By Milos Marek, Igor Schreiber
Surveying either theoretical and experimental points of chaotic habit, this e-book provides chaos as a version for plenty of likely random procedures in nature. simple notions from the idea of dynamical platforms, bifurcation conception and the houses of chaotic suggestions are then defined and illustrated by means of examples. A overview of numerical tools used either in reviews of mathematical versions and within the interpretation of experimental info can be supplied. moreover, an in depth survey of experimental commentary of chaotic habit and strategies of its research are used to emphasize common beneficial properties of the phenomenon.
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Additional resources for Chaotic behaviour of deterministic dissipative systems
Ns = 200, and set the quantile κ % as 95% in calculating the threshold of the causality strength. As shown in our testing results, four out of five indicators (except the pair associated with the BDI) significantly Granger cause the internal residue as their causality strengths exceed the corresponding thresholds over the entire sampling period. 5 Causality: F(r−>ei) Causality: F(ei−>r) Threshold of F(r−>ei) −1 Apr 08 Jul 08 Oct 08 Jan 09 Apr 09 Jul 09 Oct 09 Jan 10 Apr 10 Jul 10 Oct 10 Jan 11 Apr 11 Jul 11 Oct 11 Date Fig.
An interesting observation shows that when the time delay of the IRI starts from third order, the model yields the best results. As such, we set the lag length of the IRI in our test to be from 3 to 12. To be practical, only the data from January to August 2008 are used when performing the hyperparameter optimization. The influence of each indicator is investigated by using the indicator data and its AR components alone to predict the internal residue, before combining all selected indicators together as the input to test the prediction ability of the whole framework.
Finally, we would like to emphasize once more that our framework is structured in a systematic and flexible fashion. It can be easily expanded to incorporate more market information and to capture more market dynamics. For example, how to structure the framework and to select appropriate influential factors that are suitable Oct 08 Oct 08 Nov 08 Nov 08 Fig. 3 Adaptive Filter and Predicting Performance 49 x 10 4 Jun 10 Jun 10 Jul 10 Jul 10 Aug 10 Aug 10 Sep 10 Sep 10 Oct 10 Oct 10 Fig. 2 Comparison of the prediction results between the ARMAX and the system adaptation framework approaches for the DJIA index ARMAX System adaptation framework Improvement ((%)) Subperiod S1 Sep.