137 citations · 346 across the 10 of their papers we have counts for
5 papers · 1 filter
A note on Herglotz's theorem for time series on function spaces
Anne van Delft, Michael Eichler
In this article, we prove Herglotz's theorem for Hilbert-valued time series. This requires the notion of an operator-valued measure, which we shall make precise for our setting. He…
Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions
Michael Eichler, Rainer Dahlhaus, Johannes Dueck
Hawkes (1971) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this paper it is shown that the Granger…
Graphical modelling of multivariate time series
Michael Eichler
We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of st…
Computing maximum likelihood estimates in recursive linear models with correlated errors
Mathias Drton, Michael Eichler, Thomas S. Richardson
In recursive linear models, the multivariate normal joint distribution of all variables exhibits a dependence structure induced by a recursive (or acyclic) system of linear structu…
Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property
Mathias Drton, Michael Eichler
The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it…