What does this research mean for the field?

A data-driven framework integrating ARIMA-GARCH models and Gaussian mixture models to construct polyhedral uncertainty sets yields economically higher Sharpe ratios and more stable allocations in robust portfolio optimization compared to standard formulations. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Develop a data-driven framework to construct polyhedral uncertainty sets that account for time-varying volatility and latent market regimes in robust portfolio optimization.

September 2, 2026MathematicsOpen Access

Data-Driven Uncertainty Set Construction with ARIMA–GARCH Modeling for Robust Portfolio Optimization

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Develop a data-driven framework to construct polyhedral uncertainty sets that account for time-varying volatility and latent market regimes in robust portfolio optimization.
Filtered equity returns via ARIMA-GARCH models to eliminate serial dependence and volatility clustering, followed by Gaussian mixture model (GMM) clustering on standardized residuals.
Constructed component-wise polyhedral uncertainty sets using convex hulls within Mahalanobis distance thresholds and reformulated the robust problem into a tractable quadratic program via linear programming duality.
Evaluated the methodology using synthetic geometric experiments and rolling-window backtests across 18 quarterly rebalancing events on Indonesian equity data.
Gaussian mixture modeling identified three distinct latent regimes of roughly equal proportions in empirical equity returns exhibiting heavy tails and volatility clustering.
Out-of-sample backtests yielded economically higher Sharpe ratios relative to standard uncertainty set formulations, with statistical significance constrained by the 18 rebalancing periods.
Synthetic experiments showed that well-separated regime clusters cause convex hull aggregation to introduce conservatism, whereas overlapping clusters maintain allocation stability.

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Implication

Quantitative analysis reveals higher out-of-sample Sharpe ratios in Indonesian equity data, suggesting enhanced portfolio stability against time-varying market volatility.

Cite This Study

Setyawan et al. (2026) studied this question.

synapsesocial.com/papers/6a97e2f6c562ede874ec766c https://doi.org/10.3390/math14173116

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Implication

Quantitative analysis reveals higher out-of-sample Sharpe ratios in Indonesian equity data, suggesting enhanced portfolio stability against time-varying market volatility.

Data-Driven Uncertainty Set Construction with ARIMA–GARCH Modeling for Robust Portfolio Optimization

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Discussion

Implication

Cite This Study

Data-Driven Uncertainty Set Construction with ARIMA–GARCH Modeling for Robust Portfolio Optimization

Key Points

Discussion

Implication

Cite This Study

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