High frequency perspective on jump process, long memory property and temporal aggregation: Case of $-AUD exchange rates

The high frequency 30 min $-AUD exchange rate is investigated using a parametric FIGARCH model. The FIGARCH model is found to be the preferred specification for the 30 min returns and temporally aggregated returns, with similar values of the long memory parameter across various aggregated returns. This paper employs the Bernoulli jump process and the Poisson jump process to represent conditional mean jumps in the high frequency returns and the aggregated returns. The estimation results present that the jumps are quite significant in the conditional mean process and that the long memory parameters are remarkably reduced over the aggregated returns after the jumps are accounted for.