ets() function does not minimize AICc?

Question

I have a question that is similar to this question: ETS function in forecast package is not choosing minimized AICc

I see what the author of that question misunderstood but I basically have a reverse case based on AICc which should not be possible. Unfortunately, I cannot share my data but I think my problem is understandable from the following explanation.

I fitted a model just using

ets(data, ic="aicc")

with AICc 958.4. Because i disliked that the Gamma parameter of this model is basically 0 for reasons beyond this question, I chose to pre-define Gamma in a second model, this time

ets(data, ic="aicc", gamma=0.1)

which produced a smaller, i.e., better, AICc. (958.1 new model vs. 958.4 old model). The difference is only marginal (0.3), but I still wonder how an ets() model with more strict parameter restrictions in form of Gamma=0.1 can beat the first model. Why then didn't the first model already specify the second model automatically?

Thanks in advance

Answer 1

I am not sure how ets works, but here is one reason why a model with a manually specified parameter value can have a lower value of AICc:
There is one parameter fewer that is being estimated, hence the penalty on model complexity decreases in magnitude. Since the penalty enters with a positive sign, the AICc may also decrease. This will be the case if the drop in the log-likelihood (which enters with a negative sign) due to the change in the parameter value from the likelihood-maximizing one to the manually imposed one is smaller than the drop in the penalty.