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Dynamic Spatiotemporal ARCH Models: Small and Large Sample Results

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  • Philipp Otto
  • Osman Dou{g}an
  • Suleyman Tac{s}p{i}nar

Abstract

This paper explores the estimation of a dynamic spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model. The log-volatility term in this model can depend on (i) the spatial lag of the log-squared outcome variable, (ii) the time-lag of the log-squared outcome variable, (iii) the spatiotemporal lag of the log-squared outcome variable, (iv) exogenous variables, and (v) the unobserved heterogeneity across regions and time, i.e., the regional and time fixed effects. We examine the small and large sample properties of two quasi-maximum likelihood estimators and a generalized method of moments estimator for this model. We first summarize the theoretical properties of these estimators and then compare their finite sample properties through Monte Carlo simulations.

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  • Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar, 2023. "Dynamic Spatiotemporal ARCH Models: Small and Large Sample Results," Papers 2312.05898, arXiv.org.
    • Handle: RePEc:arx:papers:2312.05898
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    References listed on IDEAS

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    1. Yu, Jihai & de Jong, Robert & Lee, Lung-fei, 2008. "Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large," Journal of Econometrics, Elsevier, vol. 146(1), pages 118-134, September.
    2. Peter M Robinson, 2009. "Large-Sample Inference on SpatialDependence," STICERD - Econometrics Paper Series 533, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. P. M. Robinson, 2009. "Large-sample inference on spatial dependence," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 68-82, January.
    4. Lee, Lung-fei & Yu, Jihai, 2010. "Estimation of spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 154(2), pages 165-185, February.
    5. Lee, Lung-fei & Yu, Jihai, 2014. "Efficient GMM estimation of spatial dynamic panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 180(2), pages 174-197.
    6. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
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