Penalised Complexity Priors for Stationary Autoregressive Processes

Handle URI:
http://hdl.handle.net/10754/625107
Title:
Penalised Complexity Priors for Stationary Autoregressive Processes
Authors:
Sørbye, Sigrunn Holbek; Rue, Haavard ( 0000-0002-0222-1881 )
Abstract:
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Sørbye SH, Rue H (2017) Penalised Complexity Priors for Stationary Autoregressive Processes. Journal of Time Series Analysis. Available: http://dx.doi.org/10.1111/jtsa.12242.
Publisher:
Wiley-Blackwell
Journal:
Journal of Time Series Analysis
Issue Date:
25-May-2017
DOI:
10.1111/jtsa.12242
Type:
Article
ISSN:
0143-9782
Additional Links:
http://onlinelibrary.wiley.com/doi/10.1111/jtsa.12242/full
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSørbye, Sigrunn Holbeken
dc.contributor.authorRue, Haavarden
dc.date.accessioned2017-06-21T06:48:05Z-
dc.date.available2017-06-21T06:48:05Z-
dc.date.issued2017-05-25en
dc.identifier.citationSørbye SH, Rue H (2017) Penalised Complexity Priors for Stationary Autoregressive Processes. Journal of Time Series Analysis. Available: http://dx.doi.org/10.1111/jtsa.12242.en
dc.identifier.issn0143-9782en
dc.identifier.doi10.1111/jtsa.12242en
dc.identifier.urihttp://hdl.handle.net/10754/625107-
dc.description.abstractThe 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.en
dc.publisherWiley-Blackwellen
dc.relation.urlhttp://onlinelibrary.wiley.com/doi/10.1111/jtsa.12242/fullen
dc.subjectAR(p)en
dc.subjectLatent Gaussian modelsen
dc.subjectPrior selectionen
dc.subjectR-INLAen
dc.subjectRobustnessen
dc.titlePenalised Complexity Priors for Stationary Autoregressive Processesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of Time Series Analysisen
dc.contributor.institutionDepartment of Mathematics and Statistics; UiT The Arctic University of Norway; Tromsø Norwayen
kaust.authorRue, Haavarden
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