Limit theory for the sample covariance and correlation matrix functions of a class of multivariate linear processes

DOI10.1080/15326349908807158zbMath0701.62033OpenAlexW2026503475MaRDI QIDQ3479375

Richard A. Davis, James E. Marengo

Publication date: 1990

Published in: Communications in Statistics. Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/15326349908807158

zbMATH Keywords

sample correlation functionlimit distributionsample correlation matrixstable random variablesfinite second momentasymptotically normalfinite variancezero meanasymptotically nonnormal stableinnovation sequencemultivariate linear processesmultivariate regular variation conditionsample covariance function

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05)

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Strong approximation for cross-covariances of linear variables with long-range dependence ⋮ The sample autocorrelations of heavy-tailed processes with applications to ARCH

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