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**Bayesian nonparametric forecasting of monotonic functional time series.**
*(English)*
Zbl 1357.62278

Summary: 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.

### MSC:

62M20 | Inference from stochastic processes and prediction |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62F15 | Bayesian inference |

60J22 | Computational methods in Markov chains |

65C05 | Monte Carlo methods |

62G05 | Nonparametric estimation |

60K35 | Interacting random processes; statistical mechanics type models; percolation theory |

62P20 | Applications of statistics to economics |