First‐Order Mixed Autoregressive Model for Bivariate Mixed Time Series

The first‐order bivariate autoregressive model has been extensively studied for integer‐valued or continuous time series. However, researches on model architecture for bivariate mixed time series remain limited, and discussions regarding cross‐dependence structures in such series are notably scare. To address this gap, we propose a first‐order bivariate mixed autoregressive model (BMIAR(1)) designed to capture both serial‐dependence and cross‐dependence within bivariate mixed time series. Under the general conditions, we establish the stationarity and ergodicity of the proposed model and derive its moment properties. Furthermore, we introduce an estimation method adapted from the EM algorithm. Through extensive simulation studies and an analysis of real‐word data, we demonstrate the advantages of the BMIAR(1) framework and the effectiveness of the estimation methodology.