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Hi,

How do I estimate u[t] = rho[1]*u[t-1] + rho[2]*u[t-2] +rho[3]*u[t-3] +rho[4]*u[t-4] where u[t] is the residual series from a corresponding time series equation.

Is it just to put AR(1)..AR(4) in the original time series equation?

Thanks.

By corresponding/original time series equation if you mean something like: Yt = b0 + b1*Xt + Ut, then the answer is "Yes". You can simply estimate it as follows: