Parameter Estimation for ARMA Models with Infinite Variance Innovations

Abstract

We consider a standard ARMA process of the form Phi(B)X sub t = Theta(B)Z sub t, where the special innovations Z sub t belong to the domain of attraction of a stable law, so that neither the Z sub t nor the X sub t have a finite variance. Our aim is to estimate the coefficients of Phi and Theta. since maximum likelihood estimation is not a viable possibility (due to the unknown form of the marginal density of the innovation sequence) we adopt the so-called Whittle estimator, based on the sample periodogram of the X sequence. Despite the face that the periodogram does not, a priori, seem like a logical object to study in this non-L-sq situation, we show that our estimators are consistent, obtain their asymptotic distributions, and show that they converge to the true values faster than in the usual L-sq case.

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Document Details

Document Type
Technical Report
Publication Date
Dec 30, 1993
Accession Number
ADA275125

Entities

People

  • Claudia Kluppelberg
  • Robert J. Adler
  • Tamar Gadrich
  • Thomas Mikosch

Organizations

  • Technion – Israel Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Coefficients
  • Consistency
  • Convergence
  • Decomposition
  • Estimators
  • Industrial Engineering
  • Inequalities
  • Maximum Likelihood Estimation
  • New York
  • New Zealand
  • Operations Research
  • Probability
  • Random Variables
  • Random Walk
  • Standards
  • Transfer Functions
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Mathematical Modeling and Probability Theory.
  • Systems Analysis and Design