Comparison of the new "econophysics" approach to dealing with problems of financial to traditional econometric methods

We begin with the outlining the motivation of this research as there are still so many unanswered research questions on our complex financial and economic systems. The philosophical background and the advances of econometrics and econophysics are discussed to provide an overview of the stochastic and nonstochastic modelling and these disciplines are set as a central theme for the thesis. This thesis investigates the effectiveness of financial econometrics models such as Gaussian, ARCH (1), GARCH (1, 1) and its extensions as compared to econophysics models such as Power Law model, Boltzmann-Gibbs (BG) and Tsallis Entropy as statistical models of volatility in US S&P500, Dow Jones and NASDAQ stock index using daily data. The data demonstrate several distinct behavioural characteristics, particularly the increased volatility during 1998 to 2004. Power Laws appear to describe the large fluctuations and other characteristics of stock price changes. Surprisingly, these Power Laws models also show significant correlations for different types and sizes of markets and for different periods and sub-periods of markets. The results show the robustness of Power Law analysis, with the Power Law exponent (0.4 to 2.4) staying within the acceptable range of significance (83% to 97%), regardless of the percentage change in the index return. However, the procedure for testing empirical data against a hypothesised power-law distribution using a simple rank-frequency plot of the data and the data binning process can turn out to be a spurious result for the distribution. As for the stochastic processes such as ARCH (1) and GARCH (1, 1) the models are explicitly confined to the conditional behaviour of the data and the unconditional behaviour has often been described via moments. In reality, it is the unconditional tail behaviour that accounts for the tail behaviour and hence, we have to convert the unconditional tail behaviour and express the models as two-dimensional stochastic difference equation using the processes of Starica (Mikosch 2000). The results show the random walk prediction successfully describes the stock movements for small price fluctuations but fails to handle large price fluctuations. The Power Law tests prove superior to the stochastic tests when stock price fluctuations are substantially divergent from the mean. One of the main points of the thesis is that these empirical phenomena are not present in the stochastic process but emerge in the non-parametric process. The main objective of the thesis is to study the relatively new field of Econophysics and put its work in perspective relative to the established if not altogether successful practice of econometric analysis of stock market volatility. One of the most exciting characteristics of Econophysics is that, as a developing field, no models as yet perfectly represent the market and there is still a lot of fundamental research to be done. Therefore, we begin to explore the application of statistical physics method particularly Tsallis entropy to give a new insights into problems traditionally associated with financial markets. The results of Tsallis entropy surpass all expectations and it is therefore one of the most robust methods of analysis. However, it is now subject to some challenge from McCauley, Bassler et. al., as they found that the stochastic dynamic process (sliding interval techniques) used in fat tail distributions is time dependent.