Philipp Otto, Osman Doğan, Süleyman Taşpınar
arXiv 28 Feb 2022 · Statistics — Methodology · publishedSpatial Economic Analysis (2023) · 9 citations (OpenAlex)
arXiv:2202.13856 · PDF · DOI · OpenAlex · Extracted main text
Geo-referenced data are characterized by an inherent spatial dependence due to the geographical proximity. In this paper, we introduce a dynamic spatiotemporal autoregressive conditional heteroscedasticity (ARCH) process to describe the effects of (i) the log-squared time-lagged outcome variable, i.e., the temporal effect, (ii) the spatial lag of the log-squared outcome variable, i.e., the spatial effect, and (iii) the spatial lag of the log-squared time-lagged outcome variable, i.e., the spatiotemporal effect, on the volatility of an outcome variable. Furthermore, our suggested process allows for the fixed effects over time and space to account for the unobserved heterogeneity. For this dynamic spatiotemporal ARCH model, we derive a generalized method of moments (GMM) estimator based on the linear and quadratic moment conditions of a specific transformation. We show the consistency and asymptotic normality of the GMM estimator, and determine the best set of moment functions. We investigate the finite-sample properties of the proposed GMM estimator in a series of Monte-Carlo simulations with different model specifications and error distributions. Our simulation results show that our suggested GMM estimator has good finite sample properties. In an empirical application, we use monthly log-returns of the average condominium prices of each postcode of Berlin from 1995 to 2015 (190 spatial units, 240 time points) to demonstrate the use of our suggested model. Our estimation results show that the temporal, spatial and spatiotemporal lags of the log-squared returns have statistically significant effects on the volatility of the log-returns.
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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 | Lee, L.-f. L. and Yu, J (2014) Efficient GMM estimation of spatial dynamic panel data models with fixed effects | 0.814 | 13 | 4 | 54% |
| 2 | Lee, L.-f (2007) GMM and 2SLS estimation of mixed regressive, spatial autoregressive models | 0.737 | 3 | 3 | 67% |
| 3 | Yu, J., de Jong, R., and fei Lee, L (2008) Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and t are large | 0.644 | 3 | 2 | 67% |
| 4 | Lee, L.-f. and Yu, J (2010) A spatial dynamic panel data model with both time and individual fixed effects | 0.511 | 2 | 1 | 100% |
| 5 | Bollerslev, T., Chou, R. Y., and Kroner, K. F (1992) Arch modeling in finance: A review of the theory and empirical evidence | 0.405 | 1 | 1 | 100% |
| 6 | Engle, R. F (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation | 0.405 | 1 | 1 | 100% |
| 7 | Engle, R. F. and Bollerslev, T (1986) Modelling the persistence of conditional variances | 0.405 | 1 | 1 | 100% |
| 8 | Hlleland, S. and Karlsen, H. A (2020) A stationary spatio-temporal GARCH model | 0.405 | 1 | 1 | 100% |
| 9 | Jacquier, E., Polson, N. G., and Rossi, P. E (1994) Bayesian analysis of stochastic volatility models | 0.405 | 1 | 1 | 100% |
| 10 | Kelejian, H. H. and Prucha, I. R (2010) Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances | 0.405 | 1 | 1 | 100% |
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