A flexible model for spatial volatility with an application to the Chicago housing market

Existing volatility models normally emphasize the behaviour of prices in a temporal sense and comparatively few studies have explicitly analysed the spatial variation of volatility. This paper proposes a flexible spatial volatility model for squared returns using a Box–Cox transformation that includes the linear and log-linear forms as special cases, thus providing a unified framework for simultaneously testing space-varying volatility and its functional form. The use of the model is illustrated by a substantive application to housing price data in the US city of Chicago. The estimation results suggest that housing returns in Chicago show that the volatility exhibits strong spatial dependence and the log-linear functional form is appropriate. In the final log-linear model, a new practical indicator, called neighbourhood elasticity, is proposed that determines how volatility in one neighbourhood is linked to that in surrounding neighbourhoods.