Publication Type
Journal Article
Version
acceptedVersion
Publication Date
7-2020
Abstract
In this data‐rich era, it is essential to develop advanced techniques to analyze and understand large amounts of data and extract the underlying information in a flexible way. We provide a review study on the state‐of‐the‐art statistical time series models for univariate and multivariate functional data with serial dependence. In particular, we review functional autoregressive (FAR) models and their variations under different scenarios. The models include the classic FAR model under stationarity; the FARX and pFAR model dealing with multiple exogenous functional variables and large‐scale mixed‐type exogenous variables; the vector FAR model and common functional principal component technique to handle multiple dimensional functional time series; and the warping FAR, varying coefficient‐FAR and adaptive FAR models to handle seasonal variations, slow varying effects and the more challenging cases of structural changes or breaks respectively. We present the models’ setup and detail the estimation procedure. We discuss the models’ applicability and illustrate the numerical performance using real‐world data of high‐resolution natural gas flows in the high‐pressure gas pipeline network of Germany. We conduct 1‐day and 14‐days‐ahead out‐of‐sample forecasts of the daily gas flow curves. We observe that the functional time series models generally produce stable out‐of‐sample forecast accuracy.
Keywords
Statistical models, Semiparametric models, Time series, Stochastic processes, Functional data
Discipline
Management Sciences and Quantitative Methods | Statistics and Probability
Research Areas
Quantitative Finance
Publication
Wiley Interdisciplinary Reviews Computational Statistics
Volume
13
Issue
3
First Page
1
Last Page
23
ISSN
1939-0068
Publisher
Wiley
Embargo Period
4-20-2021
Citation
CHEN, Ying; KOCH, Thorsten; LIM, Kian Guan; XU, Xiaofei; and ZAKIYEVA, Nazgul.
A review study of functional autoregressive models with application to energy forecasting. (2020). Wiley Interdisciplinary Reviews Computational Statistics. 13, (3), 1-23.
Available at: https://ink.library.smu.edu.sg/lkcsb_research/6688
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1002/wics.1525
Included in
Management Sciences and Quantitative Methods Commons, Statistics and Probability Commons