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Retrospective Bayesian outlier detection in INGARCH series

机译：INGARCH系列中的回顾性贝叶斯异常值检测

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摘要

INGARCH models for time series of counts arising, e.g., in epidemiology or finance assume the observations to be Poisson distributed conditionally on the past, with the conditional mean being an affine-linear function of the previous observations and the previous conditional means. We model outliers within such processes, assuming that we observe a contaminated process with additive Poisson distributed contamination, affecting each observation with a small probability. Our particular concern are additive outliers, which do not enter the dynamics of the process and can represent measurement artifacts and other singular events influencing a single observation. Retrospective analysis of such outliers is difficult within a non-Bayesian framework since the uncontaminated values entering the dynamics of the process at contaminated time points are unobserved. We propose a Bayesian approach to outlier modeling in INGARCH processes, approximating the posterior distribution of the model parameters by application of a componentwise Metropolis-Hastings algorithm. Analyzing real and simulated data sets, we find Bayesian outlier detection with non-informative priors to work well in practice when there are some outliers in the data.
机译：例如在流行病学或金融学中出现的时间计数序列的INGARCH模型假设观测值是Poisson在过去的条件下分布的，条件均值是先前观测值和先前条件均值的仿射线性函数。我们在此类过程中对异常值进行建模，假设我们观察到一个带有加性Poisson分布污染的污染过程，从而以很小的概率影响每个观察。我们特别关注的是累加异常值，这些异常值不会进入过程的动态范围，并且可以表示影响单个观测值的测量伪影和其他奇异事件。在非贝叶斯框架内，很难对此类异常值进行回顾性分析，因为未观察到在污染时间点进入过程动态的未污染值。我们提出了贝叶斯方法在INGARCH过程中进行离群建模，通过应用基于分量的Metropolis-Hastings算法来近似模型参数的后验分布。通过分析实际和模拟数据集，我们发现具有非信息先验的贝叶斯离群值检测在数据中存在一些离群值时可以很好地在实践中使用。

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