Maximum entropy spectral analysis and autoregressive decomposition

Abstract

The duality between the maximum entropy method (MEM) of spectral analysis and the autoregressive (AR) representation of the data allows the application of recent advances in AR analysis to MEM in an attempt to obviate some shortcomings in this method of spectral decomposition. Specifically, this paper investigates the work of Akaike (1969a, b) on a criterion for choosing the length of the required prediction error filter and compares two methods of determining the filter coefficients. Recent work by Kromer (1970) on asymptotic properties of the AR spectral estimator is also of importance. Some preliminary results of the splitting of the normal modes of the earth are presented as an illustration of the application of MEM to geophysics.

Parametrization of spectra of plasma bubble induced VHF satellite scintillations and its geophysical significance

“…It effectively deals with the problem of fixing the order of an AR process through the evaluation of multiple correlations and that of fixing the data sample length through the use of persistence in the non-random data. The present methodology is very much similar to an earlier scheme given by Ulrych and Bishop (1975). However, an important work by Kendall and Stuart (1966) on an AR process is incorporated here.…”

The δ18O record along the Greenland Ice Core Project deep ice core and the problem of possible Eemian climatic instability

“…Spectral fingerprints. The maximum entropy spectral analysis method (MEM) [Ulrych and Bishop, 1975], used in this paper, has several properties that make it suitable for characterizing the spectral properties of our • records: (1) the resolution of the calculated spectra can be controlled by selecting an appropriate autoregressive (AR) order of the prediction error filter employed by the method, (2) by increasing the AR order, the splitting of spectral peaks indicates quasi periodicity of the corresponding signal component, (3) the frequency resolution is not fixed but adapts to the structure of the data [Lacoss, 1971], and (4) spectral peaks can be integrated analytically [Johnsen and Andersen, 1978] in order to estimate the amplitude of the corresponding data oscillations.…”

Investigation of level changes of lake Titicaca by maximum entropy spectral analysis

“…Since the main drawback of this method is still the absence of an adequate significance test procedure this information can give hints about the reliability of any presented spectral density. The upper limit mmax might be too large but is still below the critical filter order [38]. The order selection 0 of OBD is probably caused by the small number of data points and the low signal to noise ratio.…”