The Annals of Applied Statistics

An autoregressive approach to house price modeling

Chaitra H. Nagaraja, Lawrence D. Brown, and Linda H. Zhao

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A statistical model for predicting individual house prices and constructing a house price index is proposed utilizing information regarding sale price, time of sale and location (ZIP code). This model is composed of a fixed time effect and a random ZIP (postal) code effect combined with an autoregressive component. The former two components are applied to all home sales, while the latter is applied only to homes sold repeatedly. The time effect can be converted into a house price index. To evaluate the proposed model and the resulting index, single-family home sales for twenty US metropolitan areas from July 1985 through September 2004 are analyzed. The model is shown to have better predictive abilities than the benchmark S&P/Case–Shiller model, which is a repeat sales model, and a conventional mixed effects model. Finally, Los Angeles, CA, is used to illustrate a historical housing market downturn.

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Ann. Appl. Stat., Volume 5, Number 1 (2011), 124-149.

First available in Project Euclid: 21 March 2011

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Housing index time series repeat sales


Nagaraja, Chaitra H.; Brown, Lawrence D.; Zhao, Linda H. An autoregressive approach to house price modeling. Ann. Appl. Stat. 5 (2011), no. 1, 124--149. doi:10.1214/10-AOAS380.

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Supplemental materials

  • Supplement to “An autoregressive approach to house price modeling”. This supplement contains extra analysis on a variety of topics related to the paper from examining the convergence of the coordinate ascent algorithm, or applying alternate loss functions, to studying the impact of each feature included in the autoregressive (AR) model.