try different distributions for the residuals

try other garch models (ngarch, aparch, arch-m...)

Hi,

First of all, you should detect the stylized facts of your time series (characteristics):

Check if there is a multimodality or not (if yes you should use Mixture Garch models...)

Check if there is a periodicity in your data (if yes you should use the class of Periodic volatility models; PGARCH, Periodic stochastic volatility...)

Check if there is asymetry or not

Check if there is a change of behavior (if yes, the Markov Switching GARCH might be helpful).

All these checks (among others) fall in the identification of the right class of models to use. You can also try to combine (when possible of course) between those classes (for example, if you have multimodality and periodicity, you can try the Mixture of Periodic GARCH models).

Francq and Zakonian have a new GARCH book, 2ed, 2019 - try that for help as well

1. Try another distributions for the innovations like t-student.

2. The more simple, the better the model. There is no more powerful model than GARCH(1,1).

3. Look at the data first. Maybe the Volatility of your series does not meet a conditional volatility model. Get back to the roots of the data.

I think you need to ignore the normality condition and employ generalized error distribution (GED). Read around the distribution. This might help. Read Reuy Tsay Textbook on Financial Econometrics.

Thanks Tihana Škrinjarić , Ouzzani Fares , Daniel Velásquez-Gaviria and Joe Greaves for your advises, i'll try every advise ,i hope it will work

Joe Greaves I employed GED and it works just for LM arch test from lag 2 to 10 but not for lag 1 , what does it mean please

thanks for all your help, all your advises helped me, it finally worked

I also agree with those that have suggested the usage of student-t and GED error distribution assumptions because they are well suited for fatter tails than the normal distribution.

The presence of ARCH effects in your model diagnostic tests (in this case ARCH LM test) is an indication that the model in use has not managed to fully absorb all the serial correlation in your variance equation. Therefore, the model is mis-specified and you need to use a higher order GARCH. That means if you were using GARCH(1.1) then try to increase the lags to (2.2) and keep increasing lags till the auto-correlation is all soaked up assuming that you used all the GARCH procedures correctly.