A COMBINED APPROACH TO MODELING NONSTATIONARY HETEROSCEDASTIC PROCESSES

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Context. Nonlinear nonstationary processes are observed today in various fields of studies: economy, finances, ecology, demography etc. Very often special approaches are required for model development and forecasts estimation for the processes mentioned. The modeling methodologies have to take into consideration possible uncertainties that are encountered during data processing and model structure and parameter estimation. Objective. To develop a modified methodology for constructing models for nonlinear processes that allows for achieving high quality of forecasts. More specifically heteroscedastic processes are considered that create a wide class of nonlinear nonstationary processes and are considered in many areas of research. Method. To reach the aim of the study mentioned the following methods are used: systemic approach to model building and forecasting, modified methodology for modeling nonlinear processes, methods for identification and taking into consideration possible uncertainties. To cope with the structural uncertainties following techniques: refinement of model order applying recurrent adaptive approach to modeling and automatic search for the “best” structure using complex statistical criteria; adaptive estimation of input delay time, and the type of data distribution with its parameters; describing detected nonlinearities with alternative analytical forms with subsequent estimation of the forecasts generated. Results. The proposed modified methodology for modeling nonlinear nonstationary processes, adaptation scheme for model building, new model structures proposed. As a result of performing computational experiments, it was found that nonlinear models constructed provide a possibility for computing high quality forecasts for the process under study and their variance. Conclusions. Application of the modeling methodology proposed provides a possibility for structural and parametric adaptation of the models constructed with statistical data. The models developed exhibit acceptable adequacy and quality of short-term forecasting.