Applying free random variables to random matrix analysis of financial data. Part I: The Gaussian case
We apply the concept of free random variables to doubly correlated (Gaussian) Wishart random matrix models, appearing, for example, in a multivariate analysis of financial time series, and displaying both inter-asset cross-covariances and temporal auto-covariances. We give a comprehensive introduction to the rich financial reality behind such models. We explain in an elementary way the main techniques of free random variables calculus, with a view to promoting them in the quantitative finance community. We apply our findings to tackle several financially relevant problems, such as a universe of assets displaying exponentially decaying temporal covariances, or the exponentially weighted moving average, both with an arbitrary structure of cross-covariances.
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Volume (Year): 11 (2011)
Issue (Month): 7 ()
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