What I know now is that smaller AIC values and larger likelihood values indicate better fit. I am trying to compare two models fitted to the same data. Model 2 should fit the data better, but not necessarily.
I use R, forecast package and msts- and tbats functions for fitting the models.
> fit1$likelihood  90854.67 > fit1$AIC  90884.67 > par1 # par1 <- length(fit1$parameters$vect), number of fitted parameters  4 > 2*par1-2*log(fit1$likelihood) # AIC  -14.83403 > fit2$likelihood  90766.44 > fit2$AIC  90824.44 > par2 # par2 <- length(fit2$parameters$vect), number of fitted parameters  7 > 2*par2-2*log(fit2$likelihood) # AIC  -8.83209
So, AIC value for fit2 is smaller than for fit1 (that is what I hope to get). But, the likelihood for fit1 is bigger than for fit2. What should I believe?
Also, if I have done the calculation of the parameters correctly, why are those AIC values calculated "by hand" so different that those which I get from the fits directly?
fit1 and fit2 are tbats-objects.