Details
| Original language | English |
|---|---|
| Pages (from-to) | 1721-1747 |
| Number of pages | 27 |
| Journal | Statistical papers |
| Volume | 64 |
| Issue number | 5 |
| Early online date | 29 Sept 2022 |
| Publication status | Published - Oct 2023 |
Abstract
In time-series analysis, particularly in 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 postal 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.
Keywords
- Real estate prices, Spatial GARCH, Spatiotemporal statistics, Volatility clusters
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Statistical papers, Vol. 64, No. 5, 10.2023, p. 1721-1747.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A general framework for spatial GARCH models
AU - Otto, Philipp
AU - Schmid, Wolfgang
N1 - Funding Information: Open Access funding enabled and organized by Projekt DEAL. Funding was provided by Deutsche Forschungsgemeinschaft (Grant No. 412992257).
PY - 2023/10
Y1 - 2023/10
N2 - In time-series analysis, particularly in 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 postal 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.
AB - In time-series analysis, particularly in 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 postal 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.
KW - Real estate prices
KW - Spatial GARCH
KW - Spatiotemporal statistics
KW - Volatility clusters
UR - http://www.scopus.com/inward/record.url?scp=85139154461&partnerID=8YFLogxK
U2 - 10.1007/s00362-022-01357-1
DO - 10.1007/s00362-022-01357-1
M3 - Article
VL - 64
SP - 1721
EP - 1747
JO - Statistical papers
JF - Statistical papers
SN - 0932-5026
IS - 5
ER -