Nonparametric high resolution spectral estimation
The uniform rate of convergence of the integrated relative mean square error over an (with the sample size T) increasing class \({\mathcal X}_ T\) of stationary processes is studied for several estimates of the spectral density. The class \({\mathcal X}_ T\) is chosen in a way such that estimates with a good uniform rate of convergence over \({\mathcal X}_ T\) may be termed `high resolution spectral estimates'. By using this criterion several effects are explained theoretically, for example the leakage effect. The advantages of using data tapers are proved and the use of local and global bandwidths are studied. Furthermore, the behaviour of segment estimates is studied. Simulations are presented for the illustration of some effects.
uniform rate of convergence of the integrated relative mean square error
scientific article; zbMATH DE number 4113798
scientific article