I am currently working on a group project estimating VaR and ES for a series of returns. One of the tasks is to estimate the degrees of freedom of a t distribution.
I am using the following approach:
make_loglik <- function(x){ Vectorize( function(nu) sum(dt(x, df=nu, log=TRUE)) )}
t_nu_mle <- function(x) {
loglik <- make_loglik(x)
res <- optimize(loglik, interval=c(0.01, 2000), maximum=TRUE)$maximum
res
}
Which yields for example:
set.seed(123)
t <- rt(20000,df=3)
t_nu_mle(t)
[1] 2.986434
However on the empirical data that is given in the assignment I get a different value for the DF using for example the package MASS:
library(MASS)
fitdistr(t, "t")
Additionally, my other group members obtain different results as well when using the actual data set.
Is my function above flawed? What could be the issue here?
