Метод структурного аналізу гетероскедастичного часового ряду з використанням бустингової EGARCH-моделі

Abstract

A comprehensive method for the structural analysis of a heteroscedastic time series is developed in this study. The approach combines an original boosting-based model of the conditional mean with an EGARCH specification of the conditional variance. The method is designed to quantitatively localize and formally identify hidden dynamic modes of the process driven by substantial external perturbations. A model-complexity index is introduced to quantify the degree of structural complication in the process and to indicate when additional boosting-based corrections to the forecast are required. The method also incorporates a multiscale assessment of disturbance-intensity levels, an analysis of the dependence between the conditional mean and conditional variance, and clustering of the decision vectors of trees within the ensemble. This enables the detection of distinct patterns and modes without relying on auxiliary features. It is noted that the method can be extended to other classes of heteroscedastic process models that may be used in place of the EGARCH component. An algorithm is proposed for identifying intervals of elevated volatility and heightened structural complexity, as well as for assessing their statistical significance using volatility-, entropy-, and econometrics-based metrics. The practical application of the method is demonstrated using public air quality monitoring data for the city of Vinnytsia, specifically the PM1 indicator. The results show high predictive accuracy (coefficient of determination — 0.97) and make it possible to localize short-term stochastic disturbances and long-term structural anomalies that remain undetected by classical ARIMA, ARIMA-GARCH, Prophet, or multifactor intelligent models based on feature-engineering techniques such as those provided by the Python library tsfresh. A generalized analytical conclusion was generated automatically with the assistance of a Large Language Model. The study shows that the proposed structural-complexity index can reveal anomalies within the internal structure of the process that are not accompanied by increases in conditional variance and that reflect the emergence of new systematic influences or changes in the process’s dynamic mechanism. The example provided confirms the effectiveness of the method for systems-analysis tasks and forms a basis for its further use in decision-support systems for assessing environmental conditions and other complex systems.