I am doing research estimating the value at risk for non-normally distributed assets. I need help in the process of estimating the parameters of Student's t distribution and which method to use. I would highly appreciate any assistance in this issue.
The pdfs of Student-t distributions have asymptotically Paretian tails, and the tail shape parameter (aka the maximal moment exponent) is equal to the distribution's degrees of freedom parameter. Assuming you have enough observations, you could estimate the Pareto parameter using the so-called Hill method (named after Bruce Hill, 1975). A word of caution: Use of the Hill method (and derived methods) is often criticized in fairly broad and rather unqualified ways. The main point to remember when using Hill's method is to use only observations that fall "safely" in the distribution's tails. Where this region lies differs from distribution to distribution. The only reasonably "safe" way is to plot the data in double-log coordinates: if the distribution does have Paretian tails, you'll see it in the graph, and you'll know where to set the cutoff for the observations that belong in the respective left and right tails.
In software R use the function fitdistr ( package MASS). For more information: http://stat.ethz.ch/R-manual/R-patched/library/MASS/html/fitdistr.html
A modified version of the Hill estimator can be used to estimate degrees of freedom if the assumption is the tails are t distributed. You can calculate (I) hill estimator from data (ii) hill estimator from theoretical normal distribution with same cut off. Then use the fact that the bias of hill estimator is largest for normal distribution and decreases as distribution is more fat tailed.