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.