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
.
This exercise is part of the course
GARCH Models in Python
Exercise instructions
- Calculate correlation between GARCH standardized residuals
resid_eur
andresid_cad
. - Calculate covariance with GARCH volatility
vol_eur
,vol_cad
and the correlation computed in the previous step. - Plot the calculated
covariance
.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Calculate correlation
corr = np.____(____, ____)[0,1]
print('Correlation: ', corr)
# Calculate GARCH covariance
covariance = ____ * ____ * ____
# Plot the data
plt.plot(____, color = 'gold')
plt.title('GARCH Covariance')
plt.show()