I have time-series data of national-level population estimates from 1990 to 2015. I also have subnational-level population estimates (thus, the distribution of national data), but only for years 2000 through 2015. With only a small subset of countries from which I can knowledgeably assume there were no events that caused significant population re-distribution, I would like to extrapolate subnational data for 1990 to 2000, taking into account both (1) the complete time-series trends of national data, and (2) the trends of that country's incomplete subnational data.
Is there a method for such extrapolation? And how would one adjust standard errors accordingly?