Dear Ghazi Al-Assaf ,

I would like to recommend you to perform a statistical test for outliers (anomalies) in empirical data before building the model. Given that the data distribution are non-Gaussian, then normalizing transformations can be recommended for anomaly detection and building the non-linear model. See, for example, the link

https://www.researchgate.net/publication/282329599_Statistical_anomaly_detection_techniques_based_on_normalizing_transformations_for_non-Gaussian_data

Conference Paper Statistical anomaly detection techniques based on normalizin...

EGARCH and TARCH are to basic model for asymmetric case, as in yours

I suggest you read the following textbook:

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-EHEP003218.html

dear ghazi

please take a look at the 5 parts of illustration lectures on y-tube set by hossain acadamy . it worth to watch at this link. good luck

www.sayedhossain.com/