Experimental characterisation of aircraft dynamic stall can be a challenging and complex system identification activity. In this article, the authors present a method that combines dynamic wind tunnel testing with parameter estimation techniques to study the nonlinear pitching moment dynamics of a 1/12 scale Hawk model undergoing moment stall. The instrumentation setup allows direct calculation of angular acceleration terms, such as pitch acceleration, and avoids post-processing steps involving differentiation of signals. Data collected from tests, carried out at 20 m/s and 30 m/s, are used for a brief aerodynamic analysis of the observed stall hysteresis. Then an output-error-based parameter estimation process is used to parameterise dynamic stall models and furthermore, illustrate that in a scenario where the model's heave motion is constrained. The observed nonlinear behaviour arises from the nonlinear angle of attack and linear pitch rate components.