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Estimating MA Parameters through Factorization of the Autocovariance Matrix and an MA‐Sieve Bootstrap
Author(s) -
McMurry Timothy L.,
Politis Dimitris N.
Publication year - 2018
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12296
Subject(s) - autocovariance , mathematics , sieve (category theory) , cholesky decomposition , estimator , convergence (economics) , series (stratigraphy) , matrix (chemical analysis) , statistics , factorization , algorithm , mathematical analysis , combinatorics , paleontology , eigenvalues and eigenvectors , physics , materials science , fourier transform , quantum mechanics , economics , composite material , biology , economic growth
A new method to estimate the moving‐average (MA) coefficients of a stationary time series is proposed. The new approach is based on the modified Cholesky factorization of a consistent estimator of the autocovariance matrix. Convergence rates are established, and the new estimates are used to implement an MA‐type sieve bootstrap. Finite‐sample simulations corroborate the good performance of the proposed methodology.