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. / Doctor of Philosophy (PhD)

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2007. / Title from title screen (site viewed Dec. 4, 2007). PDF text: xviii, 149 p. : ill. ; 7 Mb. UMI publication number: AAT 3271931. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

The statistics describing variations of turbulent motions within the so called inertial range of length scales depend on the scale over which the motions are varying and the "average" rate at which the turbulent kinetic energy is being dissipated on the molecular scale. This hypothesis stemmed from the similarity arguments published by A. N. Kolmogorov in 1941 and implies specific scaling relations between the average amplitude and length scale of turbulent motions. Turbulent motions agree to a good approximation with Kolmogorov scaling provided the fluid flow admits to the underlying assumptions. More recently it has been recognized that the large spatial variations in the rate of turbulent kinetic energy dissipation may be a partial explanation for deviations from Kolmogorov scaling. This recognition is due in part to the observation that the total volume occupied by turbulent motions of a given scale decreases as the scale decreases. These observations imply that active small scale turbulence is intermittent. This study aims to better understand how scaling relations describing more active regions are different from the relations describing turbulence where the small scales are less active. The thesis is that the relations are different. An 18 hour segment of wind data measured in near-neutral stratification 45 meters above a relatively flat ground is analyzed. There is virtually no trend in the mean wind speed, so the describing statistics are essentially stationary. Small scale activity is measured in terms of the difference in wind speed (structure function) at a separation distance of 1/16 of a second, which translates to about a meter. The differences in wind speed are raised to the sixth power and then averaged over 4 second (50 meter) windows. Non-overlapping windows containing a local maximum in the averaged sixth order structure function form one (MASC) ensemble of more active small scale samples and the local minima form another (LASC) ensemble of less active small scale samples. The variations in wind speed as a function of length scale within each ensemble are decomposed five different ways. Each of the five decompositions obey scaling relationships that are approximately linear in log-log coordinates. The MASC and LASC ensembles include 32% and 46% of the record, respectively. The turbulent kinetic energy as a function of scale falls off at a slower rate in the MASC ensemble versus the LASC ensemble and in magnitude the energy is greater at all scales in the MASC ensemble. This implies the transfer rate of turbulent kinetic energy toward small scales is more rapid on average in the MASC samples. Samples in the MASC ensemble occupied 30% less of the record, implying the flattening effect on the spectral slope exhibited by the samples contained in the MASC ensemble is less influential than the steepening influence of samples of the type in the LASC ensemble. The results are robust with respect to the choice of a basis set in representing the variance as a function of scale. / Graduation date: 1994

Thesis (Ph. D.)--Chalmers tekniska högskola and Göteborgs universitet, 2006. / Includes bibliographical references (p. 219-224) and index.

Thesis (Ph.D.)--McMaster University, 2004. / Supervisor: Harald D. H. Stöver.

Thesis (Ph. D.)--Oregon State University, 1983. / Typescript (photocopy). Includes bibliographical references (leaves 130-132). Also available on the World Wide Web.

Chalmers Univ. of Technology and Göteborg Univ., Diss.--Göteborg, 2006.

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [214]-224)

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Physics and Material Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves 140-167)