A long-memory integer-valued time series model, INARFIMA, for financial application

A model to account for the long-memory property in a count data framework is proposed and applied to high-frequency stock transactions data. By combining features of the INARMA and ARFIMA models, an Integer-valued Auto Regressive Fractionally Integrated Moving Average (INARFIMA) model is proposed. The unconditional and conditional first- and second-order moments are given. The CLS, FGLS and GMM estimators are discussed. In its empirical application to two stock series for AstraZeneca and Ericsson B, we find that both series have a fractional integration property.