I came across a code in Matlab on how to generate the data with autocorrelation "X=cumsum(rand(n,p)-r)", where n is the number of observations, p is the number of variables and r is the correlation coefficient. The results I am getting used to be a structured patterned when plotted on scatter plot or control chart (MEWMA), the value of autocorrelation (rk) used to be very close to 1(0.9998). That is not what I want.
We are trying to create auto-correlated random values which will be used as timeseries. We have no existing data we refer to and just want to create the vector from scratch.
On the one hand we need of course a random process with distribution and its SD.
On the other hand the autocorrelation influencing the random process has to be described. The values of the vector are autocorrelated with decreasing strength over several timelags. e.g. lag1 has 0.5, lag2 0.3, lag1 0.1 etc.
Thanks Mr Farborz for the information.
As you rightly said there is no existing data and we are creating from the scratch. Yes i agree with you as i said in the question raised was that i want to generate a set of multivariate data with autocorrelation on say 3 variables and the level of correlation is controlled. say 0.5.
All i need is to have a code or procedure by which will generate the data set with such autocorrelation at a specified level of correlation within the variable, such that i can have a set of data that i can use for other things when generated.
I hope i made my point clear with this? The other points you suggested also should be at mind when considering the procedure of generating the data set above.
Thank you once again.
Hi, if I understood correctly what you want to do, I think the simplest way would be to generate data from an autoregressive AR(1) process (see, e.g., http://en.wikipedia.org/wiki/Autoregressive_model). For an AR(1) process you have: X(i+1)=rho_1*X(i)+e(i), where rho_1=autocorrelation at lag 1 and e(i) a random noise term with zero mean and constant variance. I hope this helps.
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