Robust estimation of the area of adequacy of forecasting one-parameter model of exponential smoothing

Abstract

The problem of parameter synthesis of a forecasting one-parameter model of exponential smoothing for predictive estimation of indicators of the organizational and technical system is considered. To select intervals of a given quality in the range of admissible values of the internal parameter, the criterion of absolute error of multiple forecasts is selected. It allowed the formation of an analytical retrospective model with «soft» constraints. As a result, a method of robust estimation of the adequacy area of the forecasting one-parameter exponential smoothing model is developed, which allows one to analytically evaluate the limits of the adequacy area of the forecasting model depending on the requirements for its retrospective accuracy. The proposed method allows the user to specify a set of permissible retrospective errors depending on the requirements of forecasting specifications. The proposed method can be used for parameter adjustment of one-parameter forecasting models and serves as a decision support tool in the forecasting process. The simulation results are interval estimates, which are preferable to point ones in the process of parameter synthesis. Unlike search methods, the analytical form of retrospective dependencies allows you to obtain a solution with high accuracy and, if necessary, provides the analyst with the opportunity for graphical analysis of the adequacy area of the model. The example shows the fragment of estimating the dynamics of the time series in a retrospective analysis with a depth of three values and specified limit relative errors of 1–4 %. Under such conditions, the area for a reasonable selection of the adjustment parameter is determined by the combined intervals of a width of about 20 % of the initial range of acceptable values.