Statistical analysis of the non-stationary binomial AR(1) model with change point

Abstract

In this paper, we conduct the statistical inference for a new class of non-stationary binomial AR(1) models with change point. The parameter estimation problem is considered, as well as the testing problem for the possible change point. For this task, a residual-based cumulative sum (CUSUM) test is employed, and we show that the limiting null distributions take the form of the functions of Brownian bridge. In the simulation study, we evaluate the performance of the estimation methods and the respective CUSUM test. We furthermore propose a method for the forecasting of the model. Finally, two real data applications were provided in the field of epidemiology.