Robust bayesian estimation of autoregressive-moving-average models

Glen Barnett, Robert Kohn, Simon Sheather

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


A Bayesian approach is presented for modeling a time series by an autoregressive-moving-average model. The treatment is robust to innovation and additive outliers and identifies such outliers. It enforces stationarity on the autoregressive parameters and invertibility on the moving-average parameters, and takes account of uncertainty about the correct model by averaging the parameter estimates and forecasts of future observations over the set of permissible models. Posterior moments and densities of unknown parameters and observations are obtained by Markov chain Monte Carlo in O(n) operations, where n is the sample size. The methodology is illustrated by applying it to a data set previously analyzed by Martin, Samarov and Vandaele (Robust methods for ARIMA models. Applied Time Series Analysis of Economic Data, ASA-Census-NBER Proceedings of the Conference on Applied Time Series Analysis of Economic Data (ed. A. Zellner), 1983, pp. 153-69) and to a simulated example.

Original languageEnglish
Pages (from-to)11-28
Number of pages18
JournalJournal of Time Series Analysis
Issue number1
StatePublished - Jan 1997


  • Invertibility
  • Markov chain Monte Carlo
  • Order selection
  • Outliers
  • Stationarity

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


Dive into the research topics of 'Robust bayesian estimation of autoregressive-moving-average models'. Together they form a unique fingerprint.

Cite this