On the Central Limit Theorem for Toeplitz Quadratic Forms of Stationary Sequences

DOI10.1137/S0040585X97981299zbMath1090.60021OpenAlexW2018491016MaRDI QIDQ5472343

Artur A. Sahakyan, Mamikon S. Ginovyan

Publication date: 9 June 2006

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97981299

zbMATH Keywords

asymptotic variancespectral densityslowly varying functionsstationary Gaussian sequenceToeplitz-type quadratic forms

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10)

Related Items (13)

Statistical inference for stationary linear models with tapered data ⋮ Limit theorems for Toeplitz quadratic functionals of continuous-time stationary processes ⋮ Some convergence results on quadratic forms for random fields and application to empirical covariances ⋮ Unnamed Item ⋮ Error bounds for approximations of traces of products of truncated Toeplitz operators ⋮ The trace problem for Toeplitz matrices and operators and its impact in probability ⋮ Functional limit theorems for Toeplitz quadratic functionals of continuous time Gaussian stationary processes ⋮ Limit theorems for quadratic forms of Lévy-driven continuous-time linear processes ⋮ Limit theorems for tapered Toeplitz quadratic functionals of continuous-time Gaussian stationary processes ⋮ A note on approximations of traces of products of truncated Toeplitz matrices ⋮ On the trace approximation problem for truncated Toeplitz operators and matrices ⋮ Limit theorems for Toeplitz-type quadratic functionals of stationary processes and applications ⋮ Statistical estimation for stationary models with tapered data

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