MODELING THE RISKS OF THE MODERN EDUCATIONAL PROCESS USING HETEROSCEDASTICITY MODELS - SKIDAN, VLADYSLAVA; DEMKIVSKA, TETIANA; VOLIVACH, ANTОNINA; CHUPRYNKA, NANALIYA (Herald of Khmelnytskyi National University. Technical sciences, 2025)
The paper analyzes educational risks, justifies the feasibility of using heteroscedastic process models to predict educational risks, and provides examples of educational risks that can be predicted using heteroscedastic models. A time series was selected for the study, which reflects the dynamics of observations of the weekly number of connections to the online platform before and during the pandemic. To analyze the given series for heteroscedasticity, the method of visual analysis of the residuals of a low-order autoregressive model was used. The econometric package EViews was used for modeling. If volatility is observed (i.e., the variance of the residuals changes over time), this can be observed in the form of an increase or decrease in the spread of the residuals over time or a periodic increase or decrease in the spread. An ARCH(2) model was constructed and tested for adequacy based on the squares of the residuals of a low-order autoregressive model. Analysis of the statistical characteristics of this model showed its inadequacy. To improve the modeling, the ARCH(2) model was expanded by introducing an autoregressive component into its composition. For this purpose, a series of conditional variance was constructed, ACF and CHACF were analyzed for the obtained series, and the order of the autoregressive component models was determined, with which the previously constructed ARCH(2) model can be expanded. A series of GARCH models of different orders was constructed and the best model was determined among the set of constructed models that can be used to describe the dynamics of a given time series. The constructed GARCH(2,3) model provides an opportunity to predict the future volatility of connections to the online platform. This can be useful for developing educational risk management strategies and resource planning. Based on the identified patterns of heteroscedasticity, one can try to develop quantitative indicators that would signal an increase or decrease in educational risks in a timely manner. Such research can deepen understanding of the nature of educational risks in the context of using online platforms and contribute to the development of more effective strategies for managing them.
Keywords: time series; heteroskedastic process; model; adequacy criterion; static characteristics; autocorrelation and partial autocorrelation function