Abstract 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.

中文翻译：

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离散双变量移动平均过程建模

摘要本文提出了一种非平稳二阶整数值移动平均数（BINMA（1））模型，该模型各自的创新性是边际COM-泊松且无关。与其他这样的双变量时间序列模型相反，上面的序列之间的依赖性是通过当前序列与先前时间点上其他序列的幸存元素之间的关系构建的。在这些假设下，BINMA（1）过程显示出可以适应不同水平以及过度分散，均布和欠布散的组合。由于在非平稳条件下构造联合似然函数几乎不费力，因此提出了一种广义准似然（GQL）估计方法来估计动态效果和依赖参数。还建立了GQL估计量的渐近和一致性性质。提出了蒙特卡洛实验和实际应用来分析日内股票交易，以验证所提出的模型和估计方法。