The Hannan-Quinn information criterion (HQIC) is a criterion for comparing statistical models fitted to the same data. If is the maximized likelihood,
is the number of estimated parameters, and is the number of observations, it is defined by
The model with the smallest HQIC is preferred. Asymptotically, its penalty for additional parameters grows more slowly than that of the Bayesian
information criterion and more rapidly than the constant penalty of the Akaike
information criterion.
is the maximized likelihood,
is the number of estimated parameters, and 
is the number of observations, it is defined by
