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**Bayesian functional forecasting with locally-autoregressive dependent processes.**
*(English)*
Zbl 1435.62348

Summary: Motivated by the problem of forecasting demand and offer curves, we introduce a class of nonparametric dynamic models with locally-autoregressive behaviour, and provide a full inferential strategy for forecasting time series of piecewise-constant non-decreasing functions over arbitrary time horizons. The model is induced by a non Markovian system of interacting particles whose evolution is governed by a resampling step and a drift mechanism. The former is based on a global interaction and accounts for the volatility of the functional time series, while the latter is determined by a neighbourhood-based interaction with the past curves and accounts for local trend behaviours, separating these from pure noise. We discuss the implementation of the model for functional forecasting by combining a population Monte Carlo and a semi-automatic learning approach to approximate Bayesian computation which require limited tuning. We validate the inference method with a simulation study, and carry out predictive inference on a real dataset on the Italian natural gas market.

### MSC:

62M20 | Inference from stochastic processes and prediction |

62R10 | Functional data analysis |

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

62P20 | Applications of statistics to economics |

### Keywords:

approximate Bayesian computation; autoregression; Bayesian nonparametrics; functional data analysis; prediction; time series
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\textit{G. K. K. King} et al., Bayesian Anal. 14, No. 4, 1121--1141 (2019; Zbl 1435.62348)

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