Home  Journals  Financial Analytics: Science and Experience  2(376) - 2026 April–June

Comparative analysis of the use of deep and machine learning models for forecasting non-stationary financial time series using the example of the IMOEX index

Received: 30 January 2026

Accepted: 25 February 2026

Available online: 28 May 2026

Subject Heading: FINANCIAL INSTRUMENTS

JEL Classification: C45, G23, G28, G51

Pages: 78-86

https://doi.org/10.24891/dtxvot

Subject. Comparison of machine learning and deep learning architectures in the task of forecasting non-stationary financial time series using the example of the daily closing prices of the Moscow Exchange Index (IMOEX).
Objectives. Critically evaluate modern architectures and demonstrate methodological pitfalls and statistical artifacts in predicting absolute prices, as well as evaluate the real predictive value of models, not just formal metrics.
Methods. Based on the historical daily data of the IMOEX index (2010–2025), 20 signs were generated. The sample is split chronologically (80/10/10) to avoid data leakage. We compared the performance of 8 models (including LSTM, N-Linear, PatchTST, Chronos) using MAE, RMSE, and R² metrics.
Results. The hypothesis of a statistical artifact has been confirmed. The high R? (> 0.97) of most models is due to the fact that they simply repeat a consistent forecast (R² = 0.976). The leaders are the fundamental Chronos model and the simple linear N-Linear (R² = 0.98). They slightly exceeded the baseline forecast. PatchTST showed a low result (R² = 0.32) due to conflicts in methodology and architecture.
Conclusions. The value of the model for non–stationary series lies in its ability to bypass a strong persistent baseline. The opposite architectures showed the best results: the complex Chronos and the simple N-Linear. This proves that there is no single "best" solution. Quantum analytics needs both types of tools: fundamental models for accuracy (LFT) and linear models for speed (HFT).

Keywords: time series forecasting, deep learning, nonstationarity, statistical artifact, fundamental models

References:

1. Staudemeyer R.C., Morris E.R. Understanding LSTM – a tutorial into Long Short-Term Memory Recurrent Neural Networks. arXiv, September, 2019. DOI: 10.48550/arXiv.1909.09586
2. Evans C., Pappas K., Xhafa F. Utilizing artificial neural networks and genetic algorithms to build an algo-trading model for intra-day foreign exchange speculation. Mathematical and Computer Modelling, 2013, vol. 58, iss. 5-6, pp. 1249–1266. DOI: 10.1016/j.mcm.2013.02.002
3. Zhou Haoyi, Zhang Shanghang, Peng Jieqi et al. Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting. arXiv, December, 2021. DOI: 10.48550/arXiv.2012.07436
4. Wu Haixu, Xu Jiehui, Wang Jianmin, Long Mingsheng. Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting. arXiv, June 2021. DOI: 10.48550/arXiv.2106.13008
5. Zhou Tian, Ma Ziqing, Wen Qingsong et al. FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting. arXiv, January 2022. DOI: 10.48550/arXiv.2201.12740
6. Zeng Ailing, Chen Muxi, Zhang Lei, Xu Qiang. Are Transformers Effective for Time Series Forecasting? arXiv, May 2022. DOI: 10.48550/arXiv.2205.13504
7. Ansari A.F., Stella L., Turkmen C. et al. Chronos: Learning the Language of Time Series. arXiv, March 2024. DOI: 10.48550/arXiv.2403.07815
8. Prata M., Masi G., Berti L. et al. Lob-based deep learning models for stock price trend prediction: a benchmark study. Artificial Intelligence Review, 2024, vol. 57. DOI: 10.1007/s10462-024-10715-4
9. Uçkan T. Integrating PCA with deep learning models for stock market Forecasting: An analysis of Turkish stocks markets. Journal of King Saud University – Computer and Information Sciences, 2024, vol. 36, iss. 8, no. 102162. DOI: 10.1016/j.jksuci.2024.102162
10. Hu Yifan, Li Yuante, Liu Peiyuan et al. FinTSB: A Comprehensive and Practical Benchmark for Financial Time Series Forecasting. arXiv, February 2025. DOI: 10.48550/arXiv.2502.18834
11. Gülmez B. Stock price prediction with optimized deep LSTM network with artificial rabbits optimization algorithm. Expert Systems With Applications, 2023, vol. 227, no. 120346. DOI: 10.1016/j.eswa.2023.120346
12. Li Zhe, Qi Shiyi, Li Yiduo, Xu Zenglin. Revisiting Long-term Time Series Forecasting: An Investigation on Linear Mapping. arXiv, May 2023. DOI: 10.48550/arXiv.2305.10721
13. Li A. Volatility Forecasting in Global Financial Markets Using TimeMixer. arXiv, September 2024. DOI: 10.48550/arXiv.2410.09062
14. Nie Yuqi, Nam H. Nguyen, Phanwadee Sinthong, Jayant Kalagnanam. A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. arXiv, November 2022. DOI: 10.48550/arXiv.2211.14730
15. Goulding C.L, Harvey C.R., Mazzoleni M.G. Breaking Bad Trends. Financial Analysts Journal, 2024, vol. 80, iss. 1, pp. 84–98. DOI: 10.1080/0015198X.2023.2270084
16. Zhao Yuwen, Hu Baojun, Wang Sizhe. Prediction of Brent crude oil price based on LSTM model under the background of low-carbon transition. arXiv, September 2023. DOI: 10.48550/arXiv.2409.12376

View all articles of issue

ISSN 2311-8768 (Online)
ISSN 2073-4484 (Print)

Journal current issue

ISSUE 2 JUNE 2026

Archive