Modeling Financial Time Series with Artificial Neural Networks

Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

SymbolDesign: A User-centered Method to Design Pen-based Interfaces and Extend the Functionality of Pointer Input Devices

A method called "SymbolDesign" is proposed that can be used to design user-centered interfaces for pen-based input devices. It can also extend the functionality of pointer input devices such as the traditional computer mouse or the Camera Mouse, a camera-based computer interface. Users can create their own interfaces by choosing single-stroke movement patterns that are convenient to draw with the selected input device and by mapping them to a desired set of commands. A pattern could be the trace of a moving finger detected with the Camera Mouse or a symbol drawn with an optical pen. The core of the SymbolDesign system is a dynamically created classifier, in the current implementation an artificial neural network. The architecture of the neural network automatically adjusts according to the complexity of the classification task. In experiments, subjects used the SymbolDesign method to design and test the interfaces they created, for example, to browse the web. The experiments demonstrated good recognition accuracy and responsiveness of the user interfaces. The method provided an easily-designed and easily-used computer input mechanism for people without physical limitations, and, with some modifications, has the potential to become a computer access tool for people with severe paralysis.