The Autoregressive Method: A Method of Approximating and Estimating Positive Functions

Abstract

The Fourier transform was considered for a positive function f(.) (or its sample Fourier transform) as a possibly complex covariance function of a hypothetical stationary complex-valued time series. This model time series by an autoregressive process of order p whose spectral density approximates (or estimates) the function f(.). The equivalence of this interpretation with the theory of orthogonal polynomials on the unit circle was studied; also the consistency of the autoregressive estimator as p increases with the sample size.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1976
Accession Number
ADA031122

Entities

People

  • Jean-pierre Carmichael

Organizations

  • University at Buffalo

Tags

Communities of Interest

  • Cyber

DTIC Thesaurus Topics

  • Algorithms
  • Complex Variables
  • Covariance
  • Data Mining
  • Data Science
  • Distribution Functions
  • Gaussian Processes
  • Information Science
  • Numbers
  • Order Statistics
  • Probability
  • Probability Density Functions
  • Random Variables
  • Statistical Algorithms
  • Statistics
  • Step Functions
  • Stochastic Processes

Readers

  • Statistical inference.