I have a set of real estate data; historic sales price, square meters, location (latitude, longitude), neighbourhood, city, sold date and bunch of other features. I have used a boosting model to estimate the price of an individual house. I would like to estimate the price of a house 1 month ahead; but this requires extrapolating and something boosting is not capable of.
For this reason, I am trying to create inflation adjusted houses prices which will be fed into the boosting model. Old sale prices will therefore be inflation adjusted to 1 month ahead. This way I can capture inflation, and extrapolate over time. My objective is to create a separate model that can capture local changes in housing prices and extrapolate them forward. Essentially a price index.
I have aggregated the data at a city level by taking the median price per square meter for each month. The data exhibits strong AR characteristics. However, when I try this same approach on a neighbourhood (more local) level the AR characteristics disappear. I am unfortunately limited to 2 years of data.
What approach would you suggest to modelling a local price index that can be extrapolated with such a dataset? Kriging appears to be powerful, but is not made for extrapolation..