On Some Non-stationary Bivariate INAR(p) Models with Applications to Intra-day Stock Transaction Series

This paper introduces a non-stationary bivariate integer-valued auto-regressive process of order p (BINAR( p ) with non-stationary moments. The BINAR( p ) uses the conventional binomial thinning procedure and the cross correlation between the two related series is induced from the paired innovation terms. The conditional maximum likelihood (CML) approach is used to estimate the model parameters. Monte Carlo simulation experiments with bivariate Poisson innovations are implemented to assess the consistency and asymptotic properties of the proposed BINAR( p ). In the application part, we consider two bivariate time series: The Ask and bid quotes from AT &T and the intra-day transactions of Mauritius Commercial Bank (MCB) and State Bank of Mauritius Holdings (SBMH). These series were fitted using the BINAR( p ) with paired Poisson, Negative Binomial and Poisson-Lindley innovations and the results demonstrate that BINAR( p ) with Negative Binomial yield better fitting and slightly lesser mean square error.