Covariance matrix estimation for stationary time series
Xiao, Han ; Wu, Wei Biao
arXiv, 1105.4563 / Harvested from arXiv
Text on arXiv
We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351-376] idea and relate eigenvalues of covariance matrices to the spectral densities or Fourier transforms of the covariances. We develop a large deviation result for quadratic forms of stationary processes using m-dependence approximation, under the framework of causal representation and physical dependence measures.
Publié le : 2011-05-23
Classification:  Mathematics - Statistics Theory 
@article{1105.4563,
     author = {Xiao, Han and Wu, Wei Biao},
     title = {Covariance matrix estimation for stationary time series},
     journal = {arXiv},
     volume = {2011},
     number = {0},
     year = {2011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1105.4563}
}

Xiao, Han; Wu, Wei Biao. Covariance matrix estimation for stationary time series. arXiv, Tome 2011 (2011) no. 0, . http://gdmltest.u-ga.fr/item/1105.4563/