The Autocovariance Function Determined Via the Z-Transform, with Application to Box Jenkins Forecasting Models.

Abstract

A Method is presented which yields the autocovariance function of a stationary discrete-time stochastic process in closed form. Special reference is made to the Box Jenkins forecasting methodology in which the underlying process is generated by passing white noise through a linear filter. The impulse response of the filter and its Z-transform, the transfer function, are obtained from the equation which defines the filter. The bilateral Z-transform of the autocovariance function is then derived from the transfer function, and is inverted following a partially fraction expansion. Several examples of this procedure are worked out in detail, and a summary of solutions for a number of cases is given. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1978
Accession Number
ADA056214

Entities

People

  • Eginhard J. Muth

Organizations

  • University of Florida

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Coefficients
  • Delphi Method
  • Difference Equations
  • Engineering
  • Equations
  • Power Spectra
  • Probability
  • Random Variables
  • Rational Functions
  • Security
  • Simultaneous Equations
  • Stationary Processes
  • Stochastic Processes
  • Systems Engineering
  • Transfer Functions
  • White Noise

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Computational Modeling and Simulation