I have time series $R$, which shows, how
something changes at the regional level.
I have several time series $U_i$, which show, how
something changes at a special unit $I$ level.
There are many units in the region. $R$ has no missing data. Different $U_i$ have their own missing periods.
I want to forecast $U$ after a missing period using information of $R$ and information of $U$ when it was availible.
My thoghts till now:
Suppose $R$ is known on interval $[0, 365]$. Suppose $U_i$ is known on interval $[0,300]$. Let's take $R$ and $U_i$ both on interval $[0,300]$, take difference between them and trying to predict that difference with linear regression. So for interval $[301,365]$, I will have differences and to restore $U_i$, I will just have to take out my differences from $R$.
I don't like my solution, because:
- We need a model for each $U_i$.
- Because, sometimes data is more sparse and I don't even have a $[0,300]$ known interval, so not able to train regression properly.