Abstract
AbstractThe present article examines the performance of the Shiryaev–Roberts (SR) procedure for Markov‐dependent count time series, using the Poisson INARCH(1) model as the representative data‐generating count process. For the purpose of easier performance evaluation, a comparative analysis with existing cumulative sum (CUSUM) results from the literature is provided. In particular, the zero‐state and the steady‐state behavior of the two control schemes is considered with regard to the average run length (ARL), the median run length, and the extra quadratic loss as performance measures. The comparison shows that SR performs at least as well as its more popular competitor in detecting changes in the process distribution. In terms of usability, however, the SR procedure has a practical advantage, which is illustrated by an application to a real data set. Moreover, a parametric bootstrap study based on a second data example investigates the effects of parameter estimation on the chart's true ARL to false alarm. In sum, the research reveals the SR chart to be the better tool for monitoring Markov‐dependent counts.
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