Document Type : Research Article
Authors
Faculty of Statistics, Mathematics and Computer, Allameh Tabataba'i University, Tehran, Iran
Abstract
Forecasting financial market volatility has always been a major challenge in economics and financial engineering. In this study, a hybrid approach based on FIGARCH and PLM-GARCH models combined with Long Short-Term Memory (LSTM) neural networks is proposed for modeling financial time series. The analyzed dataset of the Iran energy index covers October 30, 2016, to January 25, 2023 with 1396 observations. The PLM-GARCH model is capable of identifying long-term dependencies and periodic structures in the conditional variance of time series, while the LSTM network improves prediction accuracy by learning complex and nonlinear patterns. In this approach, the PLM-GARCH model is first used to estimate volatility, and then the residuals from the model are fed as inputs into the LSTM network to extract nonlinear behaviors. Experimental results showed that the combined PLM- GARCH-LSTM model (RMSE = 0.00209, MAPE ≈ 5.1%) outperforms the FIGARCH-LSTM model (RMSE = 0.00224, MAPE ≈ 5.8%) and significantly improves prediction accuracy. These find- ings suggest that combining econometric periodic methods with deep learning can be a powerful tool for forecasting financial volatility.
Keywords
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lockdowns on electricity demand. Electric Power Systems Research, 216:109015, 2023.
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with an application to airline company data. Data Science and Management, 6:239–246,
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neural network regression toward time-series forecasting. IEEE Transactions on Systems,
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GARCH-type models. Physica A, 616:128574, 2023.
forecasting model based on a new partition method. IEEE Access, 9:80236–80252, 2021.
[2] T. G. Andersen and T. Bollerslev. Heterogeneous information arrivals and return volatility
dynamics: Uncovering the long-run in high frequency returns. Journal of Finance, 52(3):975–
1005, 1997.
[3] E. Arif, E. Herlinawati, D. Devianto, M. Yollanda, and D. Permana. Hybridization of long
short-term memory neural network in fractional time series modeling of inflation. Frontiers
in Big Data, 6:1282541, 2024.
[4] R. T. Baillie. Long memory processes and fractional integration in econometrics. Journal of
Econometrics, 73(1):5–59, 1996.
[5] T. Bollerslev. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3):307–327, 1986.
[6] T. Bollerslev and H. O. Mikkelsen. Modeling and pricing long memory in stock market
volatility. Journal of Econometrics, 73(1):151–184, 1996.
[7] S. Bordignon, M. Caporin, and F. Lisi. Periodic long memory GARCH models. Econometric
Reviews, 27(5):569–582, 2008.
[8] G. E. P. Box and G. M. Jenkins. Time Series Analysis: Forecasting and Control. Holden-Day,
San Francisco, 1976.
[9] A. H. Bukhari, M. A. Raja, M. Sulaiman, and S. Islam. Fractional neurosequential ARFIMALSTM for financial market forecasting. IEEE Access, 8:71326–71338, 2020.
[10] K. Chen, Z. Chen, S. Wang, and Z. He. Short-term load forecasting with deep residual
networks. IEEE Transactions on Smart Grid, 10(4):3943–3952, 2019.
[11] K. Chen, Y. Zhou, and F. Dai. A LSTM-based hybrid model for financial time series forecasting. Expert Systems with Applications, 190:116261, 2022.
[12] R. Cont. Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance, 1(2):223–236, 2001.
[13] D. Devianto, K. Ramadani, A. Maiyatri, Y. Asdi, and M. Yollanda. The hybrid model of
autoregressive integrated moving average and fuzzy time series Markov chain on long-memory
data. Frontiers in Applied Mathematics and Statistics, 8:1045241, 2022.
[14] D. Devianto, M. Yollanda, A. Maiyatri, and F. Yanuar. The soft computing FFNN method
for adjusting heteroscedasticity on the time series model of currency exchange rate. Frontiers
in Applied Mathematics and Statistics, 9:1045218, 2023.
[15] D. A. Dickey and W. A. Fuller. Distribution of the estimators for autoregressive time series
with a unit root. Journal of the American Statistical Association, 74(366):427–431, 1979.
[16] R. F. Engle. Autoregressive conditional heteroskedasticity with estimates of the variance of
United Kingdom inflation. Econometrica, 50(4):987–1007, 1982.
[17] T. Fischer and C. Krauss. Deep learning with long short-term memory networks for financial
market predictions. European Journal of Operational Research, 270(2):654–669, 2018.
[18] K. Gajamannage, Y. Park, and D. I. Jayathilake. Real-time forecasting of time series in
financial markets using sequentially trained dual-LSTMs. Expert Systems with Applications,
223:119879, 2023.
[19] J.-C. Gamboa. Deep learning for time-series analysis. arXiv preprint arXiv:1701.01887,
2017.
[20] L. R. Glosten, R. Jagannathan, and D. E. Runkle. On the relation between the expected
value and the volatility of the nominal excess return on stocks. The Journal of Finance,
48(5):1779–1801, 1993.
