Approximating posterior probabilities in a linear model with possibly noninvertible moving average errors

JOURNAL OF MULTIVARIATE ANALYSIS

卷:99

Article

Pokta, Suriani²  Hart, Jeffrey D.¹ 

[1] Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA

[2] Allergan Pharmaceut Inc, Irvine, CA 92623 USA

关键词: BIC;    Information matrix;    Likelihood analysis;    Model selection;    Overdifferencing;    Noninvertible moving average process;   

DOI  :  10.1016/j.jmva.2007.04.004

来源: Elsevier

【 摘 要 】

The method of Laplace is used to approximate posterior probabilities for a collection of polynomial regression models when the errors follow a process with a noninvertible moving average component. These results are useful in the problem of period-change analysis of variable stars and in assessing the posterior probability that a time series with trend has been overdifferenced. The nonstandard covariance structure induced by a noninvertible moving average process can invalidate the standard Laplace method. A number of analytical tools is used to produce corrected Laplace approximations. These tools include viewing the covariance matrix of the observations as tending to a differential operator. The use of such an operator and its Green's function provides a convenient and systematic method of asymptotically inverting the covariance matrix. In certain cases there are two different Laplace approximations, and the appropriate one to use depends upon unknown parameters. This problem is dealt with by using a weighted geometric mean of the candidate approximations, where the weights are completely data-based and such that, asymptotically, the correct approximation is used. The new methodology is applied to an analysis of the prototypical long-period variable star known as Mira. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free