Exercise

# Simulate ARCH and GARCH series

In this exercise, you will simulate an ARCH(1) and GARCH(1,1) time series respectively using a predefined function `simulate_GARCH(n, omega, alpha, beta = 0)`

.

Recall the difference between an ARCH(1) and a GARCH(1,1) model is: besides an autoregressive component of \(\alpha\) multiplying lag-1 residual squared, a GARCH model includes a moving average component of \(\beta\) multiplying lag-1 variance.

The predefined function will simulate an ARCH/GARCH series based on `n`

(number of simulations), `omega`

, `alpha`

, and `beta`

(0 by default) you specify. It will return simulated residuals and variances. Afterwards you will plot and observe the simulated variances from the ARCH and GARCH process.

Instructions

**100 XP**

- Simulate an ARCH(1) process with
`omega`

= 0,1.`alpha`

= 0.7. - Simulate a GARCH(1,1) process with
`omega`

= 0,1.`alpha`

= 0.7, and`beta`

= 0.1. - Plot the simulated ARCH variances and GARCH variances respectively.