I try to test a time series for white noise. The ultimate goal is to show that scaling volatility from daily to longer time periods by the square-root of time rule is justified.
Fore white noise I found the classical tests such as the Ljung-Box test. An example of its application can be found in Forecasting: principles and practice.
What I was wondering is the following: tests like the Ljung-Box test look at auto-correlations which need to be (close to) zero for White noise.
On the other hand we need a constant volatility thus homoscedasticity. Why is it that the "white noise" tests do not test this property of white noise? Or do they test it indirectly?
How can I test homoscedasticity in the time series setting. Tests such as Breusch-Pagan need covariates if I see it correctly.