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Bayesian outlier detection in non-Gaussian autoregressive time series. (English) Zbl 1435.62339

In the article the Bayesian approach to outlier detection is proposed for a wide variety of count and positive time series. Time series process \(\{X_t; t=0,\pm1,\pm2,\dots\}\) is described by convolution closed infinitely divisible (CCID) autoregression model \(X_t=R_t(X_{t-1})+e_t\). Under certain conditions on \(R_t(\cdot)\) and \(e_t\), this CCID class includes Poisson and generalized Poisson, negative binomial, gamma, Gaussian and inverse Gaussian distributions. The observed process is \(Y_t=X_t+\eta_t \delta_t \) where \(\eta_t \delta_t\) is the additive outlier which has no effect on future dynamics of \(\{X_t\}\). Here \(\delta_t \in \{0,1\}\) indicates the occurrence of outlier, \(\eta_t\) describes its size, \(\delta_t\) and \(\eta_t\) are independent.
According to Bayesian approach prior distributions are assigned to parameters of autoregression model and outliers. Simulations are implemented with the use of MCMC technique. Some illustrative and two real-life examples of outlier detection are presented.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F15 Bayesian inference
62G32 Statistics of extreme values; tail inference
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References:

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