The object of research. The object of research is modeling and forecasting nonlinear nonstationary processes presented in the form of time-series data. Investigated problem. There are several popular approaches to solving the problems of adequate model constructing and forecasting nonlinear nonstationary processes, such as autoregressive models and recurrent neural networks. However, each of them has its advantages and drawbacks. Autoregressive models cannot deal with the nonlinear or combined influence of previous states or external factors. Recurrent neural networks are computationally expensive and cannot work with sequences of high length or frequency. The main scientific result. The model for forecasting nonlinear nonstationary processes presented in the form of the time series data was built using convolutional neural networks. The current study shows results in which convolutional networks are superior to recurrent ones in terms of both accuracy and complexity. It was possible to build a more accurate model with a much fewer number of parameters. It indicates that one-dimensional convolutional neural networks can be a quite reasonable choice for solving time series forecasting problems. The area of practical use of the research results. Forecasting dynamics of processes in economy, finances, ecology, healthcare, technical systems and other areas exhibiting the types of nonlinear nonstationary processes. Innovative technological product. Methodology of using convolutional neural networks for modeling and forecasting nonlinear nonstationary processes presented in the form of time-series data. Scope of the innovative technological product. Nonlinear nonstationary processes presented in the form of time-series data.
The article considers the problem of forecasting nonlinear nonstationary processes, presented in the form of time series, which can describe the dynamics of processes in both technical and economic systems. The general technique of analysis of such data and construction of corresponding mathematical models based on autoregressive models and recurrent neural networks is described in detail. The technique is applied on practical examples while performing the comparative analysis of models of forecasting of quantity of channels of service of cellular subscribers for a given station and revealing advantages and disadvantages of each method. The need to improve the existing methodology and develop a new approach is formulated.
Background. The problem of forecasting nonlinear nonstationary processes presented in the form of time series is very relevant, since such series can describe dynamics of the processes in both technical and economic systems. To establish the best model, various metrics are used to assess the quality of forecasts, such as R^2, RMSE, MAE, MAPE. However, in many tasks, when optimizing the model according to the selected criterion, the model becomes worse in relation to another criterion. Therefore it is important to understand which metric must be used to optimize and assess the quality of the forecast in the given task. Objective. The aim of the paper is to develop a criteria base for assessing forecasts of nonlinear nonstationary processes, as well as an approach to choosing a metric in accordance to the specificity of the set forecasting problem. Methods. The paper presents a comparative analysis of the basic metrics for the regression problem, their theoretical and practical meaning, advantages and disadvantages in various cases. New approaches are proposed based on the results of the analysis. Results. Based on the analysis of the selected data, it is shown that by optimizing the model according to the selected criterion, the model becomes worse in relation to another criterion. A criterion basis for assessing forecasts of nonlinear nonstationary processes has been formed, as well as an approach to the selection of a quality criterion in accordance with the specifics of the set forecasting problem. To minimize an absolute error, the RMSE (MSE, R^2) and MAE metrics are analysed and recommended, depending on the need to work with outliers. The RMSLE metric is proposed for solving the problems of minimizing the relative metric, for solving the shown problems of the MAPE metric for this class of problems. Conclusions. The paper shows the importance of choosing a metric that must be used to optimize and assess the quality of the forecasts in the given task. The obtained criterion base and approach can be used in further research to solve practical prob- lems in modelling and forecasting nonlinear nonstationary processes and to develop new methods or general method for solving such problems.
The study is directed towards development of an adaptive decision support system for modeling and forecasting nonlinear nonstationary processes in economy, finances and other areas of human activities. The structure and parameter adaptation procedures for the regression and probabilistic models are proposed as well as the respective information system architecture and functional layout are developed. The system development is based on the system analysis principles such as adaptive model structure estimation, optimization of model parameter estimation procedures, identification and taking into consideration of possible uncertainties met in the process of data processing and mathematical model development. The uncertainties are inherent to data collecting, model constructing and forecasting procedures and play a role of negative influence factors to the information system computational procedures. Reduction of their influence is favourable for enhancing the quality of intermediate and final results of computations. The illustrative examples of practical application of the system developed proving the system functionality are provided.
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