Predicting missing data. Looking for good data predicting technique I am analysing data for Countries Trade GDP. Some of the countries have missing GDP value for given a year. However, I have Grand Total for the entire region for that year. Is there a good data science technique to fill the missing Trade in GDP for the below example.
there are several ways how to interpolate the missing data depending on how long history record do you have available:


you can compute ration of GDPs r_i (where all r_i sums to 1) in year Y-1 of each state with missing values in year Y; then you know the amount of GDP in year Y which should be spread among missing (GDP_total - GDP_known) and multiply by r_i
a more sophisticated way would be computing the gradient from the timeline Y-1, Y-2, Y-3, ... and you predict a value for year Y for each missing state; then you would again compute ration r_i among missing and distribute remaining GDP accordingly. This regression can be done also backward if you know Y+1, Y+2, Y+3, ... or interpolation from Y-1 and Y+1.