How to generate uniform distributed samples with given auto-correlation function As I mentioned in the question title, I want to generate specific uniformly distributed samples.
I need them to model a real world scenario. For my real data, I estimated a function, which approximates the auto-correlation function by a e-function. I also modeled a distribution model for my real data.
I can generate samples, which follow my distribution model with the inverse transform sampling.
If i think correct, instead of "standard" uniform distributed samples, which i feed into the inverse transform sampling, i need to adapt those uniform distributed samples, so that their auto-correlation function follows my estimated e-function.
Now the question is, if i am correct, how to adapt my uniform distributed samples, that they correspond to my requirements.
It would be great if, somebody could help.
EDIT 1:
Here is a plot of the auto-correlation function of my real data (different scenarios) and the modeled function (green). The ACF of my uniform distributed samples should follow the green (respectively blue) line.

EDIT 2:
Thank you so much so far for the answers. To make my problem a bit clearer, i added a illustration of the problem. For a simulation, i need to generate samples, which follow my distribution model (with inverse transform sampling a easy task) AND have the same auto-correlation behavior like the real data.
My idea was, that i need to adapt the uniformly distributed samples, which i feed into the inverse transform sampling, so that their ACF follows my model.
The problem is, that i don't know if this idea is correct and that i don't know how to adapt the uniformly distributed samples.


If I understand correctly your problem, you need to simulate random variables which marginally follow an uniform distribution while the joint distribution is a multivariate uniform distribution with some correlation between your marginals.
Formally:
$X_i\sim U(0,1), \forall_i, i = 1,2,...,K$ , where $X\sim U(a_i, b_i, Cor)$.
In the method I am firstly proposing, your uniform random variables will be uniformly distributed between 0 and 1. However, I also provide a "Normal to Anything" kind of approach.
One trick is to use generate a Multivariate normal distribution, specifying a correlation matrix. Let's say $\Sigma$ is your auto-correlation structure for your $K$ random variables.
$$X \sim MVN(\mu, \Sigma)$$
$\mu$ is a vector of means of size $K$, while $\Sigma$ is a $K*K$ matrix
Then you have to transform your quantiles to probabilities from any normal distribution you want, for one $X$:
$$CDF_{Normal}(X_{i}, \mu_i, \Sigma_{ii}) \sim U(0,1)$$
Now if you assume that your variables are not uniformly distributed between a common support $[a,b], \forall K$ but a variable-dependent support instead. You just need to convert your probabilities obtained previously with an inverse uniform distribution specifying a and b.  For a random variable,
$$\theta^{-1}(CDF_{Normal}(X_{i}, \mu_i, \Sigma_{ii}), a_i, b_i)$$
It is worth noting that you will respect globally your correlation structure, while under-estimate it a little bit.
I can provide script to illustrate the method.
Hope this helps.
