Interpretable Machine Learning for Price Index Forecasting: A Case Study with Rolling Windows and SHAP
Received: 18 September 2025 | Revised: 13 October 2025 and 30 October 2025 | Accepted: 10 November 2025 | Online: 8 December 2025
Corresponding author: Ali Ben Mrad
Abstract
Economic forecasting of indicators, such as the Price Index, remains a challenging task due to the strong non-stationarity and nonlinearities inherent in financial and macroeconomic time series. This study uses Portugal as a case study and compares several Machine Learning (ML) models, including Linear Regression, Ridge, Lasso, Support Vector Regression (SVR), Random Forests, Multi-Layer Perceptrons (MLPs), and XGBoost, under two evaluation protocols: a traditional static split and a rolling-window approach. The results show that static evaluation leads to poor predictive performance, with R² values close to zero or negative, highlighting the limitations of conventional validations when dealing with non-stationary data. In contrast, the rolling-window approach over a five-year horizon significantly improves predictive accuracy, with XGBoost achieving R² values above 0.94, thus confirming the adaptability of this method. To ensure interpretability, the study applied SHapley Additive Explanations (SHAP) to analyze both local and global feature contributions. The findings underline the predominant role of exchange rate, inflation, and oil prices in explaining the Portuguese Price Index. Combining rolling-window learning with explainable AI (XAI), thus, provides a robust and interpretable framework for policymakers and investors to better understand economic dynamics.
Keywords:
price index forecasting, machine learning, XGBoost, explainable artificial intelligence, interpretable machine learning, rolling-window evaluation, economic policy forecastingDownloads
References
R. T. Baillie, "Long Memory Processes and Fractional Integration in Econometrics," Journal of Econometrics, vol. 73, no. 1, pp. 5–59, July 1996. DOI: https://doi.org/10.1016/0304-4076(95)01732-1
J. Xi, "Machine Learning Using Nonstationary Data." SSRN Preprint, 2025. DOI: https://doi.org/10.2139/ssrn.5215521
M. Schnaubelt, "A Comparison of Machine Learning Model Validation Schemes for Non-stationary Time Series Data," arXiv, 2019.
S. Lundberg and S.-I. Lee, "A Unified Approach to Interpreting Model Predictions," arXiv, 2017.
G. E. P. Box, G. M. Jenkins, G. C. Reinsel, and G. M. Ljung, Time series analysis: forecasting and control, 5th ed. Hoboken, NJ, USA: John Wiley & Sons, Inc, 2016.
R. F. Engle, "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, vol. 50, no. 4, July 1982, pp. 987–1007. DOI: https://doi.org/10.2307/1912773
T. Bollerslev, "Generalized Autoregressive Conditional Heteroskedasticity," Journal of Econometrics, vol. 31, no. 3, pp. 307–327, Apr. 1986. DOI: https://doi.org/10.1016/0304-4076(86)90063-1
G. P. Zhang, "Time Series Forecasting Using a Hybrid ARIMA and Neural Network Model," Neurocomputing, vol. 50, pp. 159–175, Jan. 2003. DOI: https://doi.org/10.1016/S0925-2312(01)00702-0
R. S. Tsay, Analysis of Financial Time Series, 1st ed. Hoboken, NJ, USA: John Wiley & Sons, 2005. DOI: https://doi.org/10.1002/0471746193
M. G. P. Garcia, M. C. Medeiros, and G. F. R. Vasconcelos, "Real-time Inflation Forecasting with High-dimensional Models: The Case of Brazil," International Journal of Forecasting, vol. 33, no. 3, pp. 679–693, July 2017. DOI: https://doi.org/10.1016/j.ijforecast.2017.02.002
H. Hassani and E. S. Silva, "Forecasting UK Consumer Price Inflation using Inflation Forecasts," Research in Economics, vol. 72, no. 3, pp. 367–378, Sept. 2018. DOI: https://doi.org/10.1016/j.rie.2018.07.001
M. A. Alwadi, "Fuel Sales Price Forecasting using Time Series, Machine Learning, and Deep Learning Models," Engineering, Technology & Applied Science Research, vol. 15, no. 3, pp. 22360–22366, June 2025. DOI: https://doi.org/10.48084/etasr.10348
Y. Liu, Z. Li, R. Nekhili, and J. Sultan, "Forecasting cryptocurrency returns with machine learning," Research in International Business and Finance, vol. 64, 2023, Art. no. 101905. DOI: https://doi.org/10.1016/j.ribaf.2023.101905
M. Nabipour, P. Nayyeri, H. Jabani, S. Shahab, and A. Mosavi, "Predicting Stock Market Trends Using Machine Learning and Deep Learning Algorithms Via Continuous and Binary Data; a Comparative Analysis," IEEE Access, vol. 8, pp. 150199–150212, 2020. DOI: https://doi.org/10.1109/ACCESS.2020.3015966
