Innovations and Wold Decompositions of Stable Sequences.

Abstract

For symmetric stable sequences, notions of innovation and Wold decomposition (WD) are introduced, characterized, and their ramifications in prediction theory are discussed. As the usual covariance orthogonality is inapplicable, the non-symmetric James orthogonality is used, thus leading to right and left innovations and Wold decompositions, which are related to regression prediction and least p sub th moment prediction, respectively. Independent innovations and WD are also characterized; and several examples illustrating the various decompositions are presented. Keywords: Stochastic processes; Random variables; Symmetry; Linearity. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1985
Accession Number
ADA161437

Entities

People

  • Aleksander Weron
  • Clyde D. Hardin Jr.
  • Stamatis Cambanis

Organizations

  • University of North Carolina at Chapel Hill

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Banach Space
  • Classification
  • Continuity
  • Data Science
  • Decomposition
  • Gaussian Processes
  • Hilbert Space
  • Information Science
  • North Carolina
  • Orthogonality
  • Random Variables
  • Security
  • Sequences
  • Statistics
  • Stochastic Processes
  • Universities

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.