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Bayesian Outlier Detection in Non‐Gaussian Autoregressive Time Series
Author(s) -
Silva Maria Eduarda,
Pereira Isabel,
McCabe Brendan
Publication year - 2019
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12439
Subject(s) - autoregressive model , outlier , mathematics , anomaly detection , autoregressive–moving average model , series (stratigraphy) , gaussian process , time series , bayesian probability , bayesian inference , parametric statistics , gaussian , pattern recognition (psychology) , statistics , computer science , artificial intelligence , paleontology , physics , quantum mechanics , biology
This work investigates outlier detection and modelling in non‐Gaussian autoregressive time series models with margins in the class of a convolution closed parametric family. This framework allows for a wide variety of models for count and positive data types. The article investigates additive outliers which do not enter the dynamics of the process but whose presence may adversely influence statistical inference based on the data. The Bayesian approach proposed here allows one to estimate, at each time point, the probability of an outlier occurrence and its corresponding size thus identifying the observations that require further investigation. The methodology is illustrated using simulated and observed data sets.