Parameter estimation for binomial AR(1) models with applications in finance and industry

Abstract

Methods for analyzing and modeling count data time series are used in various fields of practice, and they are particularly relevant for applications in finance and economy. We consider the binomial autoregressive (AR(1)) model for count data processes with a first-order AR dependence structure and a binomial marginal distribution. We present four approaches for estimating its model parameters based on given time series data, and we derive expressions for the asymptotic distribution of these estimators. Then we investigate the finite-sample performance of the estimators and of the respective asymptotic approximations in a simulation study, including a discussion of the 2-block jackknife. We illustrate our methods and findings with a real-data example about transactions at the Korea stock market. We conclude with an application of our results for obtaining reliable estimates for process capability indices.