A chaos theory and nonlinear dynamics approach to the analysis of financial series : a comparative study of Athens and London stock markets
This dissertation presents an effort to implement nonlinear dynamic tools adapted from chaos theory in financial applications. Chaos theory might be useful in explaining the dynamics of financial markets, since chaotic models are capable of exhibiting behaviour similar to that observed in empirical financial data. In this context, the scope of this research is to provide an insight into the role that nonlinearities and, in particular, chaos theory may play in explaining the dynamics of financial markets. From a theoretical point of view, the basic features of chaos theory, as well as, the rationales for bringing chaos theory to the attention of financial researchers are discussed. Empirically, the fundamental issue of determining whether chaos can be observed in financial time series is addressed. Regarding the latter, empirical literature has been controversial. A quite exhaustive analysis of the existing literature is provided, revealing the inadequacies in terms of methodology and the testing framework adopted, so far. A new "multiple testing" methodology is developed combining methods and techniques from the fields of both Natural Sciences and the Economics, most of which have not been applied to financial data before. A serious effort has been made to fill, as much as possible, the gap which results from the lack of a proper statistical framework for the chaotic methods. To achieve this the bootstrap methodology is adopted. The empirical part of this work focuses on the comparison of two markets with different levels of maturity; the Athens Stock Exchange (ASE), an emerging market, and London Stock Exchange (LSE). Our aim is to determine whether structural differences exist in these markets in terms of chaotic dynamics. In the empirical level we find nonlinearities in both markets by the use of the BDS test. R/S analysis reveals fractality and long term memory for the ASE series only. Chaotic methods, such as the correlation dimension (and related methods and techniques) and the largest Lyapunov exponent estimation, cannot rule out a chaotic explanation for the ASE market, but no such indication could be found for the LSE market. Noise filtering by the SVD method does not alter these findings. Alternative techniques based on nonlinear nearest neighbour forecasting methods, such as the "piecewise polynomial approximation" and the "simplex" methods, support our aforementioned conclusion concerning the ASE series. In all, our results suggest that, although nonlinearities are present, chaos is not a widespread phenomenon in financial markets and it is more likely to exist in less developed markets such as the ASE. Even then, chaos is strongly mixed with noise and the existence of low-dimensional chaos is highly unlikely. Finally, short-term forecasts trying to exploit the dependencies found in both markets seem to be of no economic importance after accounting for transaction costs, a result which supports further our conclusions about the limited scope and practical implications of chaos in Finance.