Bivariate Time Series Modeling of Financial Count Data

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Abstract
A bivariate integer-valued moving average (BINMA) model is proposed. The BINMA model allows for both positive and nagative correlation between the counts. This model can be seen as an inverse of the conditional duration model in the sense that short durations in a time interval correspond to a large count and vice versa. The conditional mean, variance, and covariance of the BINMA model are given. Model extensions to include explanatory variables are suggested. Using the BINMA model for AstraZeneca and Ericsson B, it is found that there is positive correlation between the stock transactions series. Empirically, we find support for the use of long-lag bivariate moving average models for the two series.