AR and MA representation of partial autocorrelation functions, with applications

DOI10.1007/s00440-007-0074-1zbMath1138.62049arXivmath/0702648OpenAlexW3104881366MaRDI QIDQ2480813

Akihiko Inoue

Publication date: 3 April 2008

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702648

zbMATH Keywords

Long memoryVerblunsky coefficientsFractional ARIMA processesBaxter's conditionOrthogonal polynomials on the unit circle

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Stationary stochastic processes (60G10) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Applications of functional analysis in probability theory and statistics (46N30)

Related Items (13)

Exponential decay rate of partial autocorrelation coefficients of ARMA and short-memory processes ⋮ Explicit formulas for the inverses of Toeplitz matrices, with applications ⋮ Representation theorems in finite prediction, with applications ⋮ An explicit representation of Verblunsky coefficients ⋮ Szegő's theorem and its probabilistic descendants ⋮ Multivariate prediction and matrix Szegő theory ⋮ Verblunsky coefficients and Nehari sequences ⋮ Simple matrix representations of the orthogonal polynomials for a rational spectral density on the unit circle ⋮ An Open Problem on Strongly Consistent Learning of the Best Prediction for Gaussian Processes ⋮ The intersection of past and future for multivariate stationary processes ⋮ On processes with hyperbolically decaying autocorrelations ⋮ Aspects of prediction ⋮ Rigidity for matrix-valued Hardy functions

Uses Software

• longmemo

Cites Work

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