Preview

Vestnik of the Plekhanov Russian University of Economics

Advanced search

Current Approaches to Forecasting Non-Stationary Time Series

https://doi.org/10.21686/2413-2829-2026-2-45-53

Abstract

The article studies current methods of foresting non-stationary time series effective to analyze social and economic systems, finance markets and other fields with high rate of uncertainty. Comparative analysis of classical approaches (ARIMA, GARCH) and their modifications was carried out as they take into account structural changes, non-linear dependences and exogenous factors. Special attention was paid to neural network methods, including LSTM, transformers (Informer, Autoformer) and their hybrid versions that demonstrate high efficiency working with long successions. Apart from that adaptive methods were studied such as sliding window and their integration with machine learning to raise accuracy of forecasting in conditions of uncertainty. The research includes critical analysis of restrictions of classical models ARIMA and GARCH, the review of current architecture of neural nets for time series, practical aspects of choosing models depending on data characteristics, promising lines in developing methods, including adaptive algorithms and ensemble approaches.

About the Author

A. V. Slipchenko
Plekhanov Russian University of Economics
Russian Federation

Alexey V. Slipchenko - Post-Graduate Student of the Department of Applied Informatics and Information  Security

36 Stremyanny Lane, Moscow, 109992, Russian Federation



References

1. Gladilin D. L. Primenenie kovariatsionnogo analiza s printsipom «skolzyashchego okna» dlya otsenki svyaznosti nestatsionarnykh vremennykh ryadov [Application of Covariance Analysis with a Sliding Window Principle for Assessing Connectivity of Non-Stationary Time Series]. Eksperimentalnaya psikhologiya [Experimental psychology], 2020, Vol. 13, No. 2, pp. 15–28. (In Russ.).

2. Ardia D., Bluteau K., Boudt K. Bayesian Estimation of the GARCH (1, 1) Model with Student-t Innovations. The R Journal, 2019, Vol. 11, No. 2, pp. 370–384.

3. Bateni M. et al. Forecast of Rainfall Distribution Based on Fixed Sliding Window Long Short-Term Memory. Engineering Applications of Computational Fluid Mechanics, 2022, Vol. 16, No. 1, pp. 248–261.

4. Bollerslev T. Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 1986, Vol. 31, No. 3, pp. 307–327.

5. Bollerslev T. Glossary to ARCH (GARCH). Available at: https://ssrn.com/abstract=1263250 (accessed 01.05.2025).

6. Box G. E. P., Jenkins G. M., Reinsel G. C., Ljung G. M. Time Series Analysis: Forecasting and Control. 5th ed. Wiley, 2015.

7. Chang S. et al. Dilated Recurrent Neural Networks. Advances in Neural Information Processing Systems 30 (NIPS 2017), 2017, pp. 77–87.

8. Cont R. Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues. Quantitative Finance, 2001, Vol. 1, pp. 223–236.

9. Engle R. F. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 1982, Vol. 50, No. 4, pp. 987–1007.

10. FAST: A Forecasting Model with Adaptive Sliding Window and Time Locality Integration for Dynamic Cloud Workloads. IEEE Transactions on Cloud Computing, 2022.

11. Glosten L. R., Jagannathan R., Runkle D. E. On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance, 1993, Vol. 48, No. 5, pp. 1779–1801.

12. Greff K., Srivastava R. K., Koutník J., Steunebrink B. R., Schmidhuber J. LSTM: A Search Space Odyssey. IEEE Transactions on Neural Networks and Learning Systems, 2017, Vol. 28, No. 10, pp. 2222–2232.

13. Hochreiter S., Schmidhuber J. Long Short-Term Memory. Neural Computation, 1997, Vol. 9, No. 8, pp. 1735–1780.

14. Hyndman R. J., Athanasopoulos G. Forecasting: Principles and Practice. 3rd ed. OTexts, 2021. Available at: https://otexts.com/fpp3/ (accessed 01.05.2025).

15. Hyndman R. J., Khandakar Y. Automatic Time Series Forecasting: The forecast Package forR. Journal of Statistical Software, 2008, Vol. 27, No. 3, pp. 1–22.

16. Kontopoulou V. I., Panagopoulos A. D., Kakkos I., Matsopoulos G. K. A Review of ARIMA vs Machine Learning Approaches for Time Series Forecasting in Data Driven Networks. Available at: https://www.researchgate.net/publication/372771636_A_Review_of_ARIMA_vs_Machine_Learning_Approaches_for_Time_Series_Forecasting_in_Data_Driven_Networks#read

17. Nelson D. B. Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 1991, Vol. 59, No. 2, pp. 347–370.

18. Smith T. et al. pmdarima: ARIMA estimators for Python. 2017. Available at: https://alkaline-ml.com/pmdarima/ (accessed 01.05.2025).

19. Vaswani A. et al. Attention is All You Need. Advances in Neural Information Processing Systems 30 (NIPS 2017), 2017, pp. 5998–6008.

20. Wu H. et al. Autoformer: Decomposition Transformers for Auto-Correlation-based Long-Term Series Forecasting. Advances in Neural Information Processing Systems 34 (NeurIPS 2021), 2021, pp. 22419–22430.

21. Yildirim H., Bekun F. V. Predicting Volatility of Bitcoin Returns with ARCH, GARCH and EGARCH Models. Financial Innovation, 2022, Vol. 8, pp. 1–15.

22. Zhou T. et al. Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting. Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI-21), 2021, Vol. 35, No. 12, pp. 11106–11115.


Review

For citations:


Slipchenko A.V. Current Approaches to Forecasting Non-Stationary Time Series. Vestnik of the Plekhanov Russian University of Economics. 2026;(2):45-53. (In Russ.) https://doi.org/10.21686/2413-2829-2026-2-45-53

Views: 271

JATS XML


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2413-2829 (Print)
ISSN 2587-9251 (Online)