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. 2025 Jun 17;20(6):e0321204.
doi: 10.1371/journal.pone.0321204. eCollection 2025.

Investigating the dynamics and uncertainties in portfolio optimization using the Fourier-Millen transform

Muhammad Hilal Alkhudaydi  1 , Aiedh Mrisi Alharthi  2
Affiliations

Investigating the dynamics and uncertainties in portfolio optimization using the Fourier-Millen transform

Muhammad Hilal Alkhudaydi et al. PLoS One. .

Abstract

Many investors and financial managers view portfolio optimisation as a critical step in the management and selection processes. This is due to the fact that a portfolio fundamentally comprises a collection of uncertain securities, such as equities. For this reason, having a solid understanding of the elements responsible for these uncertainties is absolutely necessary. Investors will always look for a portfolio that can handle the required amount of risk while still producing the desired level of expected returns. This article uses feature-based models to investigate the primary elements that contribute to the optimal composition of a specific portfolio. These models make use of physical analyses, such as the Fourier transform, wavelet transforms and the Fourier-Mellin transform. Motivated by their use in medical analysis and detection, the purpose of this research was to analyse the efficacy of these methods in establishing the primary factors that go into optimising a particular portfolio. These geometric features are input into artificial neural networks, including convolutional and recurrent networks. These are then compared with other algorithms, such as vector autoregression, in portfolio optimisation tests. By testing these models on real-world data obtained from the US stock market, we were able to obtain preliminary findings on their utility.

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Conflict of interest statement

No authors have competing interests.

Figures

Fig 1
Fig 1. An LSTM model diagram by J. Leon, Beerware.
The graph shows the the architecture of LSTM model.
Fig 2
Fig 2. A CNN architecture illustrution [36].
The graph shows the the architecture of CNN model.
Fig 3
Fig 3. Time series plot of stock prices.
The graph shows the performance of the portfolio optimization method using historical stock data.
Fig 4
Fig 4. Dendrogram of the stock prices.
Fig 5
Fig 5. Here, –1, 0, and 1 are the thresholds used to group the correlations.
Fig 6
Fig 6. Here, –0.8, 0, and 0.2 are the thresholds used to group the correlations.
Fig 7
Fig 7. First 10 principal components of the stock log returns.
Fig 8
Fig 8. Correlation heatmap of the principal components.
Fig 9
Fig 9. Cumulative returns of the principal components of the log returns.
Fig 10
Fig 10. Cumulative returns of a portfolio containing the principal components of the log returns.
Fig 11
Fig 11. Wavelet transform of some of the principal components of log returns.
Fig 12
Fig 12. Performance evaluation: the profitability of VAR(1)-AutoML, CWT-CNN, and FM-LSTM.
See this image and copyright information in PMC

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