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Vector Stochastic Processes with Pólya‐Type Correlation Structure
Author(s) -
Ma Chunsheng
Publication year - 2017
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12204
Subject(s) - covariance , marginal distribution , mathematics , covariance function , multivariate random variable , multivariate normal distribution , gaussian , type (biology) , simple (philosophy) , stochastic process , random variable , stochastic ordering , function (biology) , correlation function (quantum field theory) , gaussian process , multivariate statistics , statistics , spectral density , physics , ecology , philosophy , epistemology , quantum mechanics , biology , evolutionary biology
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.