T. Fischer and C. Krauss, "Deep Learning with Long Short-Term Memory Networks for Financial Market Predictions," European Journal of Operational Research, vol. 270, no. 2, pp. 654–669, Oct. 2018. DOI: https://doi.org/10.1016/j.ejor.2017.11.054
S. Makridakis, E. Spiliotis, and V. Assimakopoulos, "The M4 Competition: Results, Findings, Conclusion and Way Forward," International Journal of Forecasting, vol. 34, no. 4, pp. 802–808, Oct. 2018. DOI: https://doi.org/10.1016/j.ijforecast.2018.06.001
T. Chen and C. Guestrin, "XGBoost: A Scalable Tree Boosting System," in 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, Aug. 2016, pp. 785–794. DOI: https://doi.org/10.1145/2939672.2939785
S. Hochreiter and J. Schmidhuber, "Long Short-Term Memory," Neural Computation, vol. 9, no. 8, pp. 1735–1780, Nov. 1997. DOI: https://doi.org/10.1162/neco.1997.9.8.1735
D. M. Q. Nelson, A. C. M. Pereira, and R. A. De Oliveira, "Stock Market’s Price Movement Prediction with LSTM Neural Networks," in 2017 International Joint Conference on Neural Networks (IJCNN), Anchorage, AK, USA, May 2017, pp. 1419–1426. DOI: https://doi.org/10.1109/IJCNN.2017.7966019
L. J. Tashman, "Out-of-Sample Tests of Forecasting Accuracy: an Analysis and Review," International Journal of Forecasting, vol. 16, no. 4, pp. 437–450, Oct. 2000. DOI: https://doi.org/10.1016/S0169-2070(00)00065-0
M. El Mahjouby, K. El Fahssi, M. Taj Bennani, M. Lamrini, and M. El Far, "Machine Learning Techniques for Predicting and Classifying Exchange Rates between US Dollars and Japanese Yen," Engineering, Technology & Applied Science Research, vol. 14, no. 5, pp. 16266–16271, Oct. 2024. DOI: https://doi.org/10.48084/etasr.8216
F. Doshi-Velez and B. Kim, "Towards A Rigorous Science of Interpretable Machine Learning," arXiv, 2017.
M. T. Ribeiro, S. Singh, and C. Guestrin, "‘Why Should I Trust You?’: Explaining the Predictions of Any Classifier," in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco California USA, Aug. 2016, pp. 1135–1144. DOI: https://doi.org/10.1145/2939672.2939778
M. Sundararajan, A. Taly, and Q. Yan, "Axiomatic Attribution for Deep Networks," in 34th International Conference on Machine Learning, Sydney, Australia, 2017, Art. no. 70.
M. T. Ribeiro, S. Singh, and C. Guestrin, "Anchors: High-Precision Model-Agnostic Explanations," Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32, no. 1, Apr. 2018. DOI: https://doi.org/10.1609/aaai.v32i1.11491
D. Martens, J. Vanthienen, W. Verbeke, and B. Baesens, "Performance of Classification Models from a User Perspective," Decision Support Systems, vol. 51, no. 4, pp. 782–793, Nov. 2011. DOI: https://doi.org/10.1016/j.dss.2011.01.013
L. Antwarg, R. M. Miller, B. Shapira, and L. Rokach, "Explaining Anomalies Detected by Autoencoders using SHAPLEY Additive Explanations," Expert Systems with Applications, vol. 186, Dec. 2021, Art. no. 115736. DOI: https://doi.org/10.1016/j.eswa.2021.115736
A. Barredo Arrieta et al., "Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI," Information Fusion, vol. 58, pp. 82–115, June 2020. DOI: https://doi.org/10.1016/j.inffus.2019.12.012
N. Köse, Y. E. Gür, and E. Üna, "Deep Learning and Machine Learning Insights Into the Global Economic Drivers of the Bitcoin Price," Journal of Forecasting, vol. 44, no. 5, pp. 1666-1698, 2025. DOI: https://doi.org/10.1002/for.3258
W. Sun, Y. Wang, L. Zhang, X. H. Chen, and Y. H. Hoang, "Enhancing Economic Cycle Forecasting Based on Interpretable Machine Learning and News Narrative Sentiment," Technological Forecasting and Social Change, vol. 215, June 2025, Art. no. 124094. DOI: https://doi.org/10.1016/j.techfore.2025.124094
N. Anesti, E. Kalamara, and G. Kapetanios, "Forecasting with Machine Learning Methods and Multiple Large Datasets," Econometrics and Statistics, Sept. 2024, Art. no. SSRN5311094. DOI: https://doi.org/10.1016/j.ecosta.2024.08.003
A. B. Mrad, "Price Index Dataset." GitHub, 2025, [Online]. Available: https://github.com/AliBenMrad/price-index-dataset/raw/refs/heads/main/BD%20Portugal%20NS.xlsx.
Downloads
How to Cite
License
Copyright (c) 2025 Ali Ben Mrad, Hamad Mohammad Alsowayyan
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.
