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Questions tagged [random-matrix-theory]

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Distribution of sample covariance times inverse covariance times sample covariance

I want to understand the distribution of the random variable: $$S_n = \frac{1}{n^2} 1'\hat \Sigma \Sigma ^{-1} \hat \Sigma 1$$. 1 is a vector of ones of size n, and the variance is of size nxn. $\hat \...
alejandroll10's user avatar
2 votes
2 answers
355 views

Discussion on random matrix theory and impact on PCA

I've written a paper for university on Random Matrices and during my research I've had an interesting idea, let me explain: Wigner's Semicircle Law has seen much advancement since its original proof ...
John Miller's user avatar
2 votes
1 answer
235 views

Covariance matrix for multiple assets - Second attempt

Ok, on the advice of administration I open a new question, hoping that in this way it becomes clearer. Like I said before, I am trying to understand how the authors of this (page 76) and this (page ...
user51121's user avatar
0 votes
1 answer
368 views

Effective Time Length of Exponentially Weighted Covariance Matrix Estimate

In [1] Pafka, Potters and Kondor mention the following in section 2: In contrast, if this covariance matrix estimate is used for portfolio optimization (i.e. for selecting the portfolio in a ...
Hans-Peter Schrei's user avatar
7 votes
0 answers
539 views

Cleaning correlation matrix, Bun Bouchaud Potters (2016) method

Stock returns correlation matrices are notoriously hard to estimate, especially when the number of assets $N$ is large with respect to the size of the readily available historical returns $T$. Many ...
user28853's user avatar
1 vote
1 answer
572 views

What does each bar in the empirical average eigenvalues spectrum of the correlation matrix of log-returns of stocks represent?

An example diagram, taken from this paper, looks like follows: What is its physical interpretation? The highest eigenvalue, the paper says, represents market mode. So, what does the difference in ...
Kristada673's user avatar
1 vote
0 answers
406 views

Marchenko–Pastur, Student distribution and returns

I have a question regarding random matrix theory. I've been studying various papers and I found some confusing definitions of Marchenko-Pastur law. The most clear was the one on wiki: wiki-Pastur-...
Jur's user avatar
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7 votes
4 answers
874 views

How to treat large (5K-10K) non-positive-definite (particularly near-singular) covariance matrices 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 ...
acmh's user avatar
  • 71
16 votes
3 answers
1k views

What are some research articles on using principle components to generate alpha?

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 ...
Ram Ahluwalia's user avatar
5 votes
1 answer
405 views

RMT (Random Matrix Theory) issue with callibrating MP distribution -

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) ==> [1] 1133 478 ...
nxstock-trader's user avatar
9 votes
3 answers
1k views

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 ...
nxstock-trader's user avatar
12 votes
1 answer
1k views

One dimensional analog of cleansing a correlation matrix via random matrix theory

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 ...
vonjd's user avatar
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22 votes
3 answers
4k views

Cleansing covariance matrices via Random matrix theory

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 ...
Ram Ahluwalia's user avatar
32 votes
5 answers
8k views

Random matrix theory (RMT) in finance

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 ...
vonjd's user avatar
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