  We propose a Bayesian nonparametric approach to modelling and predicting a
class of functional time series with application to energy markets, based on
fully observed, noise-free functional data. Traders in such contexts conceive
profitable strategies if they can anticipate the impact of their bidding
actions on the aggregate demand and supply curves, which in turn need to be
predicted reliably. Here we propose a simple Bayesian nonparametric method for
predicting such curves, which take the form of monotonic bounded step
functions. We borrow ideas from population genetics by defining a class of
interacting particle systems to model the functional trajectory, and develop an
implementation strategy which uses ideas from Markov chain Monte Carlo and
approximate Bayesian computation techniques and allows to circumvent the
intractability of the likelihood. Our approach shows great adaptation to the
degree of smoothness of the curves and the volatility of the functional series,
proves to be robust to an increase of the forecast horizon and yields an
uncertainty quantification for the functional forecasts. We illustrate the
model and discuss its performance with simulated datasets and on real data
relative to the Italian natural gas market.
