APPLICATION OF THE EXACT INVERSE OF THE TOEPLITZ MATRIX TO THE AUTOREGRESSIVE MODEL

DOI10.17654/AM097050171OpenAlexW2771897392MaRDI QIDQ4639845

F. Ouicher, K. Djeddour-Djaballah, Ahmed Bachir

Publication date: 11 May 2018

Published in: Far East Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.17654/am097050171

zbMATH Keywords

simulationToeplitz matrixCholesky decompositionautoregressive processLevinson-Durbin algorithm

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Applications of graph theory (05C90) Toeplitz, Cauchy, and related matrices (15B05) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Uses Software

• itsmr

Cites Work

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• Algebraic methods for Toeplitz-like matrices and operators
• Modeling covariance matrices via partial autocorrelations
• Test for uniformity by empirical Fourier expansion
• A note on inversion of Toeplitz matrices
• The inverse of covariance matrices for the ARMA\((p,q)\) class of processes
• DETERMINANTS OF COVARIANCE MATRICES OF DIFFERENCED AR(1) PROCESSES
• The exact likelihood function for a mixed autoregressive-moving average process
• Improved Box-Jenkins Estimators
• On the inverses of some patterned matrices arising in the theory of stationary time series

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