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

TL;DR

This paper presents a PCA-based reduced-order modeling approach to analyze complex financial system dynamics, effectively capturing key interactions among major assets with fewer variables.

Contribution

It introduces a novel application of PCA and linear regression for simplified modeling of high-dimensional financial data, revealing heterogeneous cross-asset dependencies.

Findings

Limited principal components capture dominant asset dynamics.

Cross-asset dependencies vary across markets.

Model explains significant variance with reduced complexity.

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.