Adaptive Smoothing of the Log-Spectrum with Multiple Tapering
Kurt S. Riedel, A. Sidorenko · 1996
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 ( ß 2 4 ) 4=5 over simply smoothing the log tapered periodogram. A data adaptive implementation of a variable bandwidth kernel smoother is given. 1 INTRODUCTION We consider a discrete, stationary, Gaussian time series fx j ; j = 1; : : : Ng with a smooth spectral density, S(f ), which is bounded away from zero. The autocovariance is the Fourier transform of the spectral density: Cov [x j ; x k ] = R 1 2 \\Gamma 1 2 S(f)e 2ßi(j \\Gammak)f df . When the logarithm of the spectral density, `(f) j ln[S(f )], is desired, two common approaches are: 1) to estimate the spectral density and then transform to the logarithm; and 2) to smooth the logarithm of the tapered periodogram. The first approach can be sensitive to broad-band bias ...