The Stationary Autogressive Model

Abstract

There are several ways of developing the autoregressive stochastic process as a finite-parameter model for time series analysis. This paper obtains the properties of the autoregressive process from a stationary stochastic process that satisfies the simple condition that a linear combination of current and past elements of the process is independent of (or alternatively uncorrelated with) all earlier elements of the process. This approach provides a coherent, clear, and rigorous exposition of the autoregressive model. The stationarity and independence imply that the roots of the associated polynomial equation are less than 1 in absolute value. The existence of the moving average representation is deduced and its form for distinct roots. The Yule-Walker equations, which are derived, determine the autocovariance sequence. Another set of parameters consists of the variance of the process and the partial autocorrelation sequence.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1986
Accession Number
ADA171416

Entities

People

  • Theodore W. Anderson

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Autocorrelation
  • Data Science
  • Equations
  • Information Science
  • Mathematics
  • Polynomials
  • Sequences
  • Stationary
  • Stationary Processes
  • Stochastic Processes
  • Time Series Analysis

Fields of Study

  • Mathematics

Readers

  • Statistical inference.
  • Theoretical Analysis.