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arXiv · 2212.12044

Reduced-order autoregressive dynamics of a complex financial system: a PCA-based approach

Pouriya Khalilian·Sara Azizi·Mohammad Hossein Amiri·Javad T. Firouzjaee
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Abstract

This study analyzes the dynamic interactions among the NASDAQ index, crude oil, gold, and the US dollar using a reduced-order modeling approach. Time-delay embedding and principal component analysis are employed to encode high-dimensional financial dynamics, followed by linear regression in the reduced space. Correlation and lagged regression analyses reveal heterogeneous cross-asset dependencies. Model performance, evaluated using the coefficient of determination ($R^2$), demonstrates that a limited number of principal components is sufficient to capture the dominant dynamics of each asset, with varying complexity across markets.

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Pouriya Khalilian, Sara Azizi, Mohammad Hossein Amiri, Javad T. Firouzjaee. 2025-12-23. Reduced-order autoregressive dynamics of a complex financial system: a PCA-based approach. https://arxiv.org/abs/2212.12044

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