In this paper we propose an accurate and fast-to-estimate forecasting model for discrete valued time series with long memory and seasonality. The modelisation is achieved with an autoregressive Poisson process that features seasonality and heterogeneous autoregressive components (whence the acronym SHARP: Seasonal Heterogeneous AutoRegressive Poisson). Motivated by the prominent role of the bid-ask spread as a transaction cost for trading, we apply the SHARP model to forecast the bid-ask spread of a large sample of NYSE equity stocks. Indeed, the possibility of having a good forecasting model is of great importance for many applications, in particular for algorithms of optimal execution of orders.
We define two possible extensions of the model in order to investigate the possibility of increasing the forecasting accuracy of the original SHARP approach. The first extension features the presence of spillovers in the spread dynamics among equity stocks while the second is inspired by the Realized GARCH model of Hansen, Huang and Shek (2012), and features a measurement equation which relates the observed intra-minute (weighted) average spread with the unobserved instantaneous conditional Poisson intensity. We conclude with an application of our models by showing how bid-ask spread forecasts can be exploited to reduce the total cost incurred by a trader that is willing to buy (or sell) a given amount of an equity stock.