You could setup a longitudinal regression model if you have correlation of prices throughout time. You can set these up with R or SAS if you have these software.
Using a regression model you can add as many terms (including interaction) and test whether certain effects and interactions actually make a difference.
The thing about the regression model is that if you are going to use correlation, you need to use something decent that takes into account domain knowledge. If house prices are seasonal and not just based on say lag, then it means that the correlation model will be more complicated.
The first thing I would do if I were you, would be to figure out what kind of correlation exists and then use that to derive a covariance matrix structure for the generalized least squares and fit the data to that. Since I don't know about the intricacies of real estate markets and house prices, that is as far as I will go.