DOI: https://doi.org/10.20535/kpi-sn.2020.3.209877

BAYESIAN DATA ANALYSIS IN MODELING AND FORECASTING NONLINEAR NONSTATIONARY PROCESSES

Liudmyla B. Levenchuk, Petro I. Bidyuk

Abstract


Background. Nonlinear nonstationary processes that are available in various spheres of human activity are characterized by numerous uncertainties, fuzziness, incompleteness and low precision data. To perform forecasting of such processes it is necessary to carry out correctly the data processing that is why the problem of development and practical use of the new processing methods is very urgent. The methods should provide a possibility for performing high quality input data processing aiming to quality modeling and forecasting the processes under study.

Objective. A short review of the Bayesian data analysis methods will be provided and an original methodology for identification and taking into consideration of possible uncertainties that are available in the problems of modeling and forecasting developed. And a new combined probabilistic and statistical model will be proposed for modeling and forecasting nonlinear nonstationary processes.

Methods. A combined implementation methodology has been proposed that includes the following: Bayesian data processing technics, an optimal filter for preliminary data processing, linear and nonlinear regression for formal description and forecasting conditional variance and probabilistic model in the form of Bayesian network to forecast nonlinear nonstationary processes.

Results. The proposed modeling method was tested on the problem of forecast estimation using the financial market data. The statistical data hired describe evolution of stock prices for well-known company. The computational experiments performed showed that quality of the short-term forecasts for volatility and the nonlinear nonstationary financial process itself are improved substantially thanks to the optimal filtering procedure and rational model structure selection. Application of the complex model that uses Bayesian network provided a possibility for improvement of probabilistic forecasts used for performing trade operations at the stock market.

Conclusions. Forecasts estimation for nonlinear nonstationary processes is an urgent problem that can be solved in various ways. The proposed probabilistic and statistical method for estimating probabilistic forecasts used for performing trade operations at the stock market generated high quality results and will be extended and improved in the future.


Keywords


Bayesian data analysis; Nonlinear nonstationary processes; Kalman filter; Bayesian network; Regression model; Forecasts combining

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