Applications of physics to finance and economics: returns, trading activity and income

This dissertation reports work where physics methods are applied to financial and economical problems. The first part studies stock market data (chapter 1 to 5). The second part is devoted to personal income in the USA (chapter 6). We first study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. For mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an exponential law. At longer times, the exponential law continuously evolves into Gaussian distribution. After characterizing the stock returns at mesoscopic time lags, we study the subordination hypothesis. The integrated volatility V_t constructed from the number of trades process can be used as a subordinator for a Brownian motion. This subordination is able to describe approximatly 85% of the stock returns for time lags that start at 1 hour but are shorter than one day. Finally, we show that the CIR process describes well enough the empirical V_t process, such that the corresponding Heston model is able to describe the log-returns x_t process, with approximately the maximum quality that the subordination allows. Finally, we study the time evolution of the personal income distribution. We find that the personal income distribution in the USA has a well-defined two-income-class structure. The majority of population (97-99%) belongs to the lower income class characterized by the exponential Boltzmann-Gibb(``thermal'') distribution, whereas the higher income class (1-3% of population) has a Pareto power-law (``superthermal'') distribution. We show that the ``thermal'' part is stationary in time.Comment: 24 pages and 45 figures. PhD thesis presented to the committee members on May 10th 2005. This thesis is based on 3 published papers with one chapter (chapter 5) with new unpublished result

Large scale prop-fan structural design study. Volume 1: Initial concepts

In recent years, considerable attention has been directed toward improving aircraft fuel consumption. Studies have shown that the inherent efficiency advantage that turboprop propulsion systems have demonstrated at lower cruise speeds may now be extended to the higher speeds of today's turbofan and turbojet-powered aircraft. To achieve this goal, new propeller designs will require features such as thin, high speed airfoils and aerodynamic sweep, features currently found only in wing designs for high speed aircraft. This is Volume 1 of a 2 volume study to establish structural concepts for such advanced propeller blades, to define their structural properties, to identify any new design, analysis, or fabrication techniques which were required, and to determine the structural tradeoffs involved with several blade shapes selected primarily on the basis of aero/acoustic design considerations. The feasibility of fabricating and testing dynamically scaled models of these blades for aeroelastic testing was also established. The preliminary design of a blade suitable for flight use in a testbed advanced turboprop was conducted and is described in Volume 2

Mean field approximation of two coupled populations of excitable units

The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the inter-ensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical inter-population couplings.Comment: 5 figure

Bivariate modelling of precipitation and temperature using a non-homogeneous hidden Markov model

Aiming to generate realistic synthetic times series of the bivariate process of daily mean temperature and precipitations, we introduce a non-homogeneous hidden Markov model. The non-homogeneity lies in periodic transition probabilities between the hidden states, and time-dependent emission distributions. This enables the model to account for the non-stationary behaviour of weather variables. By carefully choosing the emission distributions, it is also possible to model the dependance structure between the two variables. The model is applied to several weather stations in Europe with various climates, and we show that it is able to simulate realistic bivariate time series

The Canadian Business Cycle: A Comparison of Models

This paper examines the ability of linear and nonlinear models to replicate features of real Canadian GDP. We evaluate the models using various business-cycle metrics. From the 9 data generating processes designed, none can completely accommodate every business-cycle metric under consideration. Richness and complexity do not guarantee a close match with Canadian data. Our findings for Canada are consistent with Piger and Morley's (2005) study of the United States data and confirms the contradiction of their results with those reported by Engel, Haugh, and Pagan (2005): nonlinear models do provide an improvement in matching business-cycle features. Lastly, the empirical results suggest that investigating the merits of forecast combination would be worthwhile.Business fluctuations and cycles; Econometric and statistical methods

Text authorship identified using the dynamics of word co-occurrence networks

The identification of authorship in disputed documents still requires human expertise, which is now unfeasible for many tasks owing to the large volumes of text and authors in practical applications. In this study, we introduce a methodology based on the dynamics of word co-occurrence networks representing written texts to classify a corpus of 80 texts by 8 authors. The texts were divided into sections with equal number of linguistic tokens, from which time series were created for 12 topological metrics. The series were proven to be stationary (p-value>0.05), which permits to use distribution moments as learning attributes. With an optimized supervised learning procedure using a Radial Basis Function Network, 68 out of 80 texts were correctly classified, i.e. a remarkable 85% author matching success rate. Therefore, fluctuations in purely dynamic network metrics were found to characterize authorship, thus opening the way for the description of texts in terms of small evolving networks. Moreover, the approach introduced allows for comparison of texts with diverse characteristics in a simple, fast fashion

Quantile spectral processes: Asymptotic analysis and inference

Quantile- and copula-related spectral concepts recently have been considered by various authors. Those spectra, in their most general form, provide a full characterization of the copulas associated with the pairs $(X_t,X_{t-k})$ in a process $(X_t)_{t\in\mathbb{Z}}$, and account for important dynamic features, such as changes in the conditional shape (skewness, kurtosis), time-irreversibility, or dependence in the extremes that their traditional counterparts cannot capture. Despite various proposals for estimation strategies, only quite incomplete asymptotic distributional results are available so far for the proposed estimators, which constitutes an important obstacle for their practical application. In this paper, we provide a detailed asymptotic analysis of a class of smoothed rank-based cross-periodograms associated with the copula spectral density kernels introduced in Dette et al. [Bernoulli 21 (2015) 781-831]. We show that, for a very general class of (possibly nonlinear) processes, properly scaled and centered smoothed versions of those cross-periodograms, indexed by couples of quantile levels, converge weakly, as stochastic processes, to Gaussian processes. A first application of those results is the construction of asymptotic confidence intervals for copula spectral density kernels. The same convergence results also provide asymptotic distributions (under serially dependent observations) for a new class of rank-based spectral methods involving the Fourier transforms of rank-based serial statistics such as the Spearman, Blomqvist or Gini autocovariance coefficients.Comment: Published at http://dx.doi.org/10.3150/15-BEJ711 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm