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.
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:
- Is there any previous literature evidence of a hybrid ARMA+EGARCH model which displays a negative
- From a model practical interpretability perspective, is it more reliable to refit the above model by imposing constraints on positiveness