Using a Fourier polynomial expansion to generate a spatial predictor

Abstract

Purpose

Spatial autocorrelation in regression residuals is a major issue for the modeller because it disturbs parameter estimates and invalidates the reliability of conclusions drawn from models. The purpose of this paper is to develop an approach which generates new spatial predictors that can be mapped and qualitatively analysed while controlling for spatial autocorrelation among residuals.

Design/methodology/approach

This paper explores an alternate approach using a Fourier polynomial function based on geographical coordinates to construct an additional spatial predictor that allows to capture the latent spatial pattern hidden among residuals. An empirical validation based on hedonic modelling of sale prices variation using a large dataset of house transactions is provided.

Findings

Results show that the spatial autocorrelation problem is under control as shown by low Moran's I indexes. Moreover, this geo‐statistical approach provides coefficients on environmental amenities that are still highly significant by capturing only the remaining spatial autocorrelation.

Originality/value

The originality of this paper relies on the development of a new model that allows considering, simultaneously spatial and time dimension while measuring the marginal impact of environmental amenities on house prices avoiding competition with the weight matrix needed in most spatial econometric models.

Citation

Dubé, J., Thériault, M. and Des Rosiers, F. (2012), "Using a Fourier polynomial expansion to generate a spatial predictor", International Journal of Housing Markets and Analysis, Vol. 5 No. 2, pp. 177-195. https://doi.org/10.1108/17538271211225922