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:
- 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
?
mu
... as opposed to nonconstantmu
? Also, have you tried looking for references yourself? Did you only find papers with positiveomega
? How many have you checked? Also, is there now a functionmodelfit
? I cannot find it in the package documentation. $\endgroup$mu
(where there was a choice to have nonconstantmu
) or did you fit models that include a constant calledmu
? For simple GARCH models you cannot have negativeomega
, of course. But have you checked studies specifically using EGARCH? $\endgroup$