arXiv 26 Apr 2022 · Statistics — Methodology · publishedSpatial Statistics (2024) · 3 citations (OpenAlex)
arXiv:2204.12472 · PDF · DOI · OpenAlex · Extracted main text
This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects in the conditional variance, as they are usually present in spatial econometric applications. Furthermore, spatial and temporal cross-variable effects are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and different error distributions, the performance of the QMLE is analysed in a series of Monte-Carlo simulations. In addition, we illustrate the practical usage of the new model with a real-world example. We analyse the monthly real-estate price returns for three different property types in Berlin from 2002 to 2014. We find weak (instantaneous) spatial interactions, while the temporal autoregressive structure in the market risks is of higher importance. Interactions between the different property types only occur in the temporally lagged variables. Thus, we see mainly temporal volatility clusters and weak spatial volatility spill-overs.
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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 | Yang, K. and Lee, L.-f (2017) Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models | 0.961 | 9 | 3 | 89% |
| 2 | Otto, P. and Schmid, W (2019) Spatial and spatiotemporal GARCH models – a unified approach self | 0.874 | 5 | 2 | 100% |
| 3 | Otto, P., Schmid, W., and Garthoff, R (2018) Generalised Spatial and Spatiotemporal Autoregressive Conditional Heteroscedasticity self | 0.737 | 3 | 2 | 100% |
| 4 | Yu, J., de Jong, R., and Lee, L.-f (2008) Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large | 0.737 | 3 | 2 | 100% |
| 5 | Borovkova, S. and Lopuhaa, R (2012) Spatial GARCH: A spatial approach to multivariate volatility modeling | 0.644 | 2 | 2 | 100% |
| 6 | Engle, R. F. and Kroner, K. F (1995) Multivariate simultaneous generalized ARCH | 0.644 | 2 | 2 | 100% |
| 7 | Sato, T. and Matsuda, Y (2021) Spatial extension of generalized autoregressive conditional heteroskedasticity models | 0.644 | 2 | 2 | 100% |
| 8 | Francq, C. and Zakoian, J.-M (2011) GARCH models: Structure, Statistical Inference and Financial Applications | 0.511 | 2 | 1 | 100% |
| 9 | Bollerslev, T (1986) Generalized autoregressive conditional heteroskedasticity | 0.405 | 1 | 1 | 100% |
| 10 | Brockwell, P. J. and Davis, R. A (2006) Introduction to time series and forecasting | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 26 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Spatiotemporal Autoregressive Models for Areal Compositional Data | 0.644 | 2 | 2 |
| 2 | Spatial and Spatiotemporal Volatility Models: A Review | 0.511 | 2 | 1 |
| 3 | A Dynamic Spatiotemporal and Network ARCH Model with Common Factors | 0.405 | 1 | 1 |