# White noise test taking into account homoscedasticity

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.

## 1 Answer

"How To Test for a homogenous error process" : In the absence of the need for a Box-Cox transformation use the residuals and form k distinct subsets .....say k=5 and N = # of observations = 100 we have 1-20 ; 21-40 ; 41-60 ; 61-80 ; 81-100 . Compute the variance in each subset and form an F test comparing successive groups and conclude about a possible breakpoint. Re-estimate model with weights derived from the max F and test to see if another of the k breakpoints is significant . If so integrate/combine the weights. This ultimately yields a set of N weights leading to Weighted Least Squares or GLS . This is how I programmed AUTOBOX to solve the problem.

• Thanjk you! You mean, I calculate the volatility on each of the subsets? This came to my mind too but isn't this too "easy"? :) – Ric Feb 23 '18 at 15:13
• yes calculate the variance of each subgroup ;;; – IrishStat Feb 23 '18 at 15:27