chosen such that the horizons lie within the history , what is that the?

Question

In https://peerj.com/preprints/3190.pdf section 4.3

We use simulated historical forecasts (SHFs) by producing K forecasts at various cutoff points in the history, chosen such that the horizons lie within the history and the total error can be evaluated.

This sentence is very difficult to understand

1. chosen such , choose the horizon or the history, why use the past participle of choose ?
2. I can understand such horizons, that horizons, the horizons, they are same. But what is such that the horizons ??? I know sentence like we could eat this such that we don't go hungry , but here it doesn't look like, because there is a chosen before such that which doesn't relate to previous sentence.
3. lie within the history , why use within here ?

4. Actually I don't understand what horizons stands for at here. I only know the meanings as below

   the place in the distance where the earth and sky seem to meet:
   
   [ U ] We watched the horizon as the sun set.
   ​
   A person’s horizons are the limit of that person’s ideas, knowledge, and experience:
   
   [ pl ] Spending her junior year abroad has broadened her horizons.
   

Answer 1

This document is using words in a very technical sense. It may not be the best document to use for a better understanding of more ordinary English.

1. It is the cuttoff points that are being chosen, and they are chosen so that the horizon date from each one is within the history, that is, in the past not the future

2. Each data point has a horizon, a point in time say 90 days forward (or 30 or 180 or whatever is being used in a particular case). "The horizons" here means the dates that far ahead of the chosen cutoff points.

3. The history is the part of the time series in the past, as opposed to the part that has not yet occurred, but might be predicted. So when the author says that the cutoff points were chosen so that their horizons lie within the history, s/he means that each cutoff point is more than the horizon-time before the current date.

4. "Horizon" is being used for a date that is a fixed amount of time (which I am calling the horizon-time) after the date from which a prediction is being made. The horizon-time may be 30, 60, 90, or 366 days.