Modeling and inferences for bivariate signed integer-valued autoregressive models

This study examines a first-order bivariate signed integer-valued autoregressive (BSINAR) model, designed for analyzing time series of counts that may include negative values or exhibit negative autocorrelations or stochastic trends. For the estimation methods, we consider the minimum density power divergence estimator (MDPDE), well-known for its robustness against outliers. The limiting behavior of the MDPDE is examined under certain regularity conditions. The MDPDE is used to construct a score vector-based parameter change test. To assess the performance of the MDPDE and demonstrate its validity, we conduct a Monte Carlo simulation. The proposed methods are also applied to analyze earthquake data from the Earthquake Hazards Program of the United States Geological Survey (USGS) and financial data from Euro-Bund and BTP futures.