Parameter Estimation for ARMA Models with Infinite Variance Innovations

Abstract

We consider a standard ARMA process of the form phi(B)Xt=Theta(B)Zt, where the innovations Zt belong to the domain of attraction of a stable law, so that neither the Zt nor the Xt 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 fact that the periodogram does not, a priori, seem like a logical object to study in this non-L' 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 L2 case.

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Document Details

Document Type
Technical Report
Publication Date
Dec 30, 1993
Accession Number
ADA274654

Entities

People

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

Organizations

  • Victoria University of Wellington

Tags

Communities of Interest

  • C4I
  • 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
  • Statistical inference.