# Eviews and Forecasting Linear Regression with AR(1) Error Term

This question is geared towards those who are familiar with Eviews and forecasting with linear regression in the case of AR(1) error terms.

Consider the classical linear regression model where the error term has first order serial correlation, i.e.

$$Y_t = X_t'B + e_t, \quad e_t = \rho e_{t-1} + \nu_t, \quad 0 \leq |\rho| < 1, \quad \nu_t \text{ is } n(0,\sigma^2)$$

I used the workfile house1.wf1 that comes with Eviews to do a simple regression of housing starts vs the S&P500 index with AR(1) error terms. I was able replicate in Excel how Eviews determines the coefficients in the model and also how Eviews does dynamic point forecasts, but I wasn't able to figure out how Eviews calculates the s.e. of the forecast. Does anyone know the exact formulas and/or procedure Eviews uses? Also, does Eviews assume that the forecast error is normally distributed?

I have the book Econometric Models and Economic Forecasts by Pindyck and Rubinfeld. They mention that if you express the model above in generalized difference form

$$Y_t^* = (X_t^*)'B + \nu_t$$ where $$Y_t^* = Y_t - \rho Y_{t-1} \quad X_t^* = X_t - \rho X_{t-1}$$

then you can use the equation $$\sigma_f^2 = \sigma_\nu^2\left[1 + \frac{1}{T} + \frac{(X_{t+1}-\overline{X})^2}{\sum(X_t - \overline{X})^2}\right]$$.

Is Eviews doing something like this?

Any help is appreciated.

• Have you checked the Eviews manual? It may contain some information. If not, you can always ask in Eviews forums, since you paid for the software, you have a right to know how it works. I suspect that the Eviews use some variation of usual OLS standard errors for forecasts. Note that AR(1) model is actually GLS model. These two questions (and answers below) might help you: stats.stackexchange.com/questions/14426/prediction-with-gls, stats.stackexchange.com/questions/9131/… – mpiktas Jun 29 '15 at 6:57
• Thanks for the reply. I read the eviews manual and posted on their forum. Unfortunately, the manual only says how Eviews calculates dynamic and static point forecasts. It doesn't address calculating standard errors. I did find a post from someone that said eviews uses OLS s.e. formula (assuming no serial correlation) in the static case. In the dynamic case, an old post from an eviews mod said they use a recursive formula but that was the extent of the post. Secondly, it turns out that eviews uses nonlinear least squares to fit a linear regression equation with ar(1) error term instead of FGLS. – Gelfan Jun 29 '15 at 7:26