In this problem you will fit a t-distribution by maximum likelihood to the daily log returns for BMW. The data are in the data set bmw that is part of the evir package. Run the following code: Note:...

In this problem you will fit a t-distribution by maximum likelihood to the daily log returns for BMW. The data are in the data set bmw that is part of the evir package. Run the following code:

Note: The R code defines a function loglik bmw that is minus the loglikelihood. See Chap. 10 of An Introduction to R for more information about functions in R. Also, see page 59 of this manual for more about maximum likelihood estimation in R. optim minimizes this objective function and returns the MLE (which is mle bmw$par) and other information, including the Hessian of the objective function evaluated at the MLE (because hessian=TRUE—the default is not to return the Hessian).

 (a) What does the function dstd do, and what package is it in?

 (b) What does the function solve do?

 (c) What is the estimate of ν, the degrees-of-freedom parameter? (d) What is the standard error of ν?