2005/12/10 by Jean‐Philippe Bouchaud, Bouchaud, Jean-Philippe, Laurent Laloux +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Data Analysis #FOS: Economics and business #FOS: Physical sciences #Random Matrices and Applications #Statistical Finance (q-fin.ST) #Statistical Mechanics (cond-mat.stat-mech) #Statistics and Probability (physics.data-an) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.physics/0512090
openalex publication_date 2005/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a general method to detect and extract from a finite time sample statistically meaningful correlations between input and output variables of large dimensionality. Our central result is derived from the theory of free random matrices, and gives an explicit expression for the interval where singular values are expected in the absence of any true correlations between the variables under study. Our result can be seen as the natural generalization of the Marcenko-Pastur distribution for the case of rectangular correlation matrices. We illustrate the interest of our method on a set of macroeconomic time series.