Semi-adaptive nonparametric spectral estimation

When dominant information is available about a process, its corresponding s pectral density will exhibit a Variable order of smoothness. In such situat ions, calculating a nonparametric spectral estimate with a fixed smoothing parameter will lead to biased spectral estimates. We propose a simple metho d that allows the bandwidth of the spectral window in the smoothed periodog ram running average procedure to vary in order to compensate for the possib ly changing order of smoothness of the underlying spectral density. At each point of estimation, our approach is to extend the bandwidth until the squ ared variation of the periodogram within reaches a prespecified level. Our method may be particularly benevolent when the process is nonstationary wit h close spectral lines, although it may be implemented in any situation tha t warrants adaptive scatterplot "smoothing," such as in those cases where s harp peaks are considered to be information and not error. We illustrate ou r method on an observed and simulated dataset.