EGARCH and GARCH effects with White Noise squared residuals

I'm asked to model a series which it's returns are white noise and after adjusting a regression like $$r_t=c$$ and looking it's squared residuals (white noise too) I'm asked to adjust a GARCH and EGARCH model to them.

Surprisingly, all coefficients both in GARCH and EGARCH are significative, how is this possible if the squared residuals were white noise?

• Hi: How are you concluding that the squared residuals from the regression are white noise ? It's a little unusual that the squared residuals would be white noise since they are always positive. – mark leeds Dec 7 '20 at 22:47
• From the correlogram, I cannot reject the null in any case. – GregorSilvei Dec 7 '20 at 23:48
• Hi: I'm not sure what the best way is to do the test but its probably better to use some analytical-formal test like some analog of box-leung. I'm confident that there must be one but I don't know it off the top of my head. – mark leeds Dec 8 '20 at 2:25
• Hi: It looks like you can do a regression on the squared residuals and then use the LM test. cemfi.es/~arellano/lmtesting.pdf – mark leeds Dec 8 '20 at 2:30