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.

翻译：本研究采用降阶建模方法分析纳斯达克指数、原油、黄金与美元之间的动态相互作用。通过时滞嵌入与主成分分析对高维金融动力学进行编码，随后在降维空间中进行线性回归。相关性分析与滞后回归分析揭示了跨资产间异质的依赖关系。以决定系数（$R^2$）评估的模型性能表明，仅需少量主成分即可捕捉各资产的主导动力学特征，且不同市场呈现出各异的复杂性。