The time-varying adaptation ability of human operators in basic manual-control tasks is barely understood. Most identification methods do not explicitly take into account any time variations. An identification procedure based on both batch and recursive autoregressive exogenous (ARX) models is presented for capturing the operator's controlled-element adaptation in compensatory tracking tasks. The operator's time delay was assumed to be constant and estimated beforehand. Conditions with constant controlled-element dynamics, matching recent experimental work, and gradual and sudden transitions in the controlled-element dynamics were considered. This study introduces a procedure to fine-tune forgetting strategies for these different conditions and for different remnant intensities. Both the use of a constant scalar forgetting factor λ and a constant forgetting matrix Λ, containing separate forgetting factors for each ARX-model parameter, was analyzed. Batch ARX-model identifications applied on conditions with constant dynamics, indicate that a high bias results when the operator's remnant is not coupled to the linear operator dynamics. By means of Monte Carlo simulations, an optimal forgetting factor is found for all conditions. For the human-operator model considered, the use of a forgetting matrix did not result in an improvement over the use of a scalar forgetting factor. An evaluation of real experimental manual-control data shows that the method has potential to capture the operator's adaptive control characteristics.