Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

"2009" / Thesis (MSc (Hons))--Macquarie University, Faculty of Science, Dept. of Physics and Engineering, 2010. / Bibliography: p. 163-166. / Introduction -- Design theory and process technology -- 15GHz oscillator implementations -- 24GHz oscillator implementation -- Frequency prescaler implementation -- MMIC fabrication and measurement -- Conclusion. / Advances in Silicon Germanium (SiGe) Bipolar Complementary Metal Oxide Semiconductor (BiCMOS) technology has caused a recent revolution in low-cost Monolithic Microwave Integrated Circuit (MMIC) design. -- This thesis presents the design, fabrication and measurement of four MMICs for frequency synthesis, manufactured in a commercially available IBM 0.18μm SiGe BiCMOS technology with ft = 60GHz. The high speed and low-cost features of SiGe Heterojunction Bipolar Transistors (HBTs) were exploited to successfully develop two single-ended injection-lockable 15GHz Voltage Controlled Oscillators (VCOs) for application in an active Ka-Band antenna beam-forming network, and a 24GHz differential cross-coupled VCO and 1/6 synchronous static frequency prescaler for emerging Ultra Wideband (UWB) automotive Short Range Radar (SRR) applications. -- On-wafer measurement techniques were used to precisely characterise the performance of each circuit and compare against expected simulation results and state-of-the-art performance reported in the literature. -- The original contributions of this thesis include the application of negative resistance theory to single-ended and differential SiGe VCO design at 15-24GHz, consideration of manufacturing process variation on 24GHz VCO and prescaler performance, implementation of a fully static multi-stage synchronous divider topology at 24GHz and the use of differential on-wafer measurement techniques. -- Finally, this thesis has llustrated the excellent practicability of SiGe BiCMOS technology in the engineering of high performance, low-cost MMICs for frequency synthesis in millimeterwave (mm-wave) devices. / Mode of access: World Wide Web. / xxii, 166 p. : ill (some col.)

Le marché du stockage de l'énergie est en perpétuelle expansion, tant pour les applications nomades que fixes. Afin de répondre aux exigences requises pour les diverses applications (appareils électroniques, véhicules hybrides et électriques, stockage des énergies renouvelables…), des batteries toujours plus performantes, compactes et légères doivent être développées. Pour cela, les batteries utilisant du lithium métallique en tant qu'anode sont les plus attractives en termes de densités d'énergies. Néanmoins, l'utilisation d'électrolytes liquides conventionnels, généralement des solvants organiques inflammables, dans de tels dispositifs soulève des problématiques de sécurité. Les travaux de recherche présentés dans ce manuscrit concernent l'étude de matériaux vitreux pouvant être utilisés en tant qu'électrolyte solide afin de permettre le développement de batteries tout-solide sûres et performantes. Des verres de sulfures au lithium, attractifs pour leurs propriétés de conduction ionique, sont étudiés et caractérisés. Les propriétés de conduction ionique dans les verres étant toujours mal comprises et sujettes à controverses, l'analyse structurale des verres présente ici un réel intérêt pour une meilleure compréhension des corrélations entre structure et propriétés. Un effort de recherche a donc été porté sur l'étude de l'ordre local dans les verres préparés via différentes techniques d'analyse structurale complémentaires. Enfin, les matériaux vitreux, sont de manière générale relativement faciles à mettre en forme. Les verres étudiés dans ce manuscrit peuvent alors également être utilisés en tant qu'électrolytes sous forme de couches minces dans les micro-batteries. Des premiers essais de dépôts par pulvérisation cathodique RF magnétron de couches minces conductrices ont donc été effectués et constituent la première brique à la fabrication de micro-batteries. / The energy storage market is in constant growth for both portable and stationary applications. To satisfy the requirements of various applications (electronic devices, hybrid-electric vehicles, renewable energy storage…), always more efficient, more compact and lightweight batteries have to be developed. Then, thanks to their high energy densities, batteries using Li metal anodes are the most promising to complete this challenge. However, the use of conventional liquid electrolytes raises safety issues, mainly related to the flammability of the organic liquid. In this thesis, glassy materials, exhibiting great interest towards developing solid electrolytes are considered and might enable the development of safe and efficient all-solid-state batteries. Here, Li-sulfide glasses, attractive for their ionic conduction properties, have been studied and characterized. The ionic conduction properties of glasses are still misunderstood and controversial, the structural investigation of glasses is of great interest in order to get a better understanding of structure-properties relationship. Then, the short and intermediate range order of prepared glasses have been investigated by the mean of various complementary structural analysis techniques. Finally, glassy materials are usually quite easy to shape. Thus, studied glasses in this thesis can also be used as thin-film electrolytes in microbatteries. First tests of sputtering of conducting thin-films have been performed by RF magnetron sputtering and constitute a first step in order to design microbatteries.

L'objectif de cette thèse est de mener une étude fondamentale et expérimentale des propriétés physiques des cristaux liquides discotiques colonnaires (CLDCs) confinés dans des matrices poreuses templates hautement ordonnées à l'échelle nanométrique. Les molécules des CLDCs de forme plane, composées de noyaux polyaromatiques rigides entourées de chaînes aliphatiques flexibles fonctionnalisables, sont susceptibles de s'auto-assembler dans des colonnes favorisant ainsi le recouvrement de leurs orbitales électroniques π. Ce qui fait de ces matériaux de véritables candidats pour des applications dans l'électronique moléculaire et la photovoltaïque grâce à la possibilité de migration des porteurs de charges le long de leurs colonnes. Cependant, ces applications nécessitent une bonne maîtrise des paramètres influant sur les mécanismes d'alignement dans les phases colonnaires, sur de grands monodomaines, et de préférence à température ambiante. Une méthode très prometteuse visant à optimiser les longueurs de diffusion des porteurs de charge a été récemment proposée, basée sur la formation de nanofils orientés de CLDCs par auto-assemblage dans des matrices dites « templates » (de moulage). Toutefois, les propriétés structurales, dynamiques et les effets de confinement sur ces technologies restent aujourd'hui mal connus et morcelés et pourraient constituer un véritable verrou scientifique pour leur réalisation. Notre étude s'est portée sur les CLDCs commerciaux (HPT) et le Py4CEH (moins connus) qui sont confinés dans des alumines poreuses (AAO) et du silicium poreux (Sip) de diamètres de pores de quelques dizaines de nm. Les diagrammes de phase ont été d'abord étudiés par DSC puis les effets structuraux ont été approfondis grâce à la diffusion de neutrons. