My question is related to the thread Negative values for AIC in General Mixed Model. I often get negative AIC values from the software I use. I notice it most when I'm doing time series. But here is what I don't get. When defining the AIC like
$$AIC = 2k-2\ln(L)$$
$L$, the likelihood, is a joint probability and to my understanding must be bound between 0 and 1. Mathematically this implies the $AIC$ must be positive. So I don't know what my software is giving me for the value labeled $AIC$. Any thoughts?