Bayesian Analysis

Bayesian Functional Forecasting with Locally-Autoregressive Dependent Processes

Guillaume Kon Kam King, Antonio Canale, and Matteo Ruggiero

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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.

Article information

Bayesian Anal., Advance publication (2018), 21 pages.

First available in Project Euclid: 20 December 2018

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Digital Object Identifier

approximate Bayesian computation autoregression Bayesian nonparametrics functional data analysis prediction time series

Creative Commons Attribution 4.0 International License.


Kon Kam King, Guillaume; Canale, Antonio; Ruggiero, Matteo. Bayesian Functional Forecasting with Locally-Autoregressive Dependent Processes. Bayesian Anal., advance publication, 20 December 2018. doi:10.1214/18-BA1140.

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Supplemental materials

  • Supplementary Material for “Bayesian functional forecasting with locally-autoregressive dependent processes”. The Supplementary Material contains code and data to reproduce the results of Sections 4 and 5.