Generating correlated QUASI random numbers

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Hi I am trying to generate correlated quasi random numbers using a sobol sequence in matlab. My Problem is the Following: Using "standard" random numbers it is easy to generate the 6 correlated random variables (NumberOfSteps X NumberOfSimulations) I need, using a cholesky decomposition:



L = chol(CorrelationMatrix,"lower");

for i=1:NumberOfSimulations

Z = L*randn(4,NumberOfSteps);

for t=2:NumberOfSteps

.....Z1(i,t);

.....Z2(i,t);



Since i only want to generate the sequence once (very time consuming) the only way i found to generate two correlated r.v. is the following:



Ps = sobolset(NumberOfSteps);

Ps = scramble(Ps,'MatousekAffineOwen');

U = net(Ps,NumberOfSimulations);

Z1 = norminv(U);



Z2 = Rho.*Z1 + sqrt(1-Rho^2).*randn(NumberOfSimulations,NumberOfSteps);



Unfortunately I have No idea how I can extend this to 6 correlated random varibles. Can anyone help me?



Best regards,
Alex




matlab simulation




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  • 1




    Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 1 at 10:37














up vote
0
down vote

favorite












Hi I am trying to generate correlated quasi random numbers using a sobol sequence in matlab. My Problem is the Following: Using "standard" random numbers it is easy to generate the 6 correlated random variables (NumberOfSteps X NumberOfSimulations) I need, using a cholesky decomposition:



L = chol(CorrelationMatrix,"lower");

for i=1:NumberOfSimulations

Z = L*randn(4,NumberOfSteps);

for t=2:NumberOfSteps

.....Z1(i,t);

.....Z2(i,t);



Since i only want to generate the sequence once (very time consuming) the only way i found to generate two correlated r.v. is the following:



Ps = sobolset(NumberOfSteps);

Ps = scramble(Ps,'MatousekAffineOwen');

U = net(Ps,NumberOfSimulations);

Z1 = norminv(U);



Z2 = Rho.*Z1 + sqrt(1-Rho^2).*randn(NumberOfSimulations,NumberOfSteps);



Unfortunately I have No idea how I can extend this to 6 correlated random varibles. Can anyone help me?



Best regards,
Alex




matlab simulation




share|cite|improve this question















  • 1




    Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 1 at 10:37












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Hi I am trying to generate correlated quasi random numbers using a sobol sequence in matlab. My Problem is the Following: Using "standard" random numbers it is easy to generate the 6 correlated random variables (NumberOfSteps X NumberOfSimulations) I need, using a cholesky decomposition:



L = chol(CorrelationMatrix,"lower");

for i=1:NumberOfSimulations

Z = L*randn(4,NumberOfSteps);

for t=2:NumberOfSteps

.....Z1(i,t);

.....Z2(i,t);



Since i only want to generate the sequence once (very time consuming) the only way i found to generate two correlated r.v. is the following:



Ps = sobolset(NumberOfSteps);

Ps = scramble(Ps,'MatousekAffineOwen');

U = net(Ps,NumberOfSimulations);

Z1 = norminv(U);



Z2 = Rho.*Z1 + sqrt(1-Rho^2).*randn(NumberOfSimulations,NumberOfSteps);



Unfortunately I have No idea how I can extend this to 6 correlated random varibles. Can anyone help me?



Best regards,
Alex




matlab simulation




share|cite|improve this question











Hi I am trying to generate correlated quasi random numbers using a sobol sequence in matlab. My Problem is the Following: Using "standard" random numbers it is easy to generate the 6 correlated random variables (NumberOfSteps X NumberOfSimulations) I need, using a cholesky decomposition:



L = chol(CorrelationMatrix,"lower");

for i=1:NumberOfSimulations

Z = L*randn(4,NumberOfSteps);

for t=2:NumberOfSteps

.....Z1(i,t);

.....Z2(i,t);



Since i only want to generate the sequence once (very time consuming) the only way i found to generate two correlated r.v. is the following:



Ps = sobolset(NumberOfSteps);

Ps = scramble(Ps,'MatousekAffineOwen');

U = net(Ps,NumberOfSimulations);

Z1 = norminv(U);



Z2 = Rho.*Z1 + sqrt(1-Rho^2).*randn(NumberOfSimulations,NumberOfSteps);



Unfortunately I have No idea how I can extend this to 6 correlated random varibles. Can anyone help me?



Best regards,
Alex





matlab simulation





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asked Aug 1 at 10:34









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    Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 1 at 10:37












  • 1




    Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 1 at 10:37







1




1




Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 1 at 10:37




Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 1 at 10:37















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