w = exprnd(10,[1,10000000]);
x1 = conv(w,ones(1,100)/10,'same')+10;
histogram(w);
figure;
histogram(x1);
Above the MATLAB code,
I generated the many samples, $w$, from exponential distribution.
from $w$, I made correlated samples, $x1$ by using LPF convolution.
When getting the histogram of $x1$, it looks Gaussian, surprisingly.
How can I explain it?
To the best of my knowledge, CLT is about the sum of RVs with IID or not.
However in this case, it is about the correlated time-series.
Could you give me a little intuition?
Thank you for reading!