Spatial extension of generalized autoregressive conditional heteroskedasticity models

This paper proposes an extension of generalized autoregressive conditional heteroskedasticity (GARCH) models for a time series to those for spatial data, which are called here spatial GARCH (S-GARCH) models. S-GARCH models are re-expressed as spatial autoregressive moving-average (SARMA) models and a two-step procedure based on quasi-likelihood functions is proposed to estimate the parameters. The consistency and asymptotic normality are proven for the two-step estimators. S-GARCH models are applied to simulated and land-price data in areas of Tokyo to demonstrate the empirical properties.

Automated summary

This paper introduces an extension of GARCH models to spatial data, known as S-GARCH models. By re-expressing S-GARCH models as SARMA models and proposing a two-step estimation process based on quasi-likelihood functions, the consistency and asymptotic normality of the parameters are proven. S-GARCH models are applied to simulated and land-price data in Tokyo to illustrate their empirical properties.