TY - JOUR

T1 - Inverse moment bounds for sample autocovariance matrices based on detrended time series and their applications

AU - Cheng, Tzu Chang F.

AU - Ing, Ching Kang

AU - Yu, Shu Hui

N1 - Publisher Copyright:
© 2014 Elsevier Inc. All rights reserved.

PY - 2015/5/15

Y1 - 2015/5/15

N2 - 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.

AB - 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.

KW - Banded Cholesky factorization

KW - Detrended time series

KW - Inverse moment bounds

KW - Moment convergence

KW - Regression model with time series errors

KW - Sample autocovariance matrix

UR - http://www.scopus.com/inward/record.url?scp=84928708072&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2014.05.017

DO - 10.1016/j.laa.2014.05.017

M3 - 期刊論文

AN - SCOPUS:84928708072

SN - 0024-3795

VL - 473

SP - 180

EP - 201

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -