Algorithm and practice of forecasting technological substitutions with data-based transformed models

The S-shaped growth curves such as Gompertz, Fisher-Pry (logistic), normal, and Weibull are widely used for forecasting technological substitutions. The authors have found significant improvement in the accuracy of short-term forecasts by using the Data-Based Transformation (DBT) for these models. This paper develops a specialized algorithm for obtaining the maximum likelihood estimates of the parameters for the DBT models. The underlying optimization method is tailored to the special structure of the profile log-likelihood function of the parameters characterizing the power transformation and the dependence among observations. The algorithm is self-contained and can be implemented in a personal computer environment without calling any general optimization program. The paper then illustrates the algorithm with actual data from the technological substitution of electronic for electromechanical telephone switching systems. Using this algorithm, technological forecasting practitioners can be relieved of burdensome computations for obtaining the estimates of the DBT parameters.