ENSEMBLE OF ADAPTIVE PREDICTORS FOR MULTIVARIATE NONSTATIONARY SEQUENCES AND ITS ONLINE LEARNING

Abstract

Context. In this research, we explore an ensemble of metamodels that utilizes multivariate signals to generate forecasts. The ensemble includes various traditional forecasting models such as multivariate regression, exponential smoothing, ARIMAX, as well as nonlinear structures based on artificial neural networks, ranging from simple feedforward networks to deep architectures like LSTM and transformers. Objective. A goal of this research is to develop an effective method for combining forecasts from multiple models forming metamodels to create a unified forecast that surpasses the accuracy of individual models. We are aimed to investigate the effectiveness of the proposed ensemble in the context of forecasting tasks with nonstationary signals. Method. The proposed ensemble of metamodels employs the method of Lagrange multipliers to estimate the parameters of the metamodel. The Kuhn-Tucker system of equations is solved to obtain unbiased estimates using the least squares method. Additionally, we introduce a recurrent form of the least squares algorithm for adaptive processing of nonstationary signals. Results. The evaluation of the proposed ensemble method is conducted on a dataset of time series. Metamodels formed by combining various individual models demonstrate improved forecast accuracy compared to individual models. The approach shows effectiveness in capturing nonstationary patterns and enhancing overall forecasting accuracy. Conclusions. The ensemble of metamodels, which utilizes multivariate signals for forecast generation, offers a promising approach to achieve better forecasting accuracy. By combining diverse models, the ensemble exhibits robustness to nonstationarity and improves the reliability of forecasts.