Doctoral Dissertations

Date of Award

5-1993

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Business Administration

Major Professor

George C. Philippatos

Committee Members

Harold Black, Philip Daves, Nicholas Alikakos

Abstract

This dissertation presents an effort to implement non-linear dynamic tools adapted from chaos theory in Financial applications. Chaotic processes, although deterministic, generate time series indistinguishable from random ones due to sensitivity to inital conditions. Utilizing techniques capable of accounting for deterministically generated stochasticity offers the advantage of describing structurally unstable systems and non-equilibrium states of nature. Furthermore, dependencies pertaining to the entire probability distribution that cannot be quantified through standard statistical procedures can be detected with the proposed methodology. The present work is along the line of a recent trend towards emphasizing disorder, instability, diversity, disequilibrium, and non linear relationships in the description of complex system behavior. From a theoretical point of view special consideration is given in discriminating the non-linearities underlying chaotic processes from those modeled through non-linear stochastic specifications in Finance. Economic pathways precluding chaotic dynamics along with potential settings generating random and complex appearing behavior with a deterministic origin, are presented. Finally, the implications of a chaotic scenario for prediction, control, and asset pricing are thoroughly discussed. A novel methodology is introduced in Financial applications that serves as a criterion for selecting the appropriate time delay in reconstructing the phase space from a single observable. This approach (entropic criterion) acts also as a measure of general dependence. The empirical part of this work focuses on the potential of the aforementioned techniques in analyzing daily prices and volume series of the DJIA individual stocks, daily US index levels, as well as, weekly index levels and returns of International indices. The results suggest that the static and dynamic behavior of stock prices depend on the portfolio aggeragtion level and the holding period, but not on idiosyncartic characteristis. Daily price and volume series of individual stocks may be modeled as the outcome of a low dimensional system.

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