A hierarchical approach to covariance function estimation for time series

The covariance function in time series models is typically modeled via a parametric family. This ensures straightforward linear prediction while maintaining positive-de niteness of the covariance function. We suggest an alternative approach, which will result in data-determined shrinkage towards this parametric model. Positive-de niteness is maintained by carrying out the shrinkage in the spectral domain. We o er both a fully Bayesian hierarchical approach and an approximate hierarchical approach that will be much simpler computationally. These are implemented on the frequently analyzed Canadian lynx data and compared to other models that have been tted to these data.