Before revision: We offer a novel way of thinking about the modelling of the time-varying distributions of financial asset returns. Borrowing ideas from symbolic data analysis, we consider data representations beyond scalars and vectors.
After revision: Motivated by the need for effectively summarising, modelling, and forecasting the distributional characteristics of intra-daily returns, as well as the recent work on forecasting histogram-valued time-series in the area of symbolic data analysis, we consider data representations beyond scalars and vectors.