A retrospective analysis of the optimal parametric configuration of the Brown predictive model in the nonclassical range

Abstract

This study is aimed at the theoretical justification, formalization, planning, and conduct of an experiment involving a retrospective analysis of the optimal parametric configuration of Brown’s forecasting model. The relevance of this work stems from the acute problem of forecasting short time series, particularly those characterizing the dynamics of business processes in production and logistics systems. The object of the study is the process of parametric synthesis of Brown’s forecasting model, the subject is the conditions for its optimal parametric configuration. The goal is to assess the relevance of theoretical recommendations regarding the parametric synthesis of the model through a statistical retrospective analysis of its optimal parametric configuration. The tasks are: analyzing the feasible set of the smoothing parameter; designing a statistical experiment for the retrospective analysis of the optimal configuration; conducting a practical experiment and analyzing the results; and formulating recommendations for improving the parametric synthesis technology based on the experimental results. Methods of mathematical and statistical analysis were used to prove the existence, on the plane of internal parameters, of two symmetric characteristic regions with extreme properties. As a result, a method for retrospective analysis of the optimal parametric configuration of a model, suitable for analyzing the characteristics of the plane of its internal parameters, was proposed; the reliability of the analytical results was statistically confirmed using real data. Conditions are formulated under which the concept of the model’s effective memory length extends to the out-of-bounds set of the smoothing parameter. The main conclusion is the substantiated necessity of taking into account the configuration of root clusters and separately considering even and odd sample lengths when forming a point forecast.