Hi I tried a lot of time to send this message hope it works this time!
Hi everybody,
my objective is to find the corresponding parameter of the gumbel copula that best fit my empirical dependancy structure. i.e I already know that the gumbel copula is the best family but i want to decide on the best parameter ?
in other words
let
x <- rcopula(gumbelCopula(3), 100)
suppose we do not know that alpha=3 is the right value and we are wondering if the gumbel copula with alpha equal to 2 is a good fit
let test :
gofEVCopula(gumbelCopula(2), x)
this returns
Parameter estimate(s): 3.044912
Cramer-von Mises statistic: 0.0004143588 with p-value 0.8616384
let test :
gofEVCopula(gumbelCopula(3), x)
this returns:
arameter estimate(s): 3.044912
Cramer-von Mises statistic: 0.0004143588 with p-value 0.8556444
So if I well understand this function gofCopula only indicate that the gumbel family is a good fit and we can not decide on the best parameter of the gumbel copula as the results were the same!
So which test we could use to know that actually the gumbal copula with parameter 3 and not 2 fit best the dependancy?
Thanks a lot!