Spectral methods for small sample time series: A complete periodogram approach

The periodogram is a widely used tool to analyze second order stationary time series. An attractive feature of the that expectation approximately equal underlying spectral density However, this only an approximation, and it well known has finite sample bias, which can be severe in small samples. In article, we show bias arises because boundary observation one discrete Fourier transforms construction periodogram. Moreover, by using best linear predictors series over obtain ‘complete periodogram’ unbiased estimator density. practice, cannot evaluated as are unknown. We propose method for estimating prove resulting ‘estimated complete smaller than regular estimated tapered version estimate parameters, represented terms integrated estimators have their counterparts. proposed illustrated with simulations real data.