arXiv 19 Jun 2021 · Statistics — Methodology
arXiv:2106.10477 · PDF · DOI · OpenAlex · Extracted main text
In time-series analyses, particularly for finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased risk). In contrast, it has not been considered to be of critical importance until now to model spatial dependence in the conditional second moments. Only a few models have been proposed for modelling local clusters of increased risks. In this paper, we introduce a novel spatial GARCH process in a unified spatial and spatiotemporal GARCH framework, which also covers all previously proposed spatial ARCH models, exponential spatial GARCH, and time-series GARCH models. In contrast to previous spatiotemporal and time series models, this spatial GARCH allows for instantaneous spill-overs across all spatial units. For this common modelling framework, estimators are derived based on a non-linear least-squares approach. Eventually, the use of the model is demonstrated by a Monte Carlo simulation study and by an empirical example that focuses on real estate prices from 1995 to 2014 across the ZIP-Code areas of Berlin. A spatial autoregressive model is applied to the data to illustrate how locally varying model uncertainties (e.g., due to latent regressors) can be captured by the spatial GARCH-type models.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Otto, P., Schmid, W., and Garthoff, R (2019) Stochastic properties of spatial and spatiotemporal arch models self | 1.000 | 8 | 3 | 100% |
| 2 | Otto, P., Schmid, W., and Garthoff, R (2016) Generalized spatial and spatiotemporal autoregressive conditional heteroscedasticity self | 0.874 | 7 | 2 | 100% |
| 3 | Sato, T. and Matsuda, Y (2017) Spatial autoregressive conditional heteroskedasticity models | 0.874 | 6 | 2 | 100% |
| 4 | Otto, P., Schmid, W., and Garthoff, R (2018) Generalised Spatial and Spatiotemporal Autoregressive Conditional Heteroscedasticity self | 0.874 | 5 | 2 | 100% |
| 5 | Sato, T. and Matsuda, Y (2020) Spatial extension of generalized autoregressive conditional heteroskedasticity models | 0.874 | 5 | 2 | 100% |
| 6 | Amemiya, T (1985) Advanced econometrics | 0.644 | 4 | 2 | 50% |
| 7 | Bollerslev, T (1986) Generalized Autoregressive Conditional Heteroskedasticity | 0.644 | 2 | 2 | 100% |
| 8 | Sato, T. and Matsuda, Y (2018) Spatial GARCH models | 0.644 | 2 | 2 | 100% |
| 9 | Newey, K. and McFadden, D (1994) Large sample estimation and hypothesis | 0.511 | 3 | 2 | 33% |
| 10 | Bharucha-Reid, A. T. et al (1976) Fixed point theorems in probabilistic analysis | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 25 scored citations.