Bivariate Time Series Modeling of Financial Count Data

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.     

A bivariate integer-valued long-memory model for high-frequency financial count data

We propose a bivariate integer-valued fractional integrated (BINFIMA) model to account for the long-memory property and apply the model to high-frequency stock transaction data. The BINFIMA model allows for both positive and negative correlations between the counts. The unconditional and conditional first- and second-order moments are given. The model is capable of capturing the covariance between and within intra-day time series of high-frequency transaction data due to macroeconomic news and news related to a specific stock. Empirically, it is found that Ericsson B has mean recursive process while AstraZeneca has long-memory property.