Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity

@article{Otto2018GeneralisedSA,
  title={Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity},
  author={Philipp E. Otto and Wolfgang Schmid and Robert Garthoff},
  journal={Spatial Statistics},
  year={2018}
}
In this paper, we introduce a new spatial model that incorporates heteroscedastic variance depending on neighboring locations. The proposed process is regarded as the spatial equivalent to the temporal autoregressive conditional heteroscedasticity (ARCH) model. We show additionally how the introduced spatial ARCH model can be used in spatiotemporal settings. In contrast to the temporal ARCH model, in which the distribution is known given the full information set of the prior periods, the… Expand

Figures and Tables from this paper

Spatial and Spatiotemporal GARCH Models -- A Unified Approach
TLDR
This paper introduces a unified spatial and spatiotemporal GARCH-type model, which covers all previously proposed spatial autoregressive conditional heteroscedasticity (ARCH) models but also introduces novel spatial GARCH (spGARCH) and E-GARCH processes. Expand
Generalized Spatial and Spatiotemporal ARCH Models
TLDR
A novel spatial Garch process is introduced 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, and allows for instantaneous spill-overs across all spatial units. Expand
Stochastic properties of spatial and spatiotemporal ARCH models
In this paper, we provide some results on the class of spatial autoregressive conditional heteroscedasticity (ARCH) models, which have been introduced in recent literature to model spatialExpand
spGARCH: An R-Package for Spatial and Spatiotemporal ARCH models
In this paper, a general overview on spatial and spatiotemporal ARCH models is provided. In particular, we distinguish between three different spatial ARCH-type models. In addition to the originalExpand
Directional spatial autoregressive dependence in the conditional first- and second-order moments
Abstract In contrast to classical econometric approaches which are based on prespecified isotropic weighting schemes, we suggest that the spatial weighting matrix in the presence of directionalExpand
A Stationary Spatio‐Temporal GARCH Model
We introduce a lagged nearest‐neighbour, stationary spatio‐temporal generalized autoregressive conditional heteroskedasticity (GARCH) model on an infinite spatial grid that opens forExpand
Volatility modelling in time and space 2020
This thesis contributes to the scientific community in several aspects. We introduce both spatialand spatio-temporal extensions to the family of GARCH and ARMA-GARCH models and present asymptoticExpand
AFlexible Model for Spatial Volatility with an Application to the Chicago Housing Market
Existing volatility models normally emphasize the behavior of prices in a temporal sense and comparatively few studies have explicitly analyzed the spatial variation of volatility. This paperExpand
Spatial Statistics, or How to Extract Knowledge from Data
TLDR
This paper describes classical modeling approaches in geostatistics and spatial econometrics, and shows how large spatial and spatiotemporal data can be modeled by these approaches. Expand
General Modelling for Kalman Filter Applying to Investigating Deep Pattern of Data and Motion Modelling.
TLDR
The TVLAP model is proposed to estimate the instantaneous mean (trend) of the interested data series, specifically, time series, and is shown to be the generalization of Local-Level model and Holt's model in time series analysis community and Constant Velocity model and Constant Acceleration model in moving-object tracking field. Expand
...
1
2
...

References

SHOWING 1-10 OF 81 REFERENCES
Spatial GARCH: A Spatial Approach to Multivariate Volatility Modeling
This paper introduces a new approach to modelling the conditional variance in a multivariate setting. It is essentially a combination of the popular GARCH model class with a spatial component,Expand
A Time-Space Dynamic Panel Data Model with Spatial Moving Average Errors
This paper focuses on the estimation and predictive performance of several estimators for the time-space dynamic panel data model with Spatial Moving Average Random Effects (SMA-RE) structure of theExpand
Restricted spatial regression in practice: Geostatistical models, confounding, and robustness under model misspecification
TLDR
It is shown that RSR provides computational benefits relative to the confounded SGLMM, but that Bayesian credible intervals under RSR can be inappropriately narrow under model misspecification. Expand
Bayesian inference for non-stationary spatial covariance structure via spatial deformations
In geostatistics it is common practice to assume that the underlying spatial process is stationary and isotropic, i.e. the spatial distribution is unchanged when the origin of the index set isExpand
Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation
Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditionalExpand
Heteroskedasticity of Unknown Form in Spatial Autoregressive Models with Moving Average Disturbance Term
In this study, I investigate the necessary condition for consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. I showExpand
Nonparametric Estimation of Nonstationary Spatial Covariance Structure
Abstract Estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks. We introduce aExpand
Dynamic models for spatiotemporal data
We propose a model for non-stationary spatiotemporal data. To account for spatial variability, we model the mean function at each time period as a locally weighted mixture of linear regressions. ToExpand
The importance of scale for spatial-confounding bias and precision of spatial regression estimators.
  • C. Paciorek
  • Mathematics, Medicine
  • Statistical science : a review journal of the Institute of Mathematical Statistics
  • 2010
TLDR
In an application on the association between black carbon particulate matter air pollution and birth weight, controlling for large-scale spatial variation appears to reduce bias from unmeasured confounders, while increasing uncertainty in the estimated pollution effect. Expand
Estimation of spatial autoregressive panel data models with fixed effects
This paper establishes asymptotic properties of quasi-maximum likelihood estimators for SAR panel data models with fixed effects and SAR disturbances. A direct approach is to estimate all theExpand
...
1
2
3
4
5
...