arXiv subjects

Detlef Holstein

Publications and source records attributed to Detlef Holstein.

3 recordsLinked to original sources

arXiv2008

Optimal Markov Approximations and Generalized Embeddings

Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible memory into account and minimal statistical errors by working in embedding spaces of rather small dimension. A key ingredient is an estimate of the statistical error of entropy estimates. The method is illustrated with several examples and the consequences for prediction are evaluated by means of the root mean squard prediction error for point prediction.

nlin.CD↗

arXiv2008

Entropies in case of continuous time

Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for time-continuous entropies a new possibility for the distinction of chaos and noise. In the deterministic case an upper threshold of the joint uncertainty in the limit of infinitely high sampling rate can be found and the entropy rate can be calculated as a usual time derivative of the entropy. In a three-dimensional representation the dependence of the joint entropy on space resolution, discretization time step length and uncertainty-assessed time is shown in a unified manner. Hence the dimension and the Kolmogorov-Sinai entropy rate of any dynamics can be read out as limit cases from one single graph.

nlin.CD↗

arXiv2006

Precursors of extreme increments

We investigate precursors and predictability of extreme increments in a time series. The events we are focusing on consist in large increments within successive time steps. We are especially interested in understanding how the quality of the predictions depends on the strategy to choose precursors, on the size of the event and on the correlation strength. We study the prediction of extreme increments analytically in an AR(1) process, and numerically in wind speed recordings and long-range correlated ARMA data. We evaluate the success of predictions via receiver operator characteristics (ROC-curves). Furthermore, we observe an increase of the quality of predictions with increasing event size and with decreasing correlation in all examples. Both effects can be understood by using the likelihood ratio as a summary index for smooth ROC-curves.

physics.data-an↗