Estimating wold matrices and vector moving average processes

Jonas Krampe and Timothy L. McMurry

Journal of Time Series Analysis, 2021, vol. 42, issue 2, 201-221

Abstract: 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.

Date: 2021
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https://doi.org/10.1111/jtsa.12562

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Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:42:y:2021:i:2:p:201-221

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