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 -