Potential PCA Interpretation Problems for the Dynamics of Financial Market Data
28 Pages Posted: 9 Feb 2011
Date Written: February 7, 2011
Principal Component Analysis (PCA) is a common and popular tool for the analysis of financial market data, such as implied volatility smiles, interest rate curves and commodity future curves. We provide a critical view on PCA analysis and the corresponding results from empirical literature. In particular, it will be shown how PCA can produce patterned loading vectors if the correlation matrix just happens to belong to a particular matrix class. We will also provide evidence why the level factor is the dominating factor in virtually all empirical PCA analyses and question whether this reflects the true dynamics. In addition, we show how artifacts can be generated by PCA and how problematic the interpretation of PCA results can be, if a system is indeed driven by level, slope and curvature dynamics.
Keywords: Principal Component Analysis, PCA, Volatility Smile Dynamics, Yield Curve Dynamics, Bisymmetric Matrices, Centro-Symmetric Matrices, Level, Slope, Curvature, Twist
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