Ljung-Box test

Another powerful tool to check autocorrelations in the data is the Ljung-Box test. In this exercise, you will practice detecting autocorrelation in the standardized residuals by performing a Ljung-Box test.

The null hypothesis of Ljung-Box test is: the data is independently distributed. If the p-value is larger than the specified significance level, the null hypothesis cannot be rejected. In other words, there is no clear sign of autocorrelations and the model is valid.

You will use the same GARCH model as the previous exercise. Its standardized residuals are saved in std_resid.

This is a part of the course

“GARCH Models in Python”

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Exercise instructions

Import the module needed for Ljung-Box tests from the statsmodels package.
Perform a Ljung-Box test up to lag 10, and save the result in lb_test.
Print and review p-values from the Ljung-Box test result.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

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

# Perform the Ljung-Box test
lb_test = ____(std_resid , ____ = ____, return_df = True)

# Print the p-values
print('P-values are: ', ____.iloc[0,1])

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