Forecasting time series by long-memory models for count data with an application to price jumps

We discuss the estimation and forecast of long-memory models for count data time series. We first demonstrate by Monte Carlo simulations that the Whittle estimator is the most appropriate for recovering the memory degree of a count data time series. In the following, we introduce the possibility of forecasting count data by exploiting the infinite autoregressive representation of the model. We complete our analysis with an empirical example in which we verify the predictability of the price jump numbers.