# Generating a string of random standard normal variables that are correlated

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Natialol
on 6 Dec 2011

Commented: Garrison Greenwood
on 24 Feb 2021

Hi Everyone,

I'm a sort of newbie, I would like to know how and what the implications are of 'Generating a string of random standard normal variables that are correlated with each other'.

To get by this problem, I have been generating and correlating my desired sequence to a different random variable and then calculating the correlation between my sequence.

Thanks for the anticipated answer.

ps: Generate random standard normal's A, B, C, D so that have a correlation and standard deviation of corr and std.

Thanks again

##### 0 Comments

### Accepted Answer

Daniel Shub
on 6 Dec 2011

I am not sure if this is homework or not ...

Start off with two independent random variables with zero mean and standard deviation sigma.

sigma = 10;

X = sigma*randn(1e7, 1);

Y = sigma*randn(1e7, 1);

Then make two new random variables from these with correlation rho.

rho = 0.2;

A = X;

B = sqrt(rho^2)*X+sqrt(1-rho^2)*Y;

[std(A), std(B)]

corrcoef(A, B)

When you add a third random variable C you need to specify what you want rho_AB, rho_AC, and rho_AB to be. The basic idea is the same: start with N independent random variables and add them together with appropriate weighting to get N new random variables.

##### 3 Comments

Daniel Shub
on 6 Dec 2011

Alexander Knetsch
on 10 Nov 2020

The equation is quite good already, it doesn't allow for a negative corellation. If you change the expression for B, you can allow for this:

B = (rho/abs(rho))*sqrt(rho^2)*X+sqrt(1-rho^2)*Y;

### More Answers (2)

Oleg Komarov
on 6 Dec 2011

Given a correlation matrix C = A*A', then A = P*sqrt(D), where:

[P,D] = eig(C); % spectral decomposition

To get the correlated normal random series Z, use W = (W1, ...,W2)' (the normal random series):

Z = A*W;

Note that if you have 4 variables, then C is 4 by 4, and W should be 4 by nobs.

Chet Sharma
on 30 Jan 2018

##### 1 Comment

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