Fitting a distribution to data
My understanding of your problem: you have realizations of $X$ (property value at first point in time) and $Y$ (value at second point in time). Want to fit a distribution for $Y-X$--more generally, a "model for the data."

One way of doing this would be plot a histogram of these values and then come up with plausible distributions that might fit the data, and then use maximum likelihood estimation to find the optimal parameters. If the models are nested, then you can use, e.g., the likelihood ratio test to determine which is a better fit to the data. 

If not, then things are trickier. One good option is to hold out some of the data for testing, fit the models on the training data, predict the test data using each model, and see which one performs better.