Laplace mixture autoregressive models

Nguyen, Hien D., McLachlan, Geoffrey J., Ullmann, Jeremy F. P. and Janke, Andrew L. (2016) Laplace mixture autoregressive models. Statistics and Probability Letters, 110 18-24. doi:10.1016/j.spl.2015.11.006


Author Nguyen, Hien D.
McLachlan, Geoffrey J.
Ullmann, Jeremy F. P.
Janke, Andrew L.
Title Laplace mixture autoregressive models
Journal name Statistics and Probability Letters   Check publisher's open access policy
ISSN 0167-7152
Publication date 2016-03-01
Sub-type Article (original research)
DOI 10.1016/j.spl.2015.11.006
Open Access Status Not Open Access
Volume 110
Start page 18
End page 24
Total pages 7
Place of publication Amsterdam, AE, Netherlands
Publisher Elsevier
Collection year 2017
Language eng
Abstract Autoregressive (AR) models are an important tool in the study of time series data. However, the standard AR model only allows for unimodal marginal and conditional densities, and cannot capture conditional heteroscedasticity. Previously, the Gaussian mixture AR (GMAR) model was considered to remedy these shortcomings by using a Gaussian mixture conditional model. We introduce the Laplace mixture (LMAR) model that utilizes a Laplace mixture conditional model, as an alternative to the GMAR model. We characterize the LMAR model and provide conditions for stationarity. An MM (minorization–maximization) algorithm is then proposed for maximum pseudolikelihood (MPL) estimation of an LMAR model. Conditions for asymptotic inference and a rule for model selection for the MPL estimator are considered. An example analysis of data arising from the calcium imaging of a zebrafish brain is performed.
Keyword Autoregressive model
Calcium imaging
Laplace distribution
Minorization-Maximization algorithm
Mixture model
Zebrafish brain
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
HERDC Pre-Audit
Centre for Advanced Imaging Publications
 
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