Recently, a model has been proposed to explain the statistics of the variability of interspike intervals of ganglion cells in the retina of goldfish under steady-state stimulation. In this note, it is shown that the dynamical behaviour of the model, both under steady-state and dynamical stimuli, is characterized by input-invariance of the output random process after a time transformation. This allows to study the signal-processing properties of the model, and to test its applicability by a more complete experimental analysis.