Exercise

Observe the impact of model parameters

In this exercise, you will call the predefined function simulate_GARCH() again, and study the impact of GARCH model parameters on simulated results.

Specifically, you will simulate two GARCH(1,1) time series, they have the same omega and alpha, but different beta as input.

Recall in GARCH(1,1), since \(\beta\) is the coefficient of lag-1 variance, if the \(\alpha\) is fixed, the larger the \(\beta\), the longer the duration of the impact. In other words, high or low volatility periods tend to persist. Pay attention to the plotted results and see whether you can verify the \(\beta\) impact.

Instructions 1/2

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  • 1
    • Generate a GARCH(1,1) process with 200 simulations, omega = 0.1, alpha = 0.3, and beta = 0.2 as input.
  • 2
    • Generate a GARCH(1,1) process with 200 simulations,omega = 0.1, alpha = 0.3, and beta = 0.6 as input.