I have a spatial error model that I have estimated and would like to create a figure with the prediction interval. By spatial error model, I mean that the errors are spatially correlated and thus OLS is unbiased but inefficient (not a spatially auto-regressive model).

I used the geostatistical approach to spatial statistics and estimated a semivariogram for my data and used the semivariogram estimates to create a weighting matrix to account for the spatial autocorrelation in the data. I think the answer to this question though would help anyone using weights in their regression regardless of the exact structure of their weighting matrix.

I see from this [question](https://stats.stackexchange.com/questions/9131/obtaining-a-formula-for-prediction-limits-in-a-linear-model) that the formula for a 95% prediction interval for OLS is  

$$
\hat{y} \pm 1.96 \hat{\sigma} \sqrt{1 + \mathbf{X}^\* (\mathbf{X}'\mathbf{X})^{-1} (\mathbf{X}^\*)'}.
$$

Given my limited intuition, my guess would be that the prediction interval for the case with weights would be this (where $\Omega$ is the weighting matrix): 

$$
\hat{y} \pm 1.96 \hat{\sigma} \sqrt{1 + \mathbf{X}^\* (\mathbf{X}'\mathbf{\Omega}^{-1}\mathbf{X})^{-1} (\mathbf{X}^\*)'}
$$

and was hoping that I could get some feedback from the community here about the correctness or if I am even in the right ballpark.