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Spatial extension of generalized autoregressive conditional heteroskedasticity models

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  • Takaki Sato
  • Yasumasa Matsuda

Abstract

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.

Suggested Citation

  • Takaki Sato & Yasumasa Matsuda, 2021. "Spatial extension of generalized autoregressive conditional heteroskedasticity models," Spatial Economic Analysis, Taylor & Francis Journals, vol. 16(2), pages 148-160, April.
    • Handle: RePEc:taf:specan:v:16:y:2021:i:2:p:148-160
    DOI: 10.1080/17421772.2020.1742929
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    Cited by:

    1. Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar & Wolfgang Schmid & Anil K. Bera, 2023. "Spatial and Spatiotemporal Volatility Models: A Review," Papers 2308.13061, arXiv.org.
    2. Raffaele Mattera & Philipp Otto, 2023. "Network log-ARCH models for forecasting stock market volatility," Papers 2303.11064, arXiv.org.
    3. Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar, 2022. "Dynamic Spatiotemporal ARCH Models," Papers 2202.13856, arXiv.org.
    4. Bing Su & Fukang Zhu & Ke Zhu, 2023. "Statistical inference for the logarithmic spatial heteroskedasticity model with exogenous variables," Papers 2301.06658, arXiv.org.
    5. Philipp Otto, 2022. "A Multivariate Spatial and Spatiotemporal ARCH Model," Papers 2204.12472, arXiv.org.

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