Financial time series analysis : Chaos and neurodynamics approach

This work aims at combining the Chaos theory postulates and Artificial Neural Networks classification and predictive capability, in the field of financial time series prediction. Chaos theory, provides valuable qualitative and quantitative tools to decide on the predictability of a chaotic system. Quantitative measurements based on Chaos theory, are used, to decide a-priori whether a time series, or a portion of a time series is predictable, while Chaos theory based qualitative tools are used to provide further observations and analysis on the predictability, in cases where measurements provide negative answers. Phase space reconstruction is achieved by time delay embedding resulting in multiple embedded vectors. The cognitive approach suggested, is inspired by the capability of some chartists to predict the direction of an index by looking at the price time series. Thus, in this work, the calculation of the embedding dimension and the separation, in Takens‘ embedding theorem for phase space reconstruction, is not limited to False Nearest Neighbor, Differential Entropy or other specific method, rather, this work is interested in all embedding dimensions and separations that are regarded as different ways of looking at a time series by different chartists, based on their expectations. Prior to the prediction, the embedded vectors of the phase space are classified with Fuzzy-ART, then, for each class a back propagation Neural Network is trained to predict the last element of each vector, whereas all previous elements of a vector are used as features.

Experimental study of forces and energies during shearing of steel sheet with angled tools

Shearing is a fast and inexpensive method to cut sheet metal that has been used since the beginning of the industrialism. Consequently, published experimental studies of shearing can be found from over a century back in time. Recent studies, however, are due to the availability of low cost digital computation power, mostly based on finite element simulations that guarantees quick results. Still, for validation of models and simulations, accurate experimental data is a requisite. When applicable, 2D models are in general desirable over 3D models because of advantages like low computation time and easy model formulation. Shearing of sheet metal with parallel tools is successfully modelled in 2D with a plane strain approximation, but with angled tools the approximation is less obvious. Therefore, plane strain approximations for shearing with angled tools were evaluated by shear experiments of high accuracy. Tool angle, tool clearance, and clamping of the sheet were varied in the experiments. The results showed that the measured forces in shearing with angled tools can be approximately calculated using force measurements from shearing with parallel tools. Shearing energy was introduced as a quantifiable measure of suitable tool clearance range. The effects of the shearing parameters on forces were in agreement with previous studies. Based on the agreement between calculations and experiments, analysis based on a plane strain assumption is considered applicable for angled tools with a small (up to 2 degrees) rake angle.