: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

/pdf/nonlinear-time-series-analysis-1j3a35n4y3.pdf

Nonlinear Time Series Analysis.

Stochastic differential equations and diffusion processes

Different continuous-time models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuous-time model by discrete approximations, even though the data are recorded at discrete intervals. The principal source of rejection of existing models is the strong nonlinearity of the drift. Around its mean, where the drift is essentially zero, the spot rate behaves like a random walk. The drift then mean-reverts strongly when far away from the mean. The volatility is higher when away from the mean.

Testing Continuous-Time Models of the Spot Interest Rate

/pdf/analysis-of-observed-chaotic-data-3spe9uweeb.pdf

Analysis of observed chaotic data

An updated version of the semi-discretization method is presented for periodic systems with a single discrete time delay. The delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined. Stability charts are constructed for the damped and delayed Mathieu equation for different time-period/time-delay ratios. The convergence of the method is investigated by examples. Stability charts are constructed for 1 and 2 degree of freedom milling models. The codes of the algorithm are also attached in the appendix. Copyright © 2004 John Wiley & Sons, Ltd.

https://www.mm.bme.hu/~insperger/j2004_IJNME.pdf

Updated semi‐discretization method for periodic delay‐differential equations with discrete delay

A new definition for the symmetries of Ito and Stratonovich dynamicalsystem is given. Determining systems of symmetries for Ito andStratonovich systems have been obtained, and their relation has beendiscussed. It has been shown that some of the Lie point symmetries ofthe Fokker–Planck equation can be constructed using the symmetries ofIto dynamical systems. Conserved quantities can be found from thesymmetries of stochastic dynamical systems which do not arise from aHamiltonian. The results have been applied to an example.

Symmetries of Itô and Stratonovich Dynamical Systems and Their Conserved Quantities

The relationship between the approximateLie-Backlund symmetries and the approximate conservedforms of a perturbed equation is studied. It is shownthat a hierarchy of identities exists by which thecomponents of the approximate conserved vector or theassociated approximate Lie-Backlund symmetries aredetermined by recursive formulas. The results areapplied to certain classes of linear and nonlinear waveequations as well as a perturbed Korteweg-de Vriesequation. We construct approximate conservation laws forthese equations without regard to aLagrangian.

Approximate Symmetries and Conservation Laws with Applications

Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems

A semi-discretization method for delayed stochastic systems

A new definition is given for both exact and quasi symmetries of Ito and Stratonovich dynamical control systems Determining systems of symmetries for these systems have been obtained and their relation is discussed It is shown that conserved quantities can be found from both exact and quasi symmetries of stochastic dynamical control systems, which includes Hamiltonian control systems as a special case Systems which can be controlled via conserved quantities have been investigated Results have been applied to the control of an N-species stochastic Lotka—Volterra system

Gazanfer Unal

Papers

Symmetries of Itô and Stratonovich Dynamical Systems and Their Conserved Quantities

Approximate Symmetries and Conservation Laws with Applications

Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems

A semi-discretization method for delayed stochastic systems

Symmetries and Conserved Quantities of Stochastic Dynamical Control Systems