Exercise

# Effect of mean model on volatility predictions

In practice, returns and volatility are modeled in separate processes. Typically the mean assumptions influence predicted returns, but have a minor effect on the volatility estimations.

In this exercise, you will examine the impact of GARCH model mean assumptions on volatility estimations by comparing two GARCH models. They have been defined with different mean assumptions and fitted with S&P 500 data.

The model with "constant mean" assumption has results saved in `cmean_result`

, and estimated volatility saved in `cmean_vol`

. The model with "AR(1)" or 1-lag autoregressive mean assumption has results saved in `armean_result`

, and estimated volatility saved in `armean_vol`

. The `matplotlib.pyplot`

and `numpy`

modules have been imported as `plt`

and `np`

respectively.

Instructions

**100 XP**

- Print out and review model fitting summaries of
`cmean_result`

and`armean_result`

. - Plot the volatility estimation
`cmean_vol`

and`armean_vol`

from both models. - Use
`.corrcoef()`

function from`numpy`

package to calculate the correlation efficient.