Maximum Standardized Cumulant Deconvolution of Non-Gaussian Linear Processes

Abstract

A linear process is represented as a driving white noise convolved with a system response sequence. The concept of natural peakedness of a system response sequence is defined and its properties are investigated. Utilizing natural peakedness, the convergence theory of maximum standardized cumulant deconvolution is established and the uniqueness theorem of non-Gaussian linear process representations is proved. In addition, autoregressive models on a countable abelian group are defined and the relation between cumulant deconvolution and autoregressive models is given.