Spatio-Temporal Expanding Distance Asymptotic Framework for Locally Stationary Processes

Tingjin Chu (), Jialuo Liu, Jun Zhu and Haonan Wang
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Tingjin Chu: University of Melbourne
Jialuo Liu: Colorado State University
Jun Zhu: University of Wisconsin-Madison
Haonan Wang: Colorado State University

Sankhya A: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 12, 689-713

Abstract: Abstract Spatio-temporal data indexed by sampling locations and sampling time points are encountered in many scientific disciplines such as climatology, environmental sciences, and public health. Here, we propose a novel spatio-temporal expanding distance (STED) asymptotic framework for studying the properties of statistical inference for nonstationary spatio-temporal models. In particular, to model spatio-temporal dependence, we develop a new class of locally stationary spatio-temporal covariance functions. The STED asymptotic framework has a fixed spatio-temporal domain for spatio-temporal processes that are globally nonstationary in a rescaled fixed domain and locally stationary in a distance expanding domain. The utility of STED is illustrated by establishing the asymptotic properties of the maximum likelihood estimation for a general class of spatio-temporal covariance functions. A simulation study suggests sound finite-sample properties and the method is applied to a sea-surface temperature dataset.

Keywords: Covariance functions; Nonstationary processes; Random fields; Spatial statistics; Spatio-temporal statistics; Primary 62F12; Secondary 62M30 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13171-020-00213-4

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