Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/23882
Authors: 
Czado, Claudia
Högn, Ralph
Year of Publication: 
2003
Series/Report no.: 
Discussion papers / Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 326
Abstract: 
Three classes of models for time series on acyclic directed graphs are considered. At first a review of tree-structured models constructed from a nested partitioning of the observation interval is given. This nested partitioning leads to several resolution scales. The concept of mass balance allowing to interpret the average over an interval as the sum of averages over the sub-intervals implies linear restrictions in the tree-structured model. Under a white noise assumption for transition and observation noise there is an change-of-resolution Kalman filter for linear least squares prediction of interval averages (Chou 1991). This class of models is generalized by modeling transition noise on the same scale in linear state space form. The third class deals with models on a more general class of directed acyclic graphs where nodes are allowed to have two parents. We show that these models have a linear state space representation with white system and coloured observation noise.
Subjects: 
linear least squares prediction
tree-structured model
mass-balance
acyclic directed graph
linear state space model
linear Kalman filter
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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