Open Access
December 2019 Bayesian Functional Forecasting with Locally-Autoregressive Dependent Processes
Guillaume Kon Kam King, Antonio Canale, Matteo Ruggiero
Bayesian Anal. 14(4): 1121-1141 (December 2019). DOI: 10.1214/18-BA1140


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.


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Guillaume Kon Kam King. Antonio Canale. Matteo Ruggiero. "Bayesian Functional Forecasting with Locally-Autoregressive Dependent Processes." Bayesian Anal. 14 (4) 1121 - 1141, December 2019.


Published: December 2019
First available in Project Euclid: 20 December 2018

zbMATH: 1435.62348
MathSciNet: MR4044848
Digital Object Identifier: 10.1214/18-BA1140

Keywords: Approximate Bayesian Computation , Autoregression , Bayesian nonparametrics , Functional data analysis , prediction , time series

Vol.14 • No. 4 • December 2019
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