Parameter change test for random coefficient integer‐valued autoregressive processes with application to polio data analysis

Abstract. In this paper, we consider the problem of testing for a parameter change in a first‐order random coefficient integer‐valued autoregressive [RCINAR(1)] model. We employ the cumulative sum (CUSUM) test based on the conditional least‐squares and modified quasi‐likelihood estimators. It is shown that under regularity conditions, the CUSUM test has the same limiting distribution as the supremum of the squares of independent Brownian bridges. The CUSUM test is then applied to the analysis of the monthly polio counts data set.