2,067 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
Sparse Learning for Variable Selection with Structures and Nonlinearities
In this thesis we discuss machine learning methods performing automated
variable selection for learning sparse predictive models. There are multiple
reasons for promoting sparsity in the predictive models. By relying on a
limited set of input variables the models naturally counteract the overfitting
problem ubiquitous in learning from finite sets of training points. Sparse
models are cheaper to use for predictions, they usually require lower
computational resources and by relying on smaller sets of inputs can possibly
reduce costs for data collection and storage. Sparse models can also contribute
to better understanding of the investigated phenomenons as they are easier to
interpret than full models.Comment: PhD thesi
Limit Theory under Network Dependence and Nonstationarity
These lecture notes represent supplementary material for a short course on
time series econometrics and network econometrics. We give emphasis on limit
theory for time series regression models as well as the use of the
local-to-unity parametrization when modeling time series nonstationarity.
Moreover, we present various non-asymptotic theory results for moderate
deviation principles when considering the eigenvalues of covariance matrices as
well as asymptotics for unit root moderate deviations in nonstationary
autoregressive processes. Although not all applications from the literature are
covered we also discuss some open problems in the time series and network
econometrics literature.Comment: arXiv admin note: text overlap with arXiv:1705.08413 by other author
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