Inverse moment bounds for sample autocovariance matrices based on detrended time series and their applications

Tzu Chang F. Cheng, Ching Kang Ing, Shu Hui Yu

研究成果: 雜誌貢獻期刊論文同行評審

3 引文 斯高帕斯(Scopus)

摘要

In this paper, we assume that observations are generated by a linear regression model with short- or long-memory dependent errors. We establish inverse moment bounds for kn-dimensional sample autocovariance matrices based on the least squares residuals (also known as the detrended time series), where kn 蠐 n, kn → ∞ and n is the sample size. These results are then used to derive the mean-square error bounds for the finite predictor coefficients of the underlying error process. Based on the detrended time series, we further estimate the inverse of the n-dimensional autocovariance matrix, Rn-1, of the error process using the banded Cholesky factorization. By making use of the aforementioned inverse moment bounds, we obtain the convergence of moments of the difference between the proposed estimator and Rn-1 under spectral norm.

原文???core.languages.en_GB???
頁(從 - 到)180-201
頁數22
期刊Linear Algebra and Its Applications
473
DOIs
出版狀態已出版 - 15 5月 2015

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