Hi!

I am doing a project where I look for seasonalities in stock prices. E.g. we have created dummies for "turn of month effect", the last day of every month and the first day of the next month will have the value 1.
We need to find out whether to use OLS or GARCH methods due to heteroskedasticity.
We are analysing one effect at the time.

So first we have the day of week effect, where we regress the days of week dummies on the Log return of the index.
The data is from 1996 to 2020.

First I use the tsset command and create the times series.

Then I run the regression:
reg IndexReturn dayOfMonthDummy

and this will by the output. We cant reject the H0 of heteroskedasticity,


chi2(1) = 0.00
Prob > chi2 = 0.9776

But when I run the test from for ARCH:
estat archlm

lags(p) | chi2 df Prob > chi2
-------------+-------------------------------------------------------------
1 | 297.097 1 0.0000

I get this, which means there are ARCH effects.
We dont know what to do here. Are the time-series heteroskedastitic or not?
Thank you so much in advance.

Mathias