Re: mvnrnd and positive semidefinite covariance matrices
- From: "karvala" <karvala21@xxxxxxxxxxx>
- Date: Mon, 13 Mar 2006 19:29:22 -0000
"Frank Wu" <frank.z.wu@xxxxxxxxx> wrote in message
news:ef2c0c9.-1@xxxxxxxxxxxxxxxxxxx
Hi. Newbie question here.
Does anyone know why Matlab's mvnrnd function requires that the
covariance matrix be positive semidefinite? Is it possible to
generate random numbers from a multivariate normal distribution whose
covariance matrix is not positive semidefinite?
As context: I'm currently using the mvnrnd function to generate
random portfolio returns based off of random asset class
performances. Because the covariance matrix of the asset classes is
not positive semidefinite, I've had to use a conversion, which leads
to the portfolio not quite having the distribution that I expected.
Thanks!
A covariance matrix is always positive semidefinite (where this includes
positive definite as a subclass), by definition. If you think the
covariance matrix of your asset classes isn't, either you're thinking of
something other than covariance, or you're calculating it incorrectly. If
you're unsure of that, I suggest you consider the particular case of a
correlation matrix, and in particular examine the symmetry property of both
correlation and covariance matrices.
.
- References:
- mvnrnd and positive semidefinite covariance matrices
- From: Frank Wu
- mvnrnd and positive semidefinite covariance matrices
- Prev by Date: Iteration code going wrong somewhere
- Next by Date: Multiple use of C functions in several S-Functions on xPC
- Previous by thread: Re: mvnrnd and positive semidefinite covariance matrices
- Next by thread: Re: mvnrnd and positive semidefinite covariance matrices
- Index(es):
Relevant Pages
|
