Robust estimation for bivariate integer-valued autoregressive models based on minimum density power divergence

Abstract

This study considers a robust estimation method for bivariate integer-valued autoregressive (BINAR) models using a minimum density power divergence (MDPD) scheme. We first address this problem within a general framework of time series models to verify the strong consistency and asymptotic normality of the MDPD estimator (MDPDE) under regularity conditions. Based on these results, we assert the same asymptotic properties of MDPDE for BINAR models and propose an outlier detection rule based on MDPDE. To assess the performance of the proposed method, we conduct a simulation study. Real data analysis is also carried out for illustration, using the number of monthly earthquakes in the United States.