Penalised Complexity Priors for Stationary Autoregressive Processes
Accepted manuscript version. Published version available at https://doi.org/10.1111/jtsa.12242 . The autoregressive (AR) process of order p(AR(p)) is a central model in time series analysis. A Bayesian approach requires the user to define a prior distribution for the coefficients of the AR(p) model....
Published in: | Journal of Time Series Analysis |
---|---|
Main Authors: | , |
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
Wiley
2017
|
Subjects: | |
Online Access: | https://hdl.handle.net/10037/13016 https://doi.org/10.1111/jtsa.12242 |
id |
ftunivtroemsoe:oai:munin.uit.no:10037/13016 |
---|---|
record_format |
openpolar |
spelling |
ftunivtroemsoe:oai:munin.uit.no:10037/13016 2023-05-15T14:26:58+02:00 Penalised Complexity Priors for Stationary Autoregressive Processes Sørbye, Sigrunn Holbek Rue, Håvard 2017-05-23 https://hdl.handle.net/10037/13016 https://doi.org/10.1111/jtsa.12242 eng eng Wiley Journal of Time Series Analysis info:eu-repo/grantAgreement/RCN/ISPNATTEK/239048/Norway/Institution based strategic project - Mathematics and Statistics at UiT The Arctic University of Norway// Sørbye, S.H. & Rue, H. (2017). Penalised Complexity Priors for Stationary Autoregressive Processes. Journal of Time Series Analysis. 38(6), 923-935. https://doi.org/10.1111/jtsa.12242 FRIDAID 1471830 doi:10.1111/jtsa.12242 0143-9782 1467-9892 https://hdl.handle.net/10037/13016 openAccess VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410 VDP::Mathematics and natural science: 400::Mathematics: 410 AR( p) latent Gaussian models prior selection R‐INLA robustness. JEL. C11 C18 C22 C88 Journal article Tidsskriftartikkel Peer reviewed 2017 ftunivtroemsoe https://doi.org/10.1111/jtsa.12242 2021-06-25T17:55:48Z Accepted manuscript version. Published version available at https://doi.org/10.1111/jtsa.12242 . The autoregressive (AR) process of order p(AR(p)) is a central model in time series analysis. A Bayesian approach requires the user to define a prior distribution for the coefficients of the AR(p) model. Although it is easy to write down some prior, it is not at all obvious how to understand and interpret the prior distribution, to ensure that it behaves according to the users' prior knowledge. In this article, we approach this problem using the recently developed ideas of penalised complexity (PC) priors. These prior have important properties like robustness and invariance to reparameterisations, as well as a clear interpretation. A PC prior is computed based on specific principles, where model component complexity is penalised in terms of deviation from simple base model formulations. In the AR(1) case, we discuss two natural base model choices, corresponding to either independence in time or no change in time. The latter case is illustrated in a survival model with possible time‐dependent frailty. For higher‐order processes, we propose a sequential approach, where the base model for AR(p) is the corresponding AR(p−1) model expressed using the partial autocorrelations. The properties of the new prior distribution are compared with the reference prior in a simulation study. Article in Journal/Newspaper Arctic University of Tromsø: Munin Open Research Archive Journal of Time Series Analysis 38 6 923 935 |
institution |
Open Polar |
collection |
University of Tromsø: Munin Open Research Archive |
op_collection_id |
ftunivtroemsoe |
language |
English |
topic |
VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410 VDP::Mathematics and natural science: 400::Mathematics: 410 AR( p) latent Gaussian models prior selection R‐INLA robustness. JEL. C11 C18 C22 C88 |
spellingShingle |
VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410 VDP::Mathematics and natural science: 400::Mathematics: 410 AR( p) latent Gaussian models prior selection R‐INLA robustness. JEL. C11 C18 C22 C88 Sørbye, Sigrunn Holbek Rue, Håvard Penalised Complexity Priors for Stationary Autoregressive Processes |
topic_facet |
VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410 VDP::Mathematics and natural science: 400::Mathematics: 410 AR( p) latent Gaussian models prior selection R‐INLA robustness. JEL. C11 C18 C22 C88 |
description |
Accepted manuscript version. Published version available at https://doi.org/10.1111/jtsa.12242 . The autoregressive (AR) process of order p(AR(p)) is a central model in time series analysis. A Bayesian approach requires the user to define a prior distribution for the coefficients of the AR(p) model. Although it is easy to write down some prior, it is not at all obvious how to understand and interpret the prior distribution, to ensure that it behaves according to the users' prior knowledge. In this article, we approach this problem using the recently developed ideas of penalised complexity (PC) priors. These prior have important properties like robustness and invariance to reparameterisations, as well as a clear interpretation. A PC prior is computed based on specific principles, where model component complexity is penalised in terms of deviation from simple base model formulations. In the AR(1) case, we discuss two natural base model choices, corresponding to either independence in time or no change in time. The latter case is illustrated in a survival model with possible time‐dependent frailty. For higher‐order processes, we propose a sequential approach, where the base model for AR(p) is the corresponding AR(p−1) model expressed using the partial autocorrelations. The properties of the new prior distribution are compared with the reference prior in a simulation study. |
format |
Article in Journal/Newspaper |
author |
Sørbye, Sigrunn Holbek Rue, Håvard |
author_facet |
Sørbye, Sigrunn Holbek Rue, Håvard |
author_sort |
Sørbye, Sigrunn Holbek |
title |
Penalised Complexity Priors for Stationary Autoregressive Processes |
title_short |
Penalised Complexity Priors for Stationary Autoregressive Processes |
title_full |
Penalised Complexity Priors for Stationary Autoregressive Processes |
title_fullStr |
Penalised Complexity Priors for Stationary Autoregressive Processes |
title_full_unstemmed |
Penalised Complexity Priors for Stationary Autoregressive Processes |
title_sort |
penalised complexity priors for stationary autoregressive processes |
publisher |
Wiley |
publishDate |
2017 |
url |
https://hdl.handle.net/10037/13016 https://doi.org/10.1111/jtsa.12242 |
genre |
Arctic |
genre_facet |
Arctic |
op_relation |
Journal of Time Series Analysis info:eu-repo/grantAgreement/RCN/ISPNATTEK/239048/Norway/Institution based strategic project - Mathematics and Statistics at UiT The Arctic University of Norway// Sørbye, S.H. & Rue, H. (2017). Penalised Complexity Priors for Stationary Autoregressive Processes. Journal of Time Series Analysis. 38(6), 923-935. https://doi.org/10.1111/jtsa.12242 FRIDAID 1471830 doi:10.1111/jtsa.12242 0143-9782 1467-9892 https://hdl.handle.net/10037/13016 |
op_rights |
openAccess |
op_doi |
https://doi.org/10.1111/jtsa.12242 |
container_title |
Journal of Time Series Analysis |
container_volume |
38 |
container_issue |
6 |
container_start_page |
923 |
op_container_end_page |
935 |
_version_ |
1766300516989534208 |