A systematic approach to the synthesis of forecasting mathematical models for interrelated non-stationary time series - Щелкалин, Виталий Николаевич (Eastern-European Journal of Enterprise Technologies, 2015)
The study presents a schematic diagram suitable to describe almost any presently known combined, hybrid or decomposition model for forecasting time series. The diagram has laid the basis for the suggested methods of structural identification of sparse nonlinear models of interrelated non-stationary time series on the basis of “Caterpillar”-SSA methods, fast orthogonal search, a group accounting method, and SARIMA models. Often a plurality of measured features is insufficient for building a model of satisfactory quality. It is necessary to extend the set of features by means of functional transformations of initial signs to decrease the uncertainty of the linear model. The study suggests that components of the “Caterpillar”-SSA method expansion, applied to the forecast and exogenous time series, should be viewed as generated variables. In one of the suggested models, the method of fast orthogonal search is used for optimal thinning. In the other––the method of group arguments accounting is applied to thin the Kolmogorov-Gabor polynomial, which is built on the expansion components of the “Caterpillar”-SSA method that is applied to the forecast and exogenous time series. To correct the forecasts in both models, we used the seasonal model of auto-regression––the integrated moving average. The analysis and modeling of the considered method prove its effectiveness in the search of an optimal model structure, and the time for determining the model parameters considerably shortens alongside. Therefore, a systematic approach is a set of methods and tools that facilitates overall researching of the properties and structure of the interrelated non-stationary time series and presents them as systems with all complex inter-element relationships.