Continuous auto-regressive moving average random fields on n

• 成果类型: Article
• 署名作者: Brockwell, Peter J.; Matsuda, Yasumasa
• 署名单位: Colorado State University System; Colorado State University Fort Collins; Tohoku University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12197
• 发表日期: 2017
• 页码: 833-857
• 关键词: Transforms; driven

摘要

We define an isotropic Levy-driven continuous auto-regressive moving average CARMA(p,q) random field on Rn as the integral of a radial CARMA kernel with respect to a Levy sheet. Such fields constitute a parametric family characterized by an auto-regressive polynomial a and a moving average polynomial b having zeros in both the left and the right complex half-planes. They extend the well-balanced Ornstein-Uhlenbeck process of Schnurr and Woerner to a well-balanced CARMA process in one dimension (with a much richer class of autocovariance functions) and to an isotropic CARMA random field on Rn for n>1. We derive second-order properties of these random fields and extend the results to a larger class of anisotropic CARMA random fields. If the driving Levy sheet is compound Poisson it is trivial to simulate the corresponding random field on any bounded subset of Rn. A method for joint estimation of the CARMA kernel parameters and knot locations is proposed for compound-Poisson-driven fields and is illustrated by applications to simulated data and Tokyo land price data.