Random number generation

Quoting cyberia

Disliked

Hi all, figured I might start with a question that isn't directly related to trading forex.

How do I generate normal random variables (3 or more) that are aribtrarily correlated?

The method that MATLAB seems to use, namely:
1. Generate uncorrelated random normal observations.
2. Define correlation matrix.
3. Find Cholesky decomposition L.L^T of the correlation matrix.
4. Multiply the uncorrelated data by L

doesn't work too well with an arbitrary correlation matrix, as no element (barring the main diagonal) is required to be positive, or even non-negative.

So, with that out of the way, how would I go about generating random variables of arbitrary correlation?

Ignored

Quoting RoBiK

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Hi,

take a look at copulas: http://www.mathworks.com/products/st...opulademo.html

Ignored

Quoting cyberia

Disliked

Hi all, figured I might start with a question that isn't directly related to trading forex.

How do I generate normal random variables (3 or more) that are aribtrarily correlated?

The method that MATLAB seems to use, namely:
1. Generate uncorrelated random normal observations.
2. Define correlation matrix.
3. Find Cholesky decomposition L.L^T of the correlation matrix.
4. Multiply the uncorrelated data by L

doesn't work too well with an arbitrary correlation matrix, as no element (barring the main diagonal) is required to be positive, or even non-negative.

So, with that out of the way, how would I go about generating random variables of arbitrary correlation?

Ignored

Quoting cyberia

Disliked

Well, I was working from the logarithm of successive closing prices for the following 5 pairs (I've put them all into indirect to make it easier on self):
AUD/GBP, AUD/MXP, AUD/CHF, AUD/NZD and AUD/ISK, with the following sample correlations

AUD/GBP - AUD/MXP: -0.452885
AUD/GBP - AUD/CHF: 0.905765
AUD/GBP - AUD/NZD: 0.023389
AUD/GBP - AUD/ISK: -0.466430
AUD/MXP - AUD/CHF: -0.497812
AUD/MXP - AUD/NZD: 0.103609
AUD/MXP - AUD/ISK: 0.609864
AUD/CHF - AUD/NZD: -0.006788
AUD/CHF - AUD/ISK: -0.456123
AUD/NZD - AUD/ISK: 0.036772

As all of the pairs have mixed signs, simply inverting any of them won't solve my problem.

Bopik's copula suggestion worked fine when there is one negatively correlated pair of pairs, but fell apart with two and more.

Ignored

[font=Fixedsys]>> C=[1 -0.452885 0.905765 0.023389 -0.466430; -0.452885 1 -0.497812 0.103609 0.609864; 0.905765 -0.497812 1 -0.006788 -0.456123; 0.023389 0.103609 -0.006788 1 0.036772; -0.466430 0.609864 -0.456123 0.036772 1]

C =

1.0000     -0.45290.90580.0234     -0.4664
      -0.45291.0000     -0.49780.10360.6099
0.9058     -0.49781.0000     -0.0068     -0.4561
0.02340.1036     -0.00681.00000.0368
   -0.46640.6099     -0.45610.03681.0000

>> XU = rand(1000, 5);
>> L=chol(C)

L =

1.0000     -0.45290.90580.0234     -0.4664
 00.8916     -0.09830.12810.4471
 0 00.4122     -0.03730.0249
 0 0 00.9908     -0.0087
 0 0 0 00.7628

>> X=XU*L;
>> corr(X)

ans =

1.0000     -0.47370.91190.0535     -0.4511
   -0.47371.0000     -0.50830.08430.6187
0.9119     -0.50831.00000.0024     -0.4386
0.05350.08430.00241.00000.0348
   -0.45110.6187     -0.43860.03481.0000[/font]