Afrika Statistika

A Bayesian Approach for Identification of Additive Outlier in AR(p)

Jitendra KUMAR and Saurabh KUMAR

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Time series is the way of data analysis and modelling in which present observation is retrieved based on past observations which is called ARIMA model in case of linear dependency. If series is contaminated by an outlier, then it affects both order and parameter(s). The present paper deals an autoregressive (AR) model with an additive outlier under Bayesian prospective. For identification of an outlier, posterior odds ratio has been derived under suitable prior assumptions. An empirical analysis and realization is carried out to get applicability of proposed testing methodology.


Dans l'étude des séries temporelles, les données discrètes sont modelisées par rapport aux observations passeés, et les modèles sont appelées ARIMA dans le cas de dependances linéaires. Si la série est contaminée par un outlier, les paramètres et les valeurs sont à lois affectées. Ce papier traite du modèle autoregressif avec un outlier additionnel selon une perspective bayesienne. Pour identifier un outlier, le rapports des odds a été obtenu après voir convenablement choisi les distributions à prioiri. Une étude empirique et des études de cas sont menées pour prouver l'applicabibilité de la méthodologie utilisée.

Article information

Afr. Stat., Volume 14, Number 1 (2019), 1877-1890.

First available in Project Euclid: 24 May 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F03: Hypothesis testing 62F15: Bayesian inference 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

autoregressive model posterior odds ratio prior distribution


KUMAR, Jitendra; KUMAR, Saurabh. A Bayesian Approach for Identification of Additive Outlier in AR(p). Afr. Stat. 14 (2019), no. 1, 1877--1890. doi:10.16929/as/2019.1877.139.

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