Maximum entropy spectral analysis

Dilip M. Nachane ()
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Dilip M. Nachane: Indira Gandhi Institute of Development Research

Indira Gandhi Institute of Development Research, Mumbai Working Papers from Indira Gandhi Institute of Development Research, Mumbai, India

Abstract: The maximum entropy principle is characterized as assuming the least about the unknown parameters in a statistical model. In its applied manifestations, it uses all the available information and makes the fewest possible assumptions regarding the unavailable information. The application of this principle to parametric spectrum estimation leads to an autoregressive transfer function. By appeal to a well known theorem in stochastic processes, a rational transfer function leads to a factorizable spectrum. This result combined with a classical theorem of analysis (due to Szego") forms the basis for two important algorithms for estimating the autoregressive spectrum viz. the Levinson-Durbin and Burg algorithms. The latter leads to estimators which are asymptotically MLEs (maximum likelihood estimators).

Keywords: Entropy; Jaynes' Principle; autoregressive spectrum; spectral factorization; Levinson; Durbin (search for similar items in EconPapers)
JEL-codes: C22 C32 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2025-07
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