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.

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.

Exercise

Compute GARCH covariance

Instructions