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Nonstationary matrix covariances: compact support, long range dependence and quasi-arithmetic constructions

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Abstract

Flexible models for multivariate processes are increasingly important for datasets in the geophysical, environmental, economics and health sciences. Modern datasets involve numerous variables observed at large numbers of space–time locations, with millions of data points being common. We develop a suite of stochastic models for nonstationary multivariate processes. The constructions break into three basic categories—quasi-arithmetic, locally stationary covariances with compact support, and locally stationary covariances with possible long-range dependence. All derived models are nonstationary, and we illustrate the flexibility of select choices through simulation.

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Acknowledgments

Emilio Porcu is supported by Proyecto Fondecyt Regular number 1130647, funded by the Chilean Ministry of Education.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Colorado, Boulder, CO, 80309, USA

    William Kleiber

  2. Departamento de Matemática, Universidad Técnica Federico Santa Maria, Valparaiso, Chile

    Emilio Porcu

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  1. William Kleiber
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  2. Emilio Porcu
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Correspondence to William Kleiber.

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Kleiber, W., Porcu, E. Nonstationary matrix covariances: compact support, long range dependence and quasi-arithmetic constructions. Stoch Environ Res Risk Assess 29, 193–204 (2015). https://doi.org/10.1007/s00477-014-0867-6

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