Forecasting Apple Inc. Stock prices: A comparative analysis of ARIMA, LSTM, and ARIMA-LSTM models

Research Article
Open access

Forecasting Apple Inc. Stock prices: A comparative analysis of ARIMA, LSTM, and ARIMA-LSTM models

Yiyang Zou 1*
  • 1 Nanjing University of Information Science and Technology    
  • *corresponding author qs808796@student.reading.ac.uk
Published on 18 June 2025 | https://doi.org/10.54254/3029-0880/2025.23870
AORPM Vol.4 Issue 1
ISSN (Print): 3029-0899
ISSN (Online): 3029-0880

Abstract

Stock price fluctuation and prediction is a problem that has attracted much attention. There exist many mathematical and statistical problems behind it. In essence, the key to solving this problem lies in capturing the linear and nonlinear characteristics in the time series to predict future price movements. This study investigates the predictive capabilities of two distinct methodologies—Long Short-Term Memory (LSTM) networks and Autoregressive Integrated Moving Average (ARIMA) models—using Apple Inc. (AAPL) stock price data spanning 2016 to 2024. By synthesizing theoretical frameworks with empirical analysis, the research evaluates how each model captures linear trends and nonlinear fluctuations, ultimately proposing a hybrid ARIMA-LSTM architecture to enhance forecasting accuracy. Finally, according to the principal characteristics of the two models, the ARIMA-LSTM hybrid model is constructed. The results show that the hybrid model significantly outperforms single models in terms of RMSE and directional accuracy. Combined with error distribution visualization and volatility analysis, the hybrid model demonstrates efficient performance in achieving prediction optimization through the decomposition of linear and nonlinear components. It provides a new methodological perspective for financial time series modeling.

Keywords:

ARIMA model, LSTM model, ARIMA-LSTM model, stock prices forecasting

Zou,Y. (2025). Forecasting Apple Inc. Stock prices: A comparative analysis of ARIMA, LSTM, and ARIMA-LSTM models . Advances in Operation Research and Production Management,4(1),66-74.
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References

[1]. Box, G. E. P., & Jenkins, G. M. (1994). Time series analysis: Forecasting and control (3rd ed.). Prentice Hall.

[2]. Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735

[3]. Khashei, M., & Bijari, M. (2010). A novel hybrid ARIMA-ANN model for electricity demand forecasting. Energy Policy, 38(8), 4176–4184. https://doi.org/10.1016/j.enpol.2010.03.057

[4]. Zhang, G. P. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159–175. https://doi.org/10.1016/S0925-2312(01)00702-0

[5]. Siami-Namini, S., Tavakoli, N., & Namin, A. S. (2018). A comparative analysis of forecasting financial time series using ARIMA, LSTM, and hybrid models. Journal of Risk and Financial Management, 11(4), 89. https://doi.org/10.3390/jrfm11040089

[6]. Huang, W. (1998). Forecasting exchange rates using ARIMA and neural networks. Journal of Systems Science and Complexity, 11(3), 257–266.

[7]. Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2018). Statistical and machine learning forecasting methods: Concerns and ways forward. PLOS ONE, 13(3), e0194889. https://doi.org/10.1371/journal.pone.0194889

[8]. Zhang, Y., Li, Y., Zhang, G., & Wang, J. (2020). A hybrid ARIMA-LSTM model for COVID-19 cases prediction. Scientific Reports, 10, Article 22265. https://doi.org/10.1038/s41598-020-79304-z

[9]. Qiu, J., Wang, B., & Zhou, C. (2021). Residual learning for hybrid ARIMA-LSTM in financial time series. Expert Systems with Applications, 184, 115523. https://doi.org/10.1016/j.eswa.2021.115523

[10]. Wang, Y., Zhang, S., & Zhang, H. (2022). Linear component decomposition in hybrid ARIMA-LSTM models. IEEE Access, 10, 12345–12356. https://doi.org/10.1109/ACCESS.2022.3146789

[11]. Chen, T., Yin, H., Chen, X., & Wang, L. (2021). Hybrid ARIMA-LSTM for financial time series forecasting. IEEE Transactions on Neural Networks and Learning Systems, 32(12), 5729–5741. https://doi.org/10.1109/TNNLS.2020.3027860

[12]. Oreshkin, B. N., Carpov, D., Chapados, N., & Bengio, Y. (2020). N-BEATS: Neural basis expansion analysis for interpretable time series forecasting. Proceedings of the International Conference on Learning Representations (ICLR).