[21] B. Gulmez. Stock price prediction with optimized deep LSTM network with artificial rabbits
optimization algorithm. Expert Systems with Applications, 227:120346, 2023.
[22] S. A. Haider, S. R. Naqvi, T. Akram, G. A. Umar, A. Shahzad, M. R. Sial, et al. LSTM
neural network based forecasting model for wheat production in Pakistan. Agronomy, 9:72,
2019.
[23] T. Hasenzagl, F. Pellegrino, L. Reichlin, and G. Ricco. A model of the Fed’s view on inflation.
Economic Research Paper, 104:686–704, 2022.
[24] S. Hochreiter and J. Schmidhuber. Long short-term memory. Neural Computation, 9(8):1735–
1780, 1997.
[25] H. H. Huang, N. H. Chan, K. Chen, and C. K. Ing. Consistent order selection for ARFIMA
processes. Annals of Statistics, 50:1297–1319, 2022.
[26] C. M. Jarque and A. K. Bera. A test for normality of observations and regression residuals.
International Statistical Review, 55(2):163–172, 1987.
[27] M. E. Javanmard, Y. Tang, Z. Wang, and P. Tontiwachwuthikul. Forecast energy demand,
CO2 emissions and energy resource impacts for the transportation sector. Applied Energy,
338:120830, 2023.
[28] S. Kaushik, A.Choudhury, P. K. Sheron, N. Dasgupta, S. Natarajan, L. A. Pickett, et al.
AI in healthcare: time-series forecasting using statistical, neural, and ensemble architectures.
Frontiers in Big Data, 3:4, 2020.
[29] H. Y. Kim and C. H. Won. Forecasting the volatility of stock price index: A hybrid model
integrating LSTM with multiple GARCH-type models. Expert Systems with Applications,
103:25–37, 2021.
[30] B. Lei, Z. Liu, and Y. Song. On stock volatility forecasting based on text mining and deep
learning under high-frequency data. Journal of Forecasting, 40(8):1596–1610, 2021.
[31] R. Liu, Y. Jiang, and J. Lin. Forecasting the volatility of specific risk for stocks with LSTM.
Procedia Computer Science, 202:111–114, 2022.
[32] G. M. Ljung and G. E. P. Box. On a measure of lack of fit in time series models. Biometrika,
65(2):297–303, 1978.
[33] M. McAleer. Automated inference and learning in modeling volatility. Econometric Theory,
21(1):232–261, 2005.
[34] D. B. Nelson. Conditional heteroskedasticity in asset returns: A new approach. Econometrica,
59(2):347–370, 1991.
[35] D. M. Nelson, A. C. M. Pereira, and R. A. de Oliveira. Stock market’s price movement prediction with LSTM neural networks. In International Joint Conference on Neural Networks
(IJCNN), pages 1–6, 2018.
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deep learning approach. International Review of Financial Analysis, 87:102627, 2023.
[37] M. L. Rahman, M. Islam, and M. Roy. Modeling inflation in Bangladesh. Open Journal of
Statistics, 10:998–1009, 2020.
[38] E. Ramos-P´erez, P. J. Alonso-Gonz´alez, and J. J. N´u˜nez-Vel´azquez. Multi-transformer:
A new neural network-based architecture for forecasting S&P volatility. Mathematics,
9(15):1794, 2021.
[39] A. Shewalkar, D. Nyavanandi, and S. Ludwig. Performance evaluation of deep neural networks applied to speech recognition: RNN, LSTM and GRU. Journal of Artificial Intelligence
and Soft Computing Research, 9:235–245, 2019.
[40] Y. Wang and L. Liu. A hybrid forecasting model based on LSTM and GARCH for financial
time series. Applied Sciences, 9(3):550, 2019.
[41] J. Wu, N. Levi, R. Araujo, and Y.-G. Wang. An evaluation of the impact of COVID-19
lockdowns on electricity demand. Electric Power Systems Research, 216:109015, 2023.
[42] X. Xu, Y. Zhang, C. A. McGrory, J. Wu, and Y.-G. Wang. Forecasting stock closing prices
with an application to airline company data. Data Science and Management, 6:239–246,
2023.
[43] Y. Yang, H. Zhou, J. Wu, Z. Ding, Y.-C. Tian, D. Yue, et al. Robust adaptive rescaled lncosh
neural network regression toward time-series forecasting. IEEE Transactions on Systems,
Man, and Cybernetics, 53:5658–5669, 2023.
[44] L. Yu, S. Wang, and K. K. Lai. Financial time series forecasting with nonlinear and nonstationary characteristics: A review. Applied Soft Computing, 95:106545, 2020.
[45] Y. Yu, X. Si, C. Hu, and J. Zhang. A review of recurrent neural networks: LSTM cells and
network architectures. Neural Computation, 31:1235–1270, 2019.
[46] J. Zhao, S. Xu, and X. Zhang. Periodic volatility modeling with hybrid neural networks and
GARCH-type models. Physica A, 616:128574, 2023.
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