Exercise

# Fitting t distribution to data

A **Student t distribution** is generally a much better fit to daily, weekly, and monthly returns than a normal distribution.

You can create one by using the `fit.st()`

function in the QRM package. The resulting fitted model has a parameter estimates component `par.ests`

which can be assigned to a list `tpars`

in order to store its values of `nu`

, `mu`

, and `sigma`

for later use:

```
> tfit <- fit.st(ftse)
> tpars <- tfit$par.ests
> tpars
nu mu sigma
2.949514e+00 4.429863e-05 1.216422e-02
```

In this exercise, you will fit a Student t distribution to the daily log-returns of the Dow Jones index from 2008-2011 contained in `djx`

. Then, you will plot a histogram of the data and superimpose a red line to the plot showing the fitted t density. The `djx`

data and `QRM`

package have been loaded for you.

Instructions

**100 XP**

- Use
`fit.st()`

to fit a Student t distribution to the data in`djx`

and assign the results to`tfit`

. - Assign the
`par.ests`

component of the fitted model to`tpars`

and the elements of`tpars`

to`nu`

,`mu`

, and`sigma`

, respectively. - Fill in
`hist()`

to plot a histogram of`djx`

. - Fill in
`dt()`

to compute the fitted t density at the values`djx`

and assign to`yvals`

. Refer to the video for this equation. - Fill in
`lines()`

to add a red line to the histogram of`djx`

showing the fitted t density.