I want to recursively estimate a model on a growing sample (say from 50 to 55 periods) and get 1&2-step ahead **out-of-sample** forecasts of endogenous variables for each sub-sample (that is E_{t}y_{t+k} where t \in [50,55] and k \in [1,2] ).

In the estimation options I have: `nobs=[50:55], filter_step_ahead = [1 2], forecast = 2`

which results in `oo_.FilteredVariablesKStepAhead`

and `oo_.RecursiveForecast.Mean`

, respectively. I will denote E^F for the filtered values, E^R for the recursive forecasts and T as the final period considered.

I noticed that for all variables `oo_.RecursiveForecast.Mean`

and `oo_.FilteredVariablesKStepAhead`

coincide for the last period (E^F_T y_{T+k} = E^R_T y_{T+k} ), but not for any of the previous periods (E^F_t y_{t+k} \not= E^R_t y_{t+k} , for t \not= T). I understand that `oo_.RecursiveForecast.Mean`

keeps the forecasts for each iteration of the estimation (50:55), whilst `oo_.FilteredVariablesKStepAhead`

probably gets overwritten and at the end consists of only the last estimation (1:55 periods in this example). But how should the values of this final `oo_.FilteredVariablesKStepAhead`

be interpreted then?

Given the following description of the filtered values, I would expect both to be equivalent (i.e. E^F_t y_{t+k} = E^R_t y_{t+k} ~ \forall t)

(4. The model file â€” Dynare 5.4 documentation)

`filter_step_ahead = [INTEGER1 INTEGER2 ...]`

Triggers the computation k-step ahead filtered values, i.e. E_t y_{t+k} . Stores results in

`oo_.FilteredVariablesKStepAhead`

. Also stores 1-step ahead values in`oo_.FilteredVariables`

.`oo_.FilteredVariablesKStepAheadVariances`

is stored if`filter_covariance`

.

Is the case that the last `oo_.FilteredVariablesKStepAhead`

matrix (at T ) somehow uses information of [t+1,T] even for filtered variables for any t<T? Perhaps E^F_{t|T} y_{t+k} forecasts y_{t+k} at period t with respect to exogenous variables, but uses an estimated model based on information up to an including T whilst E^R_t y_{t+k} by definition always uses an estimated model up to an including only t . Thus by construction, `oo_.FilteredVariablesKStepAhead`

are only valid as out of sample forecasts at the last period ( E^F_T=E^R_T ).

Is this the right intuition? If so, then the only valid way to get recursive out-of-sample forecasts will be through `oo_.RecursiveForecast.Mean`

.

Many thanks,

Viktor