I am estimating a GJR-GARCH(1,1) model with variance targeting in R. As data I am using returns on some stock indices. While calculating the GARCH models I obtain $\alpha=0$ for some indices. From what I understand this means that volatility is constant. The code I am using for GJR-GARCH estimation is as follows and is based on the
garch.spec <- ugarchspec( variance.model = list(model="gjrGARCH", garchOrder=c(1,1), variance.targeting=TRUE), mean.model = list(armaOrder=c(0,0))) garch.fit <- ugarchfit( spec=garch.spec, data=data, solver="nlminb", solver.control=list(trace=0))
And an example of my results:
mu alpha1 beta1 gamma1 omega -0.0057893647 0.0000000000 0.8666747910 0.1641368776 0.0002181445
Could you please give some advice whether such results are plausible or should I be worried? Of course I can provide the data that causes problems. And obviously I am running univariate estimations so I am taking only one series of index returns at a time.
edit: using a different solver algorithm I was able to obtain different results, however, $\alpha$ still seems to be extremely low for this model.
mu alpha1 beta1 gamma1 omega 3.432135e-04 8.508012e-08 8.607153e-01 2.113815e-01 1.727337e-05
What is the reasoning behind such low values of $\alpha$, since I am obtaining very similar results in R and in Matlab, so I doubt there is a mistake in the coefficient estimation.