Monitoring Mean Shift in INAR(1)s Processes based on CLSE-CUSUM Procedure

  • Hanwool Kim Department of Statistics, Seoul National University, Seoul 08826, Korea.
  • Sangyeol Lee
Keywords: Average run length, INAR(1)s process, CLSE-based CUSUM test, CUSUM chart, small to moderate shift


In this paper, we consider a new control procedure for monitoring mean shift using the conditional least squares estimator (CLSE)-based cumulative sum (CUSUM) test for the first-order seasonal integer-valued autoregressive (INAR(1)s) processes. Numerical experiments show that the proposed CLSE-CUSUM procedure outperforms conventional CUSUM charts for small to moderate up-shifts in mean of innovation processes, in terms of average run length (ARL), standard deviation (SD) and median.


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