Application of Adaptive and Multiplicative Models for Analysis and Forecasting of Time Series

Abstract

The paper considers two forms of models: seasonal and non-seasonal analogues of oscillations.  Additive models belong to the first form, which reflects a relatively constant seasonal wave, as well as a wave that dynamically changes depending on the trend. The second ones are multiplicative models. The paper analyzes the basic adaptive models: Brown, Holt and autoregression models. The parameters of adaptation and layout are considered by the method of numerical estimation of parameters. The mechanism of reflection of oscillatory (seasonal or cyclic) development of the studied process through reproduction of the scheme of moving average and the scheme of autoregression is analyzed. The paper determines the optimal value of the smoothing coefficient through adaptive polynomial models of the first and second order. Prediction using the Winters model (exponential smoothing with multiplicative seasonality and linear growth) is proposed. The application of the Winters model allows us to determine the calculated values and forecast using the model of exponential smoothing with multiplicative seasonality and linear growth. The results are calculated according to the model of exponential smoothing and with the multiplicative seasonality of Winters. The best model is determined, which allows improving the forecast results through the correct selection of the optimal value of α. The paper also forecasts the production volume according to the Tayle-Vage model, i.e., the analysis of exponential smoothing with additive seasonality and linear growth is given to determine the calculated values α. The paper proves that the additive model makes it possible to build a model with multiplicative seasonality and exponential tendency. The paper proves statements that allow one to choose the right method for better modeling and forecasting of data.