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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$likelihood
[1] 90854.67
> fit1$AIC
[1] 90884.67
> par1 # par1 <- length(fit1$parameters$vect), number of fitted parameters
[1] 4
> 2*par1-2*log(fit1$likelihood) # AIC
[1] -14.83403
> fit2$likelihood
[1] 90766.44
> fit2$AIC
[1] 90824.44
> par2 # par2 <- length(fit2$parameters$vect), number of fitted parameters
[1] 7
> 2*par2-2*log(fit2$likelihood) # AIC
[1] -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.

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Looking at the source code of the package:

aic <- likelihood+2*(length(param.vector$vect)+nrow(x.nought))

x.nought is some additional parameter particular to the tbats model, and I can't really comment on it.

It becomes clear though the likelihood object is actually equal to $-2\ln(L)$.

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