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.

How do neighbouring populations affect local population change over time?

This study covers a period when society changed from a pre-industrial agricultural society to a post-industrial service-producing society. Parallel with this social transformation, major population changes took place. In this study, we analyse how local population changes are affected by neighbouring populations. To do so we use the last 200 years of local population change that redistributed population in Sweden. We use literature to identify several different processes and spatial dependencies in the redistribution between a parish and its surrounding parishes. The analysis is based on a unique unchanged historical parish division, and we use an index of local spatial correlation to describe different kinds of spatial dependencies that have influenced the redistribution of the population. To control inherent time dependencies, we introduce a non-separable spatial temporal correlation model into the analysis of population redistribution. Hereby, several different spatial dependencies can be observed simultaneously over time. The main conclusions are that while local population changes have been highly dependent on the neighbouring populations in the 19th century, this spatial dependence have become insignificant already when two parishes is separated by 5 kilometres in the late 20th century. Another conclusion is that the time dependency in the population change is higher when the population redistribution is weak, as it currently is and as it was during the 19th century until the start of industrial revolution.