BIOL 335 Lecture Notes - Lecture 6: Spectral Density Estimation, Kernel Density Estimation, Window Function
Document Summary
Properties of the periodogram: asymptotic unbiasedness: e[i( )] f ( ) as n , (0, , lack of consistency: var[i( )] 6 0 as n ; i. e. , i( ) is not a consistent estimator of f ( ) This is not surprising since the fourier series representation requires estimation of n parameters based on n observations: under joint multivariate normality of stationary process {xt}, i( p) and. I( q) are asymptotically independent as n for all p 6= q (0 < p, q < n/2) This explains the irregular form of the periodogram. Consequence: the periodogram needs to be modi ed to give a good estimate of a continuous spectrum. Example of a time series with a trend. Consider a sample of size n = 100 simulated from the model. {zt} wn(0, 4), t = 1, 2, . Example of a time series with seasonal variation.
