Setting forecasting model parameters using unconstrained direct search methods: an empirical evaluation

Exponential smoothing (ES) forecasting models represent an important tool that conjugates compactness, ease of implementation, and robustness. The parameterization (i.e., the determination of the parameters) of an ES model can be represented as a (non-linear) minimization problem. A solution to the problem consists of the ES model’s parameter values that minimize the forecast error. Nonetheless, the task of solving such a minimization problem represents a challenge in that it should balance the accuracy of the resulting forecasts and the computational time required, especially when the parameterization concerns hundreds of time series and models. Therefore, in this paper, we discuss the empirical performance of two derivative free search methods for solving the minimization problem, and compare them with other, well-assessed search procedures. In doing so, we propose an adaptation of the general exponential smoothing model to handle box-constraints on parameter values. In the computational experiments, the derivative free methods displayed a performance similar to that of a gradient-based method, requiring only a fraction of the computation effort.