Adaptive Kernel Estimation of the Spectral Density with Boundary Kernel Analysis
This work provides an incremental improvement in statistical estimation for time series analysis, addressing boundary issues in spectral density estimation.
The authors tackled the problem of estimating the spectral density of stationary time series by proposing a hybrid estimator that combines multiple taper estimation with kernel smoothing, which reduces expected mean square error by a factor of (π²/4)^0.8 compared to simpler methods.
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-multitaper estimate. This procedure reduces the expected mean square error by $({π^2 \over 4})^{.8}$ over simply smoothing the log tapered periodogram. The optimal number of tapers is $O(N^{8/15})$. A data adaptive implementation of a variable bandwidth kernel smoother is given. When the spectral density is discontinuous, one sided smoothing estimates are used.