Investment risk forecasting model using extreme value theory approach combined with machine learning

Melina Melina; Sukono; Herlina Napitupulu; Norizan Mohamed; Melina Melina; Sukono; Herlina Napitupulu; Norizan Mohamed

doi:10.3934/math.20241590

AIMS Mathematics

2024, Volume 9, Issue 11: 33314-33352. doi: 10.3934/math.20241590

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Investment risk forecasting model using extreme value theory approach combined with machine learning

1.
Doctoral Program in Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
2.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
3.
Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Terengganu 21030, Malaysia

Received: 20 September 2024 Revised: 09 November 2024 Accepted: 12 November 2024 Published: 22 November 2024
MSC : 60G25, 62M10, 62M20, 62M45, 62P05, 90C90, 91G70

Investment risk forecasting is challenging when the stock market is characterized by non-linearity and extremes. Under these conditions, VaR estimation based on the assumption of distribution normality becomes less accurate. Combining extreme value theory (EVT) with machine learning (ML) produces a model that detects and learns heavy tail patterns in data distributions containing extreme values while being effective in non-linear systems. We aimed to develop an investment risk forecasting model in the capital market with non-linear and extreme characteristics using the VaR method of the EVT approach combined with ML (VaR_GPD-ML(α)). The combination of methods used is a multivariate time series forecasting model with RNN, LSTM, and GRU algorithms to obtain ML-based returns. The EVT method of the POT approach was used to model extremes. The VaR method was used for investment risk estimation. The backtesting method was used to validate the model. Our results showed that determining the threshold based on the normal distribution will identify extreme values with the ideal number, minimum bias, and distribution of extreme data following GPD. The VaR_GPD-ML(α) model was valid in all samples based on backtesting at α = 0.95 and α = 0.99. Generally, this model produces a greater estimated value of investment risk than the VaR_GPD(α) model at the 95% confidence level.
- backtesting,
- extreme value theory,
- GRU,
- LSTM,
- machine learning,
- multivariate,
- non-linear,
- RNN,
- VaR
Citation: Melina Melina, Sukono, Herlina Napitupulu, Norizan Mohamed. Investment risk forecasting model using extreme value theory approach combined with machine learning[J]. AIMS Mathematics, 2024, 9(11): 33314-33352. doi: 10.3934/math.20241590

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Abstract

Investment risk forecasting is challenging when the stock market is characterized by non-linearity and extremes. Under these conditions, VaR estimation based on the assumption of distribution normality becomes less accurate. Combining extreme value theory (EVT) with machine learning (ML) produces a model that detects and learns heavy tail patterns in data distributions containing extreme values while being effective in non-linear systems. We aimed to develop an investment risk forecasting model in the capital market with non-linear and extreme characteristics using the VaR method of the EVT approach combined with ML (VaR_GPD-ML(α)). The combination of methods used is a multivariate time series forecasting model with RNN, LSTM, and GRU algorithms to obtain ML-based returns. The EVT method of the POT approach was used to model extremes. The VaR method was used for investment risk estimation. The backtesting method was used to validate the model. Our results showed that determining the threshold based on the normal distribution will identify extreme values with the ideal number, minimum bias, and distribution of extreme data following GPD. The VaR_GPD-ML(α) model was valid in all samples based on backtesting at α = 0.95 and α = 0.99. Generally, this model produces a greater estimated value of investment risk than the VaR_GPD(α) model at the 95% confidence level.

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