Exercise

# Using acf plots to reveal volatility

This exercise follows on from the previous R exercise where we looked for visible signs of volatility in a financial time series. For the Dow Jones returns from 2008-11 in `djx`

and the simulated normal and t-distributed data in `ndata`

and `tdata`

, respectively, you will calculate and plot the **sample autocorrelation functions** (acf) using the command `acf()`

.

While very little evidence of serial correlation is found in these plots, the picture changes dramatically when we look at absolute or squared return data. The real returns in the Dow Jones return series `djx`

behave very differently to the simulated data. The serial correlation in absolute or squared returns is a consequence of volatility, which causes large returns to be followed by further large returns, although not necessarily of the same sign.

`djx`

, `ndata`

, and `tdata`

are available in your workspace.

Instructions

**100 XP**

- Set up the plotting region to show 3 plots at a time (this has been done for you).
- Plot the sample acf of
`djx`

and the simulated normal and t-distributed data`ndata`

and`tdata`

. - Plot the sample acf of the absolute values of the three series.
- Plot the sample acf of the squares of the values of the three series.