ARMA+EGARCH Model with Negative Omega Parameter I am using R (version 3.2.5) to model the log-returns on a financial time series. I used the modelfit function from the "rugarch" package to fit an ARMA(0,1)+EGARCH(1,1) with a constant in the conditional mean equation and Normal errors model to the said log-returns. 
The modelfit function carries out the log-likelihood maximization on the log of the conditional variance of EGARCH in simultaneous ARMA+EGARCH model estimation. This has two consequences. Firstly, maximization of log-variance instead of variance automatically ensures that the conditional variance of the hybrid model is positive. Secondly, no restrictions are required on the signs of the parameters of the EGARCH variance equation which generally assures a faster and more reliable optimization procedure. 
Upon inspection of the signs of the optimal parameters, I found that omega is negative. The plot of the News Impact Curve (NIC) shows a curve which declines the greater positive and negative errors are. 
So my questions are:


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*Is there any previous literature evidence of a hybrid ARMA+EGARCH model which displays a negative omega parameter?

*From a model practical interpretability perspective, is it more reliable to refit the above model by imposing constraints on positiveness omega?

 A: I don't think there is a problem with negative $\omega$. The conditional variance equation of the EGARCH model as used in "rugarch" is*
$$ \sigma_t^2 = \exp (\omega+\dotsc). $$
If we neglect the terms in $\dotsc$ for the moment, we have $\omega<0$ if $\sigma_t^2<e^0=1$. By scaling your data you could always get there. And if the conditional variance is roughly constant and there is little variation around the unconditionl variance $\sigma^2$, neglecting the term in $\dotsc$ can be justified. This is just one example; you could also get negative $\omega$ in other settings if you play with the parameter values of the conditional variance equation.
Negative $\omega$ values are also encountered in applications, see e.g. Chen & Kuan (2002), Table IX.

*Note that this is not the only possible definition of the EGARCH model; see e.g. Tsay (2010, 3rd ed.) section 3.8 and 3.8.1.
References


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*Chen, Yi‐Ting, and Chung‐Ming Kuan. "Time irreversibility and EGARCH effects in US stock index returns." Journal of Applied Econometrics 17.5 (2002): 565-578.

*Tsay, Ruey S. Analysis of financial time series. Vol. 543. John Wiley & Sons, 2005 (2010 3rd ed).

