Estimating the Statistical Bandwidth of a Time Series

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY 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 autocovariance 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 02-025, well below the recommended upper bound for spectrum estimation of 0 5.

A Widely Linear Complex Autoregressive Process of Order One

“…The seismic trace consists of three components: a radial, vertical, and transverse signal [30]. We model the radial and vertical components as a complex-valued signal, as they are strongly coupled due to the presence of a Rayleigh wave.…”