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?


closed as unclear what you're asking by Jarle Tufto, Michael Chernick, mkt, COOLSerdash, mdewey Apr 19 at 12:26

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    $\begingroup$ The first thing that you need is a model (not an algorithm) for your data. You need to be able to write this model down on paper. From the description of your problem, it sounds like there are explanatory variables in your control that cause the outcome (i.e." if we make $X$ higher then we get closer to reaching the pre-established goal for the outcome $Y$). One you have this, you can estimate your model with data from time $1,2,...,t$ and use it to create forecast distributions out to time $t_{n+k+m}$. This will give you the probability of obtaining your goal. $\endgroup$ – Zachary Blumenfeld Jan 25 '16 at 2:32
  • $\begingroup$ The value that you should achieve is not data. It didn't happened yet. $\endgroup$ – Tim Feb 24 '18 at 22:30
  • $\begingroup$ Can you give some context? Is this a control problem? $\endgroup$ – kjetil b halvorsen Jun 6 '18 at 4:50

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


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