Econometric techniques for forecasting financial time series in discrete time

This thesis is a collection of three essays on financial econometrics with a common background in ultra-high frequency modeling of market activity. In the first essay, we propose an accurate and fast-to-estimate forecasting model for discrete valued time series with long memory and seasonality.1 The modelling is achieved with an autoregressive conditional 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 spreads of a large sample of NYSE equity stocks. [...]