Large (5K-10K) non positive definite (particularly near singular) covariance matrices and treatments for Cholesky decomposition
I have a very large covariance matrix (around 10000x10000) of returns, which is constructed using a sample size of 1000 for 10000 variables. My goal is to perform a (good-looking) Cholesky ...
Here's an example by Marco Avellenada from NYU titled "Statistical Arbitrage in the U.S. Equities Market". The idea of this paper involves capturing mean reversion in the residual returns of a ...
I am seeing an issue when callibrating an MP distribution. Assume a log return series for the SP500 with the following dimensions dim(xts.sp500.ret.stocksonly) ==>  1133 478 ...
Does random matrix theory (RMT) for returns' correlation matrices apply if there are high correlations?
Steps to replicate: Take the correlation matrix of a sample of stocks in the SP500, or a set of ETF's that are include some that are highly correlated (0.7 and above). Problem observed: I observe ...
The general idea of cleansing a correlation matrix via random matrix theory is to compare its eigenvalues to that of a random one to see which parts of it are beyond normal randomness. These are then ...
I am exploring de-noising and cleansing of covariance matrices via Random Matrix Theory. RMT is a competitor to shrinkage methods of covariance estimation. There are various methods expressed usually ...
The new kid on the block in finance seems to be random matrix theory. Although RMT as a theory is not so new (about 50 years) and was first used in quantum mechanics it being used in finance is a ...