Premium
Estimating wold matrices and vector moving average processes
Author(s) -
Krampe Jonas,
McMurry Timothy L.
Publication year - 2021
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.12562
Subject(s) - mathematics , autocovariance , estimator , cholesky decomposition , convergence (economics) , statistics , eigenvalues and eigenvectors , mathematical analysis , fourier transform , quantum mechanics , physics , economics , economic growth
The Wold decomposition gives a moving average (MA) representation of a purely non‐deterministic stationary process. In this article, we derive estimates of the Wold matrices for a d ‐dimensional process by using a Cholesky decomposition of a banded and tapered version of the sample autocovariance matrix, and we derive convergence rates for the estimation error of the (possibly infinite) sequence of Wold matrices. By analogy to lag‐window estimates of the spectral density, this method can be used to obtain finite vector MA models with an adaptive lag‐order. We additionally show how these results can be applied to impulse response analysis and to derive a bootstrap procedure. Our theoretical results are complemented by simulations which investigate the finite sample performance of the estimator.