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.