Point and density prediction of intra-day volume using Bayesian linear ACV models: evidence from the Polish stock market

Trading volume is one of the key measures of trading activity intensity and plays a crucial role in the financial market microstructure literature. In this paper, we examine the out-of-sample point and density forecasting performance of Bayesian Autoregressive Conditional Volume (ACV) models for intra-day volume data. Based on 5-min traded volume data for stocks quoted on the Warsaw Stock Exchange, a leading stock market in Central and Eastern Europe, we find that, in terms of point forecasts, the considered linear ACV models significantly outperform benchmarks such as the naïve and Rolling Means methods but not necessarily Autoregressive Moving Average (ARMA) models. Moreover, the point forecasts obtained within the exponential error ACV model are significantly superior to those calculated in other competing structures for which Burr or generalized gamma distributions are specified. The main finding from the analysis of density forecasts is that, in many cases, the linear ACV models with the Burr and generalized gamma distributions provide significantly better density forecasts than the linear ACV model with exponential innovations and the ARMA models in terms of the log-predictive score, calibration and sharpness.