“Caterpillar”-SSA and Box-Jenkins hybrid models and methods for time series forecasting

Abstract

Trend and decomposition approaches to non-stationary time series forecasting are considered in the paper. According to them, various hybrid models for non-stationary time series forecasting, as well as identification methods for these models based on the combined use of the “Caterpillar”-SSA and Box-Jenkins methods were proposed. Hybrid mathematical models of the trend approach to forecasting, based on the “Caterpillar”-SSA and Box-Jenkins methods lie in modeling the process as deviation of actual time series values with respect to the trend component, which is represented in the proposed models by the linear recurrence formula (LRF) of the “Caterpillar”-SSA method and its approximation by the SARIMA model. The main goal of the decomposition approach to forecasting based on the “Caterpillar”-SSA and Box-Jenkins methods is the decomposition of the original time series into multiple time series with a simpler structure, considered independently of each other using the “Caterpillar”-SSA method; forecasting the data of decomposition components by SARIMA models and calculating the total forecast by combining forecasts of the constructed simplified models. The proposed models were tested on the electricity and natural gas consumption time series, and their forecasting results were compared with the results, obtained by classical probabilistic SARIMA models, generalized for the case of several seasonal components. The obtained results allow to conclude that for effective forecasts, it is necessary to carry out decomposition of the studied time series and combine different models, describing both statistical and deterministic time series components that provides the best forecasting quality.