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A Hierarchical Approach to Covariance Function Estimation for Time Series
Author(s) -
Daniels Michael J.,
Cressie Noel
Publication year - 2001
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00222
Subject(s) - mathematics , covariance , parametric statistics , covariance function , series (stratigraphy) , positive definiteness , bayesian probability , function (biology) , algorithm , parametric model , statistics , eigenvalues and eigenvectors , positive definite matrix , paleontology , physics , quantum mechanics , evolutionary biology , biology
The covariance function in time series models is typically modelled via a parametric family. This ensures straightforward best linear prediction while maintaining positive‐definiteness of the covariance function. We suggest an alternative approach, which will result in data‐determined shrinkage towards this parametric model. Positive‐definiteness is maintained by carrying out the shrinkage in the spectral domain. We offer both a fully Bayesian hierarchical approach and an approximate hierarchical approach that will be much simpler computationally. These are implemented on the frequently analysed Canadian lynx data and compared to other models that have been fitted to these data.