11 research outputs found
Forecasting and Granger Modelling with Non-linear Dynamical Dependencies
Traditional linear methods for forecasting multivariate time series are not
able to satisfactorily model the non-linear dependencies that may exist in
non-Gaussian series. We build on the theory of learning vector-valued functions
in the reproducing kernel Hilbert space and develop a method for learning
prediction functions that accommodate such non-linearities. The method not only
learns the predictive function but also the matrix-valued kernel underlying the
function search space directly from the data. Our approach is based on learning
multiple matrix-valued kernels, each of those composed of a set of input
kernels and a set of output kernels learned in the cone of positive
semi-definite matrices. In addition to superior predictive performance in the
presence of strong non-linearities, our method also recovers the hidden dynamic
relationships between the series and thus is a new alternative to existing
graphical Granger techniques.Comment: Accepted for ECML-PKDD 201
Spatial extremes of wildfire sizes: Bayesian hieralquical models for extremes
In Portugal, due to the combination of climatological and ecological
factors, large wildfires are a constant threat and due to their economic impact, a big
policy issue. In order to organize efficient fire fighting capacity and resource management,
correct quantification of the risk of large wildfires are needed. In this paper,
we quantify the regional risk of large wildfire sizes, by fitting a Generalized Pareto
distribution to excesses over a suitably chosen high threshold. Spatio-temporal variations
are introduced into the model through model parameters with suitably chosen
link functions. The inference on these models are carried using Bayesian Hierarchical
Models and Markov chain Monte Carlo methods
Self-exciting threshold binomial autoregressive processes
We introduce a new class of integer-valued self-exciting threshold models,
which is based on the binomial autoregressive model of order one as introduced
by McKenzie (Water Resour Bull 21:645–650, 1985. doi:10.1111/j.1752-1688.1985.
tb05379.x). Basic probabilistic and statistical properties of this class of models are
discussed. Moreover, parameter estimation and forecasting are addressed. Finally, the
performance of these models is illustrated through a simulation study and an empirical
application to a set of measle cases in Germany