Electronic Journal of Statistics

Bayesian nonparametric forecasting of monotonic functional time series

Antonio Canale and Matteo Ruggiero

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist. Volume 10, Number 2 (2016), 3265-3286.

Dates
Received: December 2015
First available in Project Euclid: 16 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1479287221

Digital Object Identifier
doi:10.1214/16-EJS1190

Mathematical Reviews number (MathSciNet)
MR3572849

Zentralblatt MATH identifier
06673444

Subjects
Primary: 62G00
Secondary: 62F15: Bayesian inference 60J22: Computational methods in Markov chains [See also 65C40]

Keywords
Approximate Bayesian computation dependent processes Dirichlet process interacting particle system Moran model Polya urn prediction

Citation

Canale, Antonio; Ruggiero, Matteo. Bayesian nonparametric forecasting of monotonic functional time series. Electron. J. Statist. 10 (2016), no. 2, 3265--3286. doi:10.1214/16-EJS1190. https://projecteuclid.org/euclid.ejs/1479287221.


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