at the first d places:
  cumsum_retsquared_shifted = c( rep(0,d) , cumsum_retsquared_shifted )

  sum_d_retsquared = cumsum_retsquared - cumsum_retsquared_shifted

  # start at d0 or d0+1:
  ret = ret[(d0+1):n]
  sum_d_retsquared = sum_d_retsquared[d0:(n-1)]
  vol = sqrt( 1/d * sum_d_retsquared )
  
  # the actual calculation:
  terms = log(vol) + 1/2*ret^2/vol^2
  result = -sum(terms)

  return(result)
}



# lets fit to SPX-data:

spx = read.table("C:/Users/detlef/OneDrive/hochschule/Vorlesungen/WS2425/WBS/week6/SPX.txt",header=TRUE,sep=";")
spx

summary(spx)
head(spx)

S = spx$Adj.Close
n=length(S)
ret = rep(0,n)       
for(i in 2:n)
{
  ret[i] = (S[i]-S[i-1])/S[i-1]
}

par(mfrow=c(2,1))

plot(S,type="l")
plot(ret,type="l")

plot(log(S/S[1],2),type="l")
plot(ret,type="l")


d0 = 100
F = rep(0,d0)

for(d in 1:d0)
{
  F[d] = logL( d , d0 , ret )
}

plot( 1:d0, F )
plot( 5:d0, F[5:d0] )
plot( 10:d0, F[10:d0] )

which.max(F)               # d = 24

plot( 10:d0, F[10:d0] )
points( 24 , logL(24,d0,ret) , col="red", pch="X")