This is the third part of the series on volatility modelling. For other parts of the series follow the tag volatility.

In this exercise set we will use GARCH models to forecast volatility.

Answers to the exercises are available here.

**Exercise 1**

Load the `rugarch`

and the `FinTS`

packages. Next, load the `m.ibmspln`

dataset from the `FinTS`

package. This dataset contains monthly excess returns of the S&P500 index from Jan-1926 to Dec-1999 (Ruey Tsay (2005) Analysis of Financial Time Series, 2nd ed. ,Wiley, chapter 3).

Also, load the `forecast`

package which we will use for auto-correlation graphs.

**Exercise 2**

Excess S&P500 returns are defined as a regular `zoo`

variable. Convert this to a time series variable with correct dates.

**Exercise 3**

Plot the excess S&P500 returns along with its ACF and PACF graphs and comment on the apparent correlation.

**Exercise 4**

Plot the squared excess S&P500 returns along with its ACF and PACF graphs and comment on the apparent correlation.

**Exercise 5**

Using the results from exercise-3, estimate a suitable ARMA model for excess returns assuming normal errors.

**Exercise 6**

Using the results from exercise-4, estimate a suitable ARMA model for excess returns without assuming normal errors.

**Exercise 7**

Using the results from exercises 5 and 6, estimate a more parsimonious model that has better fit.

**Exercise 8**

Generate 10 steps ahead forecast for the model from exercise-7

**Exercise 9**

Plot the excess returns forecast.

**Exercise 10**

Plot the volatility forecast.

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