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Jonathan
Jonathan

Reputation: 230

Error in cholesky decompostion of large matrix in R

I am trying to decompose a large covariance matrix as part of a portfolio optimisation in R, but it doesn't seem to work for matrices with more than ~100 variables. Here is an example with some random data:

set.seed(123)
a <- NULL

for(i in 1:300) {
  a <- cbind(a, rnorm(100))
}

chol(cov(a))

Error in chol.default(cov(a)) : 
  the leading minor of order 101 is not positive definite

but if I reduce the sample it works fine:

b <- NULL

for(i in 1:100) {
  b <- cbind(b, rnorm(100)) 
}

chol(cov(b))

I've tried it a few times, and the error seems to occur for covariance matrices with more than 100 to 105 variables. Does anyone know the source of this problem?

EDIT 2: This works:

set.seed(123)
c <- NULL

for(i in 1:300) {
  c <- cbind(c, rnorm(300))
}

chol(cov(c))

But this does not:

d <- NULL

for(i in 1:301) {
  d <- cbind(d, rnorm(300))
}

chol(cov(d))

Error in chol.default(cov(d)) : 
  the leading minor of order 300 is not positive definite

So the number of variables may not exceed the number of observations?

Upvotes: 1

Views: 4079

Answers (1)

Lars Lau Raket
Lars Lau Raket

Reputation: 1974

If you only have a 100 observations, your covariance matrix will have rank at most 100. This is the reason that the cholesky factorization is failing.

Upvotes: 3

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