1,616 research outputs found
Covariance matrix estimation for stationary time series
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.Comment: Published in at http://dx.doi.org/10.1214/11-AOS967 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Confidence bands in nonparametric time series regression
We consider nonparametric estimation of mean regression and conditional
variance (or volatility) functions in nonlinear stochastic regression models.
Simultaneous confidence bands are constructed and the coverage probabilities
are shown to be asymptotically correct. The imposed dependence structure allows
applications in many linear and nonlinear auto-regressive processes. The
results are applied to the S&P 500 Index data.Comment: Published in at http://dx.doi.org/10.1214/07-AOS533 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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