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We consider the problem of quickest change-point detection where theobservations form a first-order autoregressive (AR) process driven bytemporally independent standard Gaussian noise. Subject to possible change areboth the drift of the AR(1) process ($\mu$) as well as its correlationcoefficient ($\lambda$), both known. The change is abrupt and persistent, andis of known magnitude, with $\vert\lambda\vert<1$ throughout. For thisscenario, we carry out a comparative performance analysis of the popularCumulative Sum (CUSUM) chart and its less well-known but worthy competitor --the Shiryaev-Roberts (SR) procedure. Specifically, the performance is measuredthrough Pollak's Supremum (conditional) Average Delay to Detection (SADD)constrained to a pre-specified level of the Average Run Length (ARL) to falsealarm. Particular attention is drawn to the sensitivity of each procedure'sSADD and ARL with respect to the value of $\lambda$ before and after thechange. The performance is studied through the solution of the respectiveintegral renewal equations obtained via Monte Carlo simulations. Thesimulations are designed to estimate the sought performance metrics in anunbiased and asymptotically strongly consistent manner, and to within aprescribed proportional closeness (also asymptotically). Our extensivenumerical studies suggest that both the CUSUM chart and the SR procedure areasymptotically second-order optimal, even though the CUSUM chart is found to beslightly better than the SR procedure, irrespective of the model parameters.Moreover, the existence of a worst-case post-change correlation parametercorresponding to the poorest detectability of the change for a given ARL tofalse alarm is established as well. To the best of our knowledge, this is thefirst time the performance of the SR procedure is studied for autocorrelateddata.

Comparative Performance Analysis of the Cumulative Sum Chart and the Shiryaev-Roberts Procedure for Detecting Changes in Autocorrelated Data