suppose I have a random sequence $X$, I want to determine whether it is an i.i.d. sequence, I used Ljung-box test to determine whether sequence $X$ is mutually independent. Can anyone tell me how to show the sequence $X$ has the same probability distribution?
P.S. I tried to generate a normal distributed sequence $y\sim N(0,1)$ and a uniform distributed sequence $z\sim U(-1,1)$. I combined those two sequence and form a new sequence $x$ such that:
The sequence $x$ can pass the Ljung-box test but it is not a identically distributed sequence.