ABSTRACT
In this chapter, we introduce the concept of distributional time series and propose the fundamentals for forecasting them. We propose the use of error measures based on distances for distributions, and to measure the error for a specific set of quantiles of interest. We adapt the main components of classic time series, namely, trend and seasonality, to distributional time series and define the autocorrelation function for distributional time series. We explain how to forecast distributional time series using exponential smoothing, k- Nearest Neighbours and autoregressive methods. Finally, we illustrate these concepts forecasting two distributional time series: one representing rainfall data and another intra-daily returns of an equity.
