I'm fitting the t-distribution to financial data and I know of two methods to do this using R:
m s df 2.608111e-05 8.305111e-03 4.425103e+00 (6.110566e-04) (6.754816e-04) (1.375033e+00)
I believe this is using the MLE method.
mean sd nu 3.079664e-05 1.127648e-02 4.228209e+00
They don't look too far apart but there still is a difference.
1. What method does (B) use to estimate the parameters? Is it the method of moments?
2. Which method provides a higher level of accuracy?
3. I know that mean is a location parameter,
sd is a scale parameter and
nu is degrees of freedom. Do these parameters have a definition of some sort, e.g a formula, or are they simply referred to as location, scale and degrees of freedom?
4. How can I show that the moments of the t distribution are the following?
mean = μ,
skewness = 0
I've researched this online and many have said it is very complicated. Moment generating function does not work and my knowledge of methods of moments and MLE is very limited.