I studied whether a monotone-constrained functional representation could improve regime classification for forward risk-accumulation curves under a time-respecting empirical design. The empirical application focused on Apple Inc. (AAPL) and used a supportive tech-growth panel consisting of AAPL, MSFT, NVDA, AMZN, QQQ, XLK, SPY, XLC, XLY, and XLI for descriptive context. I constructed forward curves over a 60-day horizon and compared cumulative forward variance with root-cumulative forward volatility, taking the latter as the main empirical specification. To represent these structurally monotone curves, I implemented a monotone-constrained component extraction procedure, denoted mFPCA for convenience, based on isotonic projection and sequential deflation, and evaluated it against an unconstrained FPCA benchmark under identical classifiers and validation schemes. All transformations, thresholds, and tuning steps were estimated on the training slice only and then transferred unchanged to the evaluation slice. Under blocked validation, the preferred AAPL specification attained Accuracy $ 0.862 $ and Macro-F1 $ 0.863 $; under rolling walk-forward evaluation, the corresponding values were $ 0.815 $ and $ 0.822 $. Relative to FPCA, the gains from mFPCA were positive but modest. Moreover, ablation results showed that cone depth did not improve the final AAPL specification, while sensitivity analysis supported $ K = 3 $ as the main component choice. Permutation importance further indicated that predictive information was concentrated primarily in the early-to-middle portion of the forward curve. Simulation evidence showed that mFPCA was more closely aligned with latent monotone structure than FPCA when judged by matched component angles, and that random $ K $-fold validation remained mildly optimistic relative to blocked validation under temporally dependent regime-shift designs. Overall, the results supported monotone-constrained representation as a credible and structurally coherent approach to forward risk classification when combined with leak-free temporal evaluation.
Citation: Çağlar SÖZEN. Monotone-constrained functional component analysis for forward risk-accumulation curves with Leak-Free temporal validation and regime classification[J]. Data Science in Finance and Economics, 2026, 6(2): 336-358. doi: 10.3934/DSFE.2026012
I studied whether a monotone-constrained functional representation could improve regime classification for forward risk-accumulation curves under a time-respecting empirical design. The empirical application focused on Apple Inc. (AAPL) and used a supportive tech-growth panel consisting of AAPL, MSFT, NVDA, AMZN, QQQ, XLK, SPY, XLC, XLY, and XLI for descriptive context. I constructed forward curves over a 60-day horizon and compared cumulative forward variance with root-cumulative forward volatility, taking the latter as the main empirical specification. To represent these structurally monotone curves, I implemented a monotone-constrained component extraction procedure, denoted mFPCA for convenience, based on isotonic projection and sequential deflation, and evaluated it against an unconstrained FPCA benchmark under identical classifiers and validation schemes. All transformations, thresholds, and tuning steps were estimated on the training slice only and then transferred unchanged to the evaluation slice. Under blocked validation, the preferred AAPL specification attained Accuracy $ 0.862 $ and Macro-F1 $ 0.863 $; under rolling walk-forward evaluation, the corresponding values were $ 0.815 $ and $ 0.822 $. Relative to FPCA, the gains from mFPCA were positive but modest. Moreover, ablation results showed that cone depth did not improve the final AAPL specification, while sensitivity analysis supported $ K = 3 $ as the main component choice. Permutation importance further indicated that predictive information was concentrated primarily in the early-to-middle portion of the forward curve. Simulation evidence showed that mFPCA was more closely aligned with latent monotone structure than FPCA when judged by matched component angles, and that random $ K $-fold validation remained mildly optimistic relative to blocked validation under temporally dependent regime-shift designs. Overall, the results supported monotone-constrained representation as a credible and structurally coherent approach to forward risk classification when combined with leak-free temporal evaluation.
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Çağlar SÖZEN. Monotone-constrained functional component analysis for forward risk-accumulation curves with Leak-Free temporal validation and regime classification[J]. Data Science in Finance and Economics, 2026, 6(2): 336-358. doi: 10.3934/DSFE.2026012
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