CamDavidsonPilon/Graphical-Lasso-in-Finance

Graphica-Lasso-in-Finance

Implementations of the graphical lasso method to estimation of covariance matrices in finance.

Background

The graphical lasso method is used to find a sparse inverse covariance matrix. Why is this useful? The (i,j)th element of the inverse covariance matrix is known as the partial-correlation between variable i and variable j. The partial autocorrelation is the correlation of two data, controlling for every other variable. If the variables are Gaussian, and the partial-correlation is 0, then the variables are conditionally independent.

This is a very intuitive property in finance. Think: if the price of sheep increases, should the price of MSFT really increase too, even if there covariance is positive? Probably not, but both might be linked through a series of ETFs like the DJ-UBS and the SP500. The covariance matrix is a victim of causality! Sheep prices and MSFT have positive covariance because they are both dependent on another set of indices, but have (close to) zero conditional correlation.

Theory

Based on the paper Sparse inverse covariance estimation with the grapical lasso by Freidman et el. (2007).