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I have a data set of house prices and their corresponding features (rooms, meter squared, etc). An additional feature is the sold date of the house. The aim is to create a model that can estimate the price of a house as if it was sold today. For example a house with a specific set of features (5 rooms, 100 meters squared) and today's date (28-1-2020), what would it sell for? Time is an important component, because prices increase (inflate over time). I am struggling to find a way to incorporate the sold date as a feature in the gradient boosting model.

I think there are a number of approaches:

  1. Convert the data into an integer, and include it directly in the model as a feature.
  2. Create a separate model for modelling the house price development over time. Let's think of this as some kind of an AR(1) model. I could then adjust all observations for inflation, so that we would get an inflation adjusted price for today. These inflation adjusted prices would be trained on the feature set.

What are your thoughts on these two options? Are there any alternative methods?

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  • $\begingroup$ It would help to understand the set-up a little better. Are you saying that you only want to estimate prices for dates that already included in the sample? (Otherwise, it seems Approach #1 would would fail). Do you have a number of sales observations on every house in your sample (repeat sales data) or only one price? $\endgroup$
    – Sharad
    Jan 28 at 0:48
  • $\begingroup$ Thanks for the response. I updated the question, I think its a bit clearer now. $\endgroup$ Jan 28 at 11:20
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The standard approach here (as you probably know) would be to estimate a hedonic regression with a time-dummy. However, the problem you're facing (if I understand it correctly) is to estimate the price for a house with a given bundle of characteristics for times that lie beyond the last sold dates in the data set.

One approach you can take is to estimate a house price index for a reference house (assuming you have enough data), project it forward, and then use the hedonic regression to customize the estimate for a specific house. The forward projection of the index is, of course, quite challenging. However, at least locally, house prices do show significant serial correlation so projecting one to two quarters ahead should give reasonable results.

I think what I've said above effectively combines your (1) and (2). Another approach would be to take out the time dummy in your model and substitute it with the appropriate value of a repeat-sales house price index (HPI) for that geographic region as of the sold date. Fortunately, there is a high-quality free repeat sales HPI available FHFA House Price Index. The FHFA HPIs are updated frequently although the data is somewhat lagged (by 1-2 months). Once again, a simple time-series model that incorporates serial correlation and seasonal effects should allow you to estimate values for times close to today's dates reasonably effectively.

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  • $\begingroup$ Thank you for the clear explanation. My issue is that my transaction prices are delayed by two months. What I also just realized is that another approach would be to use the asking price, since I have real time asking price data. Ofcourse the asking price is not equal to the transaction price, but with averaging it should come close. I will try all three methods and test them. $\endgroup$ Jan 29 at 19:01
  • $\begingroup$ You might always want to consider an ensemble approach by combining the ask price method with one of the two other methods since they reflect independent data sets. $\endgroup$
    – Sharad
    Jan 29 at 21:07

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