By Ignacio Rojas, Héctor Pomares

This quantity offers chosen peer-reviewed contributions from The foreign Work-Conference on Time sequence, ITISE 2015, held in Granada, Spain, July 1-3, 2015. It discusses themes in time sequence research and forecasting, complex tools and on-line studying in time sequence, high-dimensional and complex/big info time sequence in addition to forecasting in actual problems.

The foreign Work-Conferences on Time sequence (ITISE) offer a discussion board for scientists, engineers, educators and scholars to debate the most recent rules and implementations within the foundations, conception, types and purposes within the box of time sequence research and forecasting. It makes a speciality of interdisciplinary and multidisciplinary study encompassing the disciplines of laptop technological know-how, arithmetic, records and econometrics.

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S/ in (1). 4. In practice, it seems that the bands ˝b as well as the numbers nb have to be chosen adaptively. T/ seems appropriate. Let the parameter vector #b contain all d D 2pk C k2 C p distinct parameters in Q .! b/ /, Sf .! b/ / and S" .! b/ /, where each of the (in general) complex elements in Q .! b/ / and Sf .! b/ / is represented by a pair of real components in #b , corresponding to its real part and its imaginary part. The full model dimension is consequently equal to Bd. SX .! #b / D SX .!

1007/978-3-319-28725-6_3 27 28 T. Dickhaus and M. t/ D . t//> denotes a p-dimensional vector of “specific factors,” to be regarded as error or remainder terms. t/ at all leads and lags. t/ may, however, exhibit nontrivial (weak) serial autocorrelations. The model dimensions p and k are assumed to be fixed, while the sample size T may tend to infinity. The underlying interpretation of model (1) is that the dynamic behavior of the process X can already be described well (or completely) by a lower-dimensional “latent” process.

E 83, 021113 (2011) 13. : Optimal variables for describing evolution of no2 concentration. Phys. Lett. A 376, 2081–2089 (2012) 14. : Principal axes for stochastic dynamics. Phys. Rev. E 84, 031103 (2011) 15. : Reconstruction of complex dynamical systems affected by strong measurement noise. Phys. Rev. Lett. 97, 090603 (2006) 16. G. : Extracting strong measurement noise from stochastic time series: applications to empirical data. Phys. Rev. E 81, 041125 (2010) 17. : Evaluating strong measurement noise in data series with simulated annealing method.

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