Estimating the statistical bandwidth of a time series
Andrew T. Walden, Ruth E. White · Biometrika · 1990
In many time series and signal processing applications such as spectral estimation, signal-to-noise estimation and frequency response estimation it is imperative to have a good estimate of the bandwidth of the time series. In many scientific applications deconvolution is carried out over the signal-dominated part of the spectrum resulting in a spectrum which is dominantly unimodal, and hence a technique like that used for smoothing windows can be used to define the statistical bandwidth of the data. This paper demonstrates, using bandwidths and data lengths of interest in seismic data investigations, that the naive estimator of data bandwidths using an untapered autocovari ance is extremely biased. A method for removing the bias is found and its success demonstrated on synthetic and real data. If the tapered sample autocovariance function is used in the estimator then the best truncation point corresponds to a ratio of smoothing window bandwidth to data bandwidth in the range 0.2–0.25 well below the recommended upper bound for spectrum estimation of 0.5