# How can I make a Non-Gaussian first order autoregressive sequence of random variables independent?

Hi everybody,

Consider a sequence of Non-Gaussian first order autoregressive random variables of length $N$, $\mathbf{X}=\{x_i\}_{i=1}^N$, generated from a common stationary distribution $p(\mathbf{x})$, with covariance matrix $$\mathbf{K}_{\mathbf{x}\mathbf{x}}=Toeplitz(1, \rho, \rho^2, \ldots, \rho^{N-1}),$$ where $\rho$ is a normalized correlation coefficient.

Can you please help me find some approaches to make $\mathbf{X}$ as a sequence of independent identically distributed (i.i.d.) random variables.

Thanks a lot in advance,

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The first thing is to find the form of their inter-dependence. Without that, you are going nowhere. –  Ricky Demer Aug 25 '11 at 7:20
@ Ricky, Thanks a lot for your comment, I add the assumption of first order autoregressive. –  Farzad Aug 25 '11 at 7:30