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