I have quite a general question about Variance-gamma distribution. I am interested in how to estimate it's parameters given a set of training points?
I tried to find the answer in the internet, but surprisingly managed to find only a couple of relative links:
I am not an expert in R, but what I saw in R package was (as I understood) maximum likelihood estimation. They perform some iterative optimisation with different methods, starting with Skew Laplace to initialise the estimator.
In the paper they first estimate mean, variance, skewness, kurtosis through moments. Then they assume that asymmetry parameter $\theta$ is small, and set $\theta^2 = \theta^3 = 0$. And after all they solve combined equations to get all the parameter estimators. That's what I understood.
So my questions are:
- How exactly do they perform optimisation in R package? Maybe you know the place where it is described?
- What is the difference in the two methods? Which one is better to use in real life (well, maximum likelihood is better, but it is much more difficult to implement and the performance is not as good)? Are the assumptions about small $\theta$ strict in the first method?
- Where can I read more about Variance-Gamma parameter estimation?
I would be really grateful for every relative replies, papers and links. Thank you!