Bayes linear variance adjustment for time series
  This paper exhibits quadratic products of linear combinations of observables which identify the covariance structure underlying the univariate locally linear time series dynamic linear model. The first- and second-order moments for the joint distribution over these observables are given, allowing Bayes linear learning for the underlying covariance structure for the time series model. An example is given which illustrates the methodology and highlights the practical implications of the theory. 
Darren J Wilkinson (http://fourier.dur.ac.uk:8000/djw.html)