Exercise

# Compute GARCH covariance

Covariance describes the relationship of movement between two price return series. Recall dynamic covariance can be computed by ρ * σ1 * σ2, where σ1, σ2 are volatility estimates from GARCH models, and ρ is the simple correlation between GARCH standardized residuals.

In this exercise, you will practice computing dynamic covariance with GARCH models. Specifically you will use two foreign exchange time series data: EUR/USD and USD/CAD (shown in the plot). Their price returns have been fitted by two GARCH models, and the volatility estimates are saved in `vol_eur`

and `vol_cad`

. In addition, their standardized residuals are saved in `resid_eur`

and `resid_cad`

respectively. In addition, the `numpy`

package has been imported as `np`

.

Instructions

**100 XP**

- Calculate correlation between GARCH standardized residuals
`resid_eur`

and`resid_cad`

. - Calculate covariance with GARCH volatility
`vol_eur`

,`vol_cad`

and the correlation computed in the previous step. - Plot the calculated
`covariance`

.