Asymptotic expansions of the distributions of statistics related to the spectral density matrix in multivariate time series and their applications

Masanobu Taniguchi, Koichi Maekawa

研究成果: Article査読

1 被引用数 (Scopus)

抄録

Let {X(t)} be a multivariate Gaussian stationary process with the spectral density matrix f0(ω), where θ is an unknown parameter vector. Using a quasi-maximum likelihood estimator [formula omitted] of θ, we estimate the spectral density matrix f0(ω) by f [formula omitted] (ω). Then we derive asymptotic expansions of the distributions of functions of f [formula omitted] (ω). Also asymptotic expansions for the distributions of functions of the eigenvalues of [formula omitted](ω) are given. These results can be applied to many fundamental statistics in multivariate time series analysis. As an example, we take the reduced form of the cobweb model which is expressed as a two-dimensional vector autoregressive process of order 1 (AR(1) process) and show the asymptotic distribution of [formula omitted], the estimated coherency, and contribution ratio in the principal component analysis based on [formula omitted] in the model, up to the second-order terms. Although our general formulas seem very involved, we can show that they are tractable by using REDUCE 3.

本文言語English
ページ(範囲)75-96
ページ数22
ジャーナルEconometric Theory
6
1
DOI
出版ステータスPublished - 1990
外部発表はい

ASJC Scopus subject areas

  • Economics and Econometrics
  • Social Sciences (miscellaneous)

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