Adaptive Smoothing of the Log-Spectrum with Multiple Tapering

A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multiple taper estimate. This procedure reduces the expected mean square error by $(\pi^2/ 4)^{4/5} $ over simply smoothing the log tapered periodogram. A data adaptive implementation of a variable bandwidth kernel smoother is given.