Vector Stochastic Processes with Pólya‐Type Correlation Structure. (20th October 2016)

• Record Type: Journal Article
• Authors: Ma, Chunsheng
• Is Part Of: International statistical review. Volume 85:Number 2(2017)
• Page Start: 340
• Page End: 354
• Publication Date: 2016-10-20
• Subjects: Cross covariance -- direct covariance -- covariance matrix function -- elliptically contoured process -- Gaussian process -- infinitely divisible -- Lévy process -- Pólya‐type function; Statistics -- Periodicals; Statistics -- Bibliography -- Periodicals; Statistics -- Bibliography; Statistics -- Periodicals; Statistique; Statistique -- Périodiques; Statistique -- Bibliographie -- Périodiques; Statistique -- Étude et enseignement -- Périodiques; Statistique -- Étude et enseignement -- Bibliographie -- Périodiques; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519.2
• DOI: 10.1111/insr.12204
• Languages: English
• ISSNs: 0306-7734

Abstract

Summary: This paper introduces a simple method to construct a stationary process on the real line with a Pólya‐type covariance function and with any infinitely divisible marginal distribution, by randomising the timescale of the increment of a second‐order Lévy process with an appropriate positive random variable. With the construction method extended to the multivariate case, we construct vector stochastic processes with Pólya‐type direct covariance functions and with any specified infinitely divisible marginal distributions. This makes available a new class of non‐Gaussian vector stochastic processes with flexible correlation structure for use in modelling and simulation.