131 research outputs found
Optimal model-free prediction from multivariate time series
Forecasting a time series from multivariate predictors constitutes a
challenging problem, especially using model-free approaches. Most techniques,
such as nearest-neighbor prediction, quickly suffer from the curse of
dimensionality and overfitting for more than a few predictors which has limited
their application mostly to the univariate case. Therefore, selection
strategies are needed that harness the available information as efficiently as
possible. Since often the right combination of predictors matters, ideally all
subsets of possible predictors should be tested for their predictive power, but
the exponentially growing number of combinations makes such an approach
computationally prohibitive. Here a prediction scheme that overcomes this
strong limitation is introduced utilizing a causal pre-selection step which
drastically reduces the number of possible predictors to the most predictive
set of causal drivers making a globally optimal search scheme tractable. The
information-theoretic optimality is derived and practical selection criteria
are discussed. As demonstrated for multivariate nonlinear stochastic delay
processes, the optimal scheme can even be less computationally expensive than
commonly used sub-optimal schemes like forward selection. The method suggests a
general framework to apply the optimal model-free approach to select variables
and subsequently fit a model to further improve a prediction or learn
statistical dependencies. The performance of this framework is illustrated on a
climatological index of El Ni\~no Southern Oscillation.Comment: 14 pages, 9 figure
Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls
Long-range correlated processes are ubiquitous, ranging from climate
variables to financial time series. One paradigmatic example for such processes
is fractional Brownian motion (fBm). In this work, we highlight the potentials
and conceptual as well as practical limitations when applying the recently
proposed recurrence network (RN) approach to fBm and related stochastic
processes. In particular, we demonstrate that the results of a previous
application of RN analysis to fBm (Liu \textit{et al.,} Phys. Rev. E
\textbf{89}, 032814 (2014)) are mainly due to an inappropriate treatment
disregarding the intrinsic non-stationarity of such processes. Complementarily,
we analyze some RN properties of the closely related stationary fractional
Gaussian noise (fGn) processes and find that the resulting network properties
are well-defined and behave as one would expect from basic conceptual
considerations. Our results demonstrate that RN analysis can indeed provide
meaningful results for stationary stochastic processes, given a proper
selection of its intrinsic methodological parameters, whereas it is prone to
fail to uniquely retrieve RN properties for non-stationary stochastic processes
like fBm.Comment: 8 pages, 6 figure
An integrative quantifier of multistability in complex systems based on ecological resilience
Acknowledgements This work was supported by the German Federal Ministry of Education and Research (BMBF) via the Young Investigators Group CoSy-CC2 (grant no. 01LN1306A). C.M. acknowledges the support of Bedartha Goswami, Jobst Heitzig and Tim Kittel.Peer reviewedPublisher PD
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