Bivariate Integer-Valued Long Memory Model for High Frequency Financial Count Data

We develop a model to account for the long memory property in a bivariate count data framework. We propose a bivariate integer-valued fractional integrated (BINFIMA) model 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 CLS and FGLS estimators are discussed. 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. It is also found that Ericsson B and AstraZenica react in a similar way due to macroeconomic news.