Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1154044 | Statistics & Probability Letters | 2008 | 10 Pages |
Abstract
An estimate of the spectral density of a stationary time series can be obtained by taking the finite Fourier transform of an observed sequence x0,x1,â¦,xNâ1 of sample size N with taper a discrete prolate spheroidal sequence and computing its square modulus. It is typical to take the average K of several such estimates corresponding to different prolate spheroidal sequences with the same bandwidth W(N) as the final computed estimate. For the mean square error of such an estimate to converge to zero as Nââ, it is shown that it is necessary to have W(N)â0 with NW(N)ââ as Nââ and significantly have K(N)â¤2NW(N) but K=K(N)ââ as Nââ.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
K.S. Lii, M. Rosenblatt,