# DCC GARCH and cholesky factorization

I want to run a simulation experiment after I have estimated my DCC GARCH parameters (following Becker et al. methodology) Basically, since I am rather unfamiliar with the application of cholesky decomposition I was wondering, would it be possible to apply cholesky decomposition to the correlation matrix R that I have obtained using DCC GARCH to get sqrt{R} or is it only possible to apply cholesky to the covariance matrix? If yes, then how so? Thanks in advance!

• What do you want to do with the "standard deviation matrix"? (There is no single matrix version of a standard deviation; likewise there are many "matrix square roots", not just Cholesky) – GeoMatt22 Apr 30 '17 at 21:34
• @GeoMatt22 I want to use it to calculate the covariance matrix to model volatility (using DCC GARCH) such that cov matrix= sd *corr *sd. Can you please tell me how I can implement the cholesky decomposition of the var matrix to get the sd matrix? – Hsk Apr 30 '17 at 21:41
• I do not believe "standard deviation matrix" is a standard term, but Cholesky decomposition (and/or eigen-decomposition) are commonly used as a "covariance-matrix square root" in different contexts. How these relate to DCC GARCH would be on-topic here (but outside my expertise, sorry). Purely computing matrix factorizations, either algorithmically or in particular software, is off-topic (but info is easily available on Wikipedia and/or your software's help). – GeoMatt22 Apr 30 '17 at 22:09
• Thanks! I am going to edit my question to how cholesky decomposition can be used as a "covariance matrix square root" – Hsk Apr 30 '17 at 22:28