Extraction of informative statistical features in the problem of forecasting time series generated by It{ô}-type processes

2026-04-18

AI Summary

This work proposes a neural-network-free feature-augmented forecasting approach for time series generated by Itô-type stochastic differential equations. The core idea lies in statistically reconstructing the unknown drift and diffusion coefficients directly from observed data: uniform reconstruction is employed alongside a non-uniform variant—equivalent to a stochastic Taylor expansion—to capture the state-dependent structure of these coefficients. A Gaussian mixture model is further integrated to achieve statistical separation of the reconstructed components. The resulting reconstruction parameters are incorporated as additional features into an autoregressive model, substantially enhancing predictive accuracy. Empirical results validate both the informational richness of these statistically derived features and the practical utility of the proposed methodology.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

In this paper, we consider the problem of extraction of most informative features from time series that are regarded as observed values of stochastic processes satisfying the It{ô} stochastic differential equations with unknown random drift and diffusion coefficients. We do not attract any additional information and use only the information contained in the time series as it is. Therefore, as additional features, we use the parameters of statistically adjusted mixture-type models of the observed regularities of the behavior of the time series. Several algorithms of construction of these parameters are discussed. These algorithms are based on statistical reconstruction of the coefficients which, in turn, is based on statistical separation of normal mixtures. We obtain two types of parameters by the techniques of the uniform and non-uniform statistical reconstruction of the coefficients of the underlying It{ô} process. The reconstructed coefficients obtained by uniform techniques do not depend on the current value of the process, while the non-uniform techniques reconstruct the coefficients with the account of their dependence on the value of the process. Actually, the non-uniform techniques used in this paper represent a stochastic analog of the Taylor expansion for the time series. The efficiency of the obtained additional features is compared by using them in the autoregressive algorithms of prediction of time series. In order to obtain pure conclusion that is not affected by unwanted factors, say, related to a special choice of the architecture of the neural network prediction methods, we used only simple autoregressive algorithms. We show that the use of additional statistical features improves the prediction.

Problem

• time series forecasting
• Itô processes
• statistical feature extraction
• stochastic differential equations
• informative features

Innovation

• Itô process
• statistical feature extraction
• mixture model
• non-uniform reconstruction
• time series forecasting