Reverse forecasting in time series we have a given time series includes a specific type of data for example  from year 1980 to 2016. Also we know that we should achieve to a predefined goal(a fixed value) in year 2025. But we don't know how to reach it. 
In other words We have a time series $T = \left\{T_1,\ldots, T_n\right\}$ from time $1$ to time $n$ and we want to reach a time series $T'=\left\{T_{n+k+1},\ldots, T_{n+k+m}\right\}$ from time $n+k+1$ to $t+k+m$. But we do not have the time series between the time $n+1$ to $n+k$: $T"=\left\{T_{n+1},\ldots,T_{n+k}\right\}$. What's the solution for this problem? what algorithms can I use? what's the keywords for searching about them?
 A: You can use several approaches to do that. 
As I understood you want to perform Ex Ante forecasts and one of the many possibilities is to use restricted sample period T = {T1,..., Tn} to estimate the model. The model is then forecasted out of sample over the period Tn+1... Tn+k... 
The simple example would use AR(1) model to illustrate the main idea of this approach: 
Consider a sample of {y1,y2....yt} from the AR(1) model 
such that: 
yt= δ0 + δ1yt-1+ ut
We can obtain ex ante forecasts of yt+1,  yt+h as follows: 
1. Estimation: Using your sample {y1....yn} estimate δ0,δ1 and get fitted values δ0(hat) and δ1(hat)
2. Forecasting yt+1: using yt and fitted values  (δ0(hat) and δ1(hat)) obtain
yt+1(hat)=δ0(hat) + δ1(hat)yt
3. Forecasting yt+h: We can recursively obtain yt+h(hat) = δ0(hat) + δ1(hat)yt+h-1(hat) using yt+h-1(hat) and (δ0(hat)  δ1(hat))
Try to google predictive regression for time series, regression model forecasts, you may find many creative techniques that the researchers come up with   
