Semi-Adaptive Nonparametric Spectral Estimation

Abstract

When dominant information is available about a process, its corresponding spectral density will exhibit a variable order of smoothness. In such situations, calculating a nonparametric spectral estimate with a fixed smoothing parameter will lead to biased spectral estimates. We propose a simple method that allows the bandwidth of the spectral window in the smoothed periodogram running average procedure to vary in order to compensate for the possibly changing order of smoothness of the underlying spectral density. At each point of estimation, our approach is to extend the bandwidth until the squared variation of the periodogram within reaches a prespecified level. Our method may be particularly benevolent when the process is nonstationary with close spectral lines, although it may be implemented in any situation that warrants adaptive scatterplot “smoothing,” such as in those cases where sharp peaks are considered to be information and not error. We illustrate our method on an observed and simulated dataset.

Key Words:

• Bandwidth
• DZ algorithm
• Nonstationarity
• Smoothed periodogram
• Smoothness
• Spectral window
• Squared variation
• Time series
• Varying bandwidth