# AIC and likelihood statistics from tbats (forecast-package in R)

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.

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)\$.