I know there are already several threads on this, but none seem to explicitly cover what I want. I have a set of financial data (pulled straight from Bloomberg) and am trying to fit a t-distribution (with theoretical discussion of MLE). I know it can't be solved in closed form and am looking at EM and Newton-Raphson currently, but some issues have come up:
- I'm not sure there's any way I can justify that my data is incomplete (data is closing price of stock index over last year)
- DF is as unknown as $\mu$ and $\sigma$, so all 3 parameters need to be estimated.
- Data is univariate
The above methods seem to need known df or incomplete data. Is this strictly true? Do I need to modify the methods (if so please show) or choose new ones (if so please specify)?