Details
| Original language | English |
|---|---|
| Pages (from-to) | 623-638 |
| Number of pages | 16 |
| Journal | Statistical papers |
| Volume | 62 |
| Issue number | 2 |
| Early online date | 6 Apr 2019 |
| Publication status | Published - Apr 2021 |
Abstract
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 spatial conditional heteroscedasticity. That means that the variance in some locations depends on the variance in neighboring locations. In contrast to the temporal ARCH model, for which the distribution is known, given the full information set for the prior periods, the distribution is not straightforward in the spatial and spatiotemporal settings. Thus, we focus on the probability structure of these models. In particular, we derive the conditional and unconditional moments of the process as well as the distribution of the process, given a known error distribution. Eventually, it is shown that the process is strictly stationary under certain conditions.
Keywords
- Moments, Probability structure, Spatial ARCH, Variance 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. 62, No. 2, 04.2021, p. 623-638.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stochastic properties of spatial and spatiotemporal ARCH models
AU - Otto, Philipp
AU - Schmid, Wolfgang
AU - Garthoff, Robert
PY - 2021/4
Y1 - 2021/4
N2 - 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 spatial conditional heteroscedasticity. That means that the variance in some locations depends on the variance in neighboring locations. In contrast to the temporal ARCH model, for which the distribution is known, given the full information set for the prior periods, the distribution is not straightforward in the spatial and spatiotemporal settings. Thus, we focus on the probability structure of these models. In particular, we derive the conditional and unconditional moments of the process as well as the distribution of the process, given a known error distribution. Eventually, it is shown that the process is strictly stationary under certain conditions.
AB - 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 spatial conditional heteroscedasticity. That means that the variance in some locations depends on the variance in neighboring locations. In contrast to the temporal ARCH model, for which the distribution is known, given the full information set for the prior periods, the distribution is not straightforward in the spatial and spatiotemporal settings. Thus, we focus on the probability structure of these models. In particular, we derive the conditional and unconditional moments of the process as well as the distribution of the process, given a known error distribution. Eventually, it is shown that the process is strictly stationary under certain conditions.
KW - Moments
KW - Probability structure
KW - Spatial ARCH
KW - Variance clusters
UR - http://www.scopus.com/inward/record.url?scp=85064338135&partnerID=8YFLogxK
U2 - 10.1007/s00362-019-01106-x
DO - 10.1007/s00362-019-01106-x
M3 - Article
AN - SCOPUS:85064338135
VL - 62
SP - 623
EP - 638
JO - Statistical papers
JF - Statistical papers
SN - 0932-5026
IS - 2
ER -