Large dimension forecasting models and random singular value spectra

Details Large dimension forecasting models and random singular value spectra Large dimension forecasting models and random singular value spectra

2005-12-10

arxiv.org/abs/physics/0512090v1

Physics

Data Analysis, Statistics and Probability

20 pages, 5 figures, submitted to EPJB

Scientific paper

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.

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