Linear discrete-time process plus disturbance models are regularly used for model-based control applications. In minimum variance control applications, the disturbance model is used to predict the disturbance over the time delay horizon, and the control action is computed to eliminate the predicted disturbance effect. The disturbance model is a time series model containing Autoregressive (AR) and Moving Average (MA) elements; such models have a nonlinear parameterization. In order to generate confidence intervals for the parameters and model predictions, it is necessary to linearize the model. The resulting inference regions are local in scope. An alternative is to use a profile likelihood approach, proposed by Bates and Watts (1989). In the profiling approach, parameters are perturbed over a specified range of values, conditional estimates of the remaining parameters are obtained, and the excess sum of squares is computed for the new parameter estimates. The profiling approach eliminates the approximation due to linearization; the only approximation remaining is the coverage probability. Profiling techniques can provide a more accurate indication of the precision and behaviour of parameter estimates and model predictions. The model predictions application represents a generalized profiling problem in which functions of the estimated parameters are being consided. The likelihood function for time series model estimation is typically formulated in terms of the 1-step ahead prediction error (the random shock or innovations sequence). However, if a multi-step ahead prediction is used as the basis for estimating the parameters, the resulting prediction error is a moving average time series. One approach for developing the likelihood function for a multi-step ahead estimation approach is to formulate this estimation problem as a weighted least squares (WLS) problem. The WLS formulation can be used to impose the fact that the prediction errors are no longer independent, and allows the multi-step ahead based estimation problem to be posed as an equivalent 1-step ahead estimation problem. In this paper, the WLS formulation is presented. With the WLS approach, the statistical properties of the excess sum of squares function have to be determined; a summary of the properties is presented. The Generalized Profiling approach is illustrated using several examples with different dynamic characteristics. In particular, the impact of the prediction horizon used in the parameter estimation step is examined.