Re-estimating equation after each step of dynamic forecast

[miksterz]

Hello,

I need to do the following:

Generate out of sample forecasts for a basic AR(1) model. This is easy to do BUT:

After each step, I need to re-estimate the equation treating the previous forecasted value as an actual observation, then generate the next step ahead forecast and so on..

Using dynamic step ahead forecasts does treat the previous forecasts as actual observations but I understand it does not re-estimate the model at any point.

I would really appreciate if someone could get back to me asap.

Thanks in advance

[EViews Gareth]

Re-estimating the equation using the forecasted values will not do anything. Adding more rows of forecasted values does not change the coefficient estimates.

[miksterz]

really? could you please briefly explain why? it seems to me that adding new data to a series would change its coefficient in the equation..

[miksterz]

Re-estimating the equation using the forecasted values will not do anything. Adding more rows of forecasted values does not change the coefficient estimates.

also, do you only mean this is true for an AR1 process? because I plan on using more sophisticated equations too but just asked about AR1 for simplicity

[EViews Gareth]

Adding new data will change the coefficients. However you're not really adding new data, you're adding forecasted values in, and pretending that it is data.

Without getting to far into the realms of econometric advice, least squares estimation works by trying to minimise the sum of squares of the residuals (where residuals are actual values minus forecasted values) in the equation. When you add a new forecasted value as an "actual" value, the residual for that observation is zero. Thus, the residual is already completely minimised for that observation, so the estimation process will not change at all.

This is true of all least squares estimation, not just a simple AR.

[miksterz]

thanks a lot. that makes complete sense