Validation of GARCH model assumptions

GARCH Models in Python

Chelsea Yang

Data Science Instructor

Visual check

Raw return data

Standardized residuals

Describe the correlation of a variable with itself given a time lag
Existence of autocorrelation in the standardized residuals indicates the model may not be sound

To detect autocorrelation:

ACF plot

Red area in the plot indicates the confidence level (alpha = 5%)

from statsmodels.graphics.tsaplots import plot_acf

plot_acf(my_data, alpha = 0.05)

Test whether any of a group of autocorrelations of a time series are different from zero
H0: the data is independently distributed
P-value < 5%: the model is not sound

# Import the Python module
from statsmodels.stats.diagnostic import acorr_ljungbox

# Perform the Ljung-Box test
lb_test = acorr_ljungbox(std_resid , lags = 10)

# Check p-values
print('P-values are: ', lb_test[1])

GARCH Models in Python