Abstract: In presented paper mathematical models and methods based on joint applying ideas of the “Caterpillar”-SSA and Box-Jenkins? methods are produced. This combination of models lead to a synergy and mutually compensate the opposite by nature shortcomings of each models separately and increases the accuracy and stability of the model. The further development of technique for models constructing, technique of BoxJenkins?, and improvement of themselves autoregressive integrated moving average (ARIMA) models, designed about forty years ago and remaining in present time as one of the most efficient models for modeling, forecasting and control exceeding their own rivals on whole row of criterions such as: economy on parameters quantity, labour content of models building algorithm and resource-density of their realization, on formalization and automation of models construction is produced. A novel autoregressive spectrally integrated moving average (ARSIMA) model which describes a wider class of processes in contrast to the Box-Jenkins? models is developed. Decomposition and combined forecasting methods based on “Caterpillar”-SSA method for modeling and forecasting of time series is developed. The essence of the proposed decomposition forecasting method and combined forecasting method consist in decomposing of time series (exogenous and predicted) by the “Caterpillar”-SSA method on the components, which in turn can be decomposed into components with a more simpler structure for identification, in selection from any of these components of constructive and dropping the destructive components, and in identification of those constructive components that are proactive on the propagated time series, or vice versa if its delay interval is less than the required preemption interval of forecasting, mathematical models with the most appropriate structure (in the combined approach) or its ARIMAX models (in decomposition approach) models and calculation of their predictions to the required lead time, to use the obtained models, or as a comb filter (in the case of signals modeling), or as an ensemble of models, setting the inputs of MISO model or used as a component of the combined mathematical model whose parameters are adjusted to further cooptimization method. In such models as inputs can be also include the instantaneous amplitudes, obtained after applying the Hilbert transform to the components of the expansions. The advantages of the proposed methods for models of the processes constructing is its rigorous formalization and, therefore, the possibility of complete automation of all stages of construction and usage of the models.

Keywords: modeling, filtering, forecasting, control, "Caterpillar"-SSA method, ARIMA model, "Caterpillar"-SSA – ARIMA – SIGARCH method, ARSIMA model, ARSIMA – SIGARCH model, heteroskedasticity, LevenbergMarquardt? method, Davidon–Fletcher–Powell? method, decomposition forecasting method, combined forecasting methods, Hilbert transform.

Link:

TREND, DECOMPOSITION AND COMBINED APPROACHES OF TIME SERIES FORECASTING BASED ON THE “CATERPILLAR”-SSA METHOD

Vitalii Shchelkalin

http://www.foibg.com/ijita/vol19/ijita19-2-p11.pdf