[13]. Diebold, F. X., & Mariano, R. S. (1995). Comparing predictive accuracy. Journal of Business & Economic Statistics, 13(3), 253–263. https://doi.org/10.1080/07350015.1995.10524599

[14]. Cont, R. (2001). Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance, 1(2), 223–236. https://doi.org/10.1080/713665670

[15]. Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679–688. https://doi.org/10.1016/j.ijforecast.2006.03.001

[16]. Galeshchuk, S., & Mukherjee, S. (2017). Deep networks for financial time series prediction. International Journal of Machine Learning and Computing, 7(4), 105–110. https://doi.org/10.18178/ijmlc.2017.7.4.632

[17]. Ribeiro, M. T., Singh, S., & Guestrin, C. (2016). "Why should I trust you?": Explaining the predictions of any classifier. Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 1135–1144. https://doi.org/10.1145/2939672.2939778

[18]. Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., & Polosukhin, I. (2017). Attention is all you need. Advances in Neural Information Processing Systems (NeurIPS), 30, 5998–6008.

[19]. Hutter, F., Kotthoff, L., & Vanschoren, J. (Eds.). (2019). Automated machine learning: Methods, systems, challenges. Springer. https://doi.org/10.1007/978-3-030-05318-5

[20]. Lim, K., Luo, W., & Schmedders, K. (2021). Implied volatility and stock return predictability. Journal of Financial Economics, 142(1), 1–22. https://doi.org/10.1016/j.jfineco.2021.05.035

[21]. Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., Agarwal, S., Herbert-Voss, A., Krueger, G., Henighan, T., Child, R., Ramesh, A., Ziegler, D., Wu, J., Winter, C., ... Amodei, D. (2020). Language models are few-shot learners. Advances in Neural Information Processing Systems (NeurIPS), 33, 1877–1901.

[22]. Howard, J., & Gugger, S. (2020). fastai: A layered API for deep learning. Journal of Machine Learning Research, 21(1), 1–6.

[23]. Zhou, Z., Li, X., & Wang, Y. (2022). Edge computing for real-time financial forecasting. IEEE Internet of Things Journal, 9(18), 17845–17856. https://doi.org/10.1109/JIOT.2022.3175190

Cite this article

Zou,Y. (2025). Forecasting Apple Inc. Stock prices: A comparative analysis of ARIMA, LSTM, and ARIMA-LSTM models . Advances in Operation Research and Production Management,4(1),66-74.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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Journal：Advances in Operation Research and Production Management

Volume number: Vol.4
Issue number: Issue 1
ISSN：3029-0880(Print) / 3029-0899(Online)

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References

[1]. Box, G. E. P., & Jenkins, G. M. (1994). Time series analysis: Forecasting and control (3rd ed.). Prentice Hall.

[2]. Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735

[3]. Khashei, M., & Bijari, M. (2010). A novel hybrid ARIMA-ANN model for electricity demand forecasting. Energy Policy, 38(8), 4176–4184. https://doi.org/10.1016/j.enpol.2010.03.057

[4]. Zhang, G. P. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159–175. https://doi.org/10.1016/S0925-2312(01)00702-0

[5]. Siami-Namini, S., Tavakoli, N., & Namin, A. S. (2018). A comparative analysis of forecasting financial time series using ARIMA, LSTM, and hybrid models. Journal of Risk and Financial Management, 11(4), 89. https://doi.org/10.3390/jrfm11040089

[6]. Huang, W. (1998). Forecasting exchange rates using ARIMA and neural networks. Journal of Systems Science and Complexity, 11(3), 257–266.

[7]. Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2018). Statistical and machine learning forecasting methods: Concerns and ways forward. PLOS ONE, 13(3), e0194889. https://doi.org/10.1371/journal.pone.0194889

[8]. Zhang, Y., Li, Y., Zhang, G., & Wang, J. (2020). A hybrid ARIMA-LSTM model for COVID-19 cases prediction. Scientific Reports, 10, Article 22265. https://doi.org/10.1038/s41598-020-79304-z

[9]. Qiu, J., Wang, B., & Zhou, C. (2021). Residual learning for hybrid ARIMA-LSTM in financial time series. Expert Systems with Applications, 184, 115523. https://doi.org/10.1016/j.eswa.2021.115523

[10]. Wang, Y., Zhang, S., & Zhang, H. (2022). Linear component decomposition in hybrid ARIMA-LSTM models. IEEE Access, 10, 12345–12356. https://doi.org/10.1109/ACCESS.2022.3146789

[11]. Chen, T., Yin, H., Chen, X., & Wang, L. (2021). Hybrid ARIMA-LSTM for financial time series forecasting. IEEE Transactions on Neural Networks and Learning Systems, 32(12), 5729–5741. https://doi.org/10.1109/TNNLS.2020.3027860

[12]. Oreshkin, B. N., Carpov, D., Chapados, N., & Bengio, Y. (2020). N-BEATS: Neural basis expansion analysis for interpretable time series forecasting. Proceedings of the International Conference on Learning Representations (ICLR).

[13]. Diebold, F. X., & Mariano, R. S. (1995). Comparing predictive accuracy. Journal of Business & Economic Statistics, 13(3), 253–263. https://doi.org/10.1080/07350015.1995.10524599

[14]. Cont, R. (2001). Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance, 1(2), 223–236. https://doi.org/10.1080/713665670

[15]. Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679–688. https://doi.org/10.1016/j.ijforecast.2006.03.001

[16]. Galeshchuk, S., & Mukherjee, S. (2017). Deep networks for financial time series prediction. International Journal of Machine Learning and Computing, 7(4), 105–110. https://doi.org/10.18178/ijmlc.2017.7.4.632

[17]. Ribeiro, M. T., Singh, S., & Guestrin, C. (2016). "Why should I trust you?": Explaining the predictions of any classifier. Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 1135–1144. https://doi.org/10.1145/2939672.2939778

[18]. Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., & Polosukhin, I. (2017). Attention is all you need. Advances in Neural Information Processing Systems (NeurIPS), 30, 5998–6008.

[19]. Hutter, F., Kotthoff, L., & Vanschoren, J. (Eds.). (2019). Automated machine learning: Methods, systems, challenges. Springer. https://doi.org/10.1007/978-3-030-05318-5

[20]. Lim, K., Luo, W., & Schmedders, K. (2021). Implied volatility and stock return predictability. Journal of Financial Economics, 142(1), 1–22. https://doi.org/10.1016/j.jfineco.2021.05.035

[21]. Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., Agarwal, S., Herbert-Voss, A., Krueger, G., Henighan, T., Child, R., Ramesh, A., Ziegler, D., Wu, J., Winter, C., ... Amodei, D. (2020). Language models are few-shot learners. Advances in Neural Information Processing Systems (NeurIPS), 33, 1877–1901.

[22]. Howard, J., & Gugger, S. (2020). fastai: A layered API for deep learning. Journal of Machine Learning Research, 21(1), 1–6.

[23]. Zhou, Z., Li, X., & Wang, Y. (2022). Edge computing for real-time financial forecasting. IEEE Internet of Things Journal, 9(18), 17845–17856. https://doi.org/10.1109/JIOT.2022.3175190

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