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This paper proposes a non-stationary bivariate integer-valued moving average of order 1 (BINMA(1)) model where the respective innovations are marginal COM-Poisson and unrelated. As opposed to other such bivariate time series model, the dependence between the series in the above is constructed via the relation between the current series with survivor elements of the other series at the preceding time point. Under these assumptions, the BINMA(1) process is shown to accommodate different levels and combinations of over-, equi- and under-dispersion. Since under the non-stationary conditions, the joint likelihood function is hardly laborious to construct, a generalized quasi-likelihood (GQL) method of estimation is proposed to estimate the dynamic effects and dependence parameters. The asymptotic and consistency properties of the GQL estimators are also established. Monte-Carlo experiments and a real-life application to analyze intra-day stock transactions are presented to validate the proposed model and the estimation methodology.

The existing bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with negative binomial (NB) innovations is developed under stationary moment conditions and in particular under same level of over-dispersion index. In this paper, we propose a flexible BINAR(1) under NB innovations where the counting series are subject to two different levels of over-dispersion under same stationary moment condition. The unknown parameters of the new model are estimated using a generalized quasi-likelihood (QL) estimating equation. The performance of this estimation method is assessed through some numerical experiments under different time dimensions.