Estimation of linear functional of large spectral density matrix and application to Whittle’s approach

We study a class of thresholding autocovariance estimators, given p-dimensional stationary time series data with length n, for a high-dimensional setting where both p and n tend to infinity, with a suitable rate. Also, we give the asymptotic theory for linear functionals of thresholding periodogram matrices, together with its application to Whittle’s approach.