For an EGARCH(1,1) model the ARCH and GARCH coefficients are expected to be positive. In your case they are not. That is why you have problems with the residuals and the variances. It seems that an EGARCH model is not appropriate for your data. I don't know the reason for that, I guess nobody can tell you. So the only way to fix this is to use a different model for the variance: GARCH(1,1) for example.
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