Paper: arXiv 2212.12044
Authors: Pouriya Khalilian, Sara Azizi, Mohammad Hossein Amiri, Javad T. Firouzjaee
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.
Complexity vs Empirical Score
- Math Complexity: 5.5/10
- Empirical Rigor: 5.0/10
- Quadrant: Holy Grail — high math complexity, high empirical rigor
Why this score: The paper applies established reduced-order modeling techniques (time-delay embedding and PCA) to cross-asset dynamics with solid mathematical grounding. While well-explained and empirically tested across key asset classes, the underlying methodology is relatively standard, limiting its novel contribution to quantitative finance.
Research Flowchart
flowchart TD
A["Research Goal:<br>Model complex multi-asset financial dynamics using reduced-order modeling"] --> B["Data Inputs:<br>Daily prices for NASDAQ, Crude Oil, Gold, & US Dollar"]
B --> C["Time-Delay Embedding:<br>Construct high-dimensional phase space"]
C --> D["Principal Component Analysis (PCA):<br>Reduce dimensionality to dominant components"]
D --> E["Lagged Linear Regression:<br>Model autoregressive dynamics in reduced space"]
E --> F["Evaluation:<br>Assess performance via R² & cross-asset correlation"]
F --> G["Key Outcomes:<br>A few PCs capture dominant dynamics; reveals heterogeneous cross-asset dependencies"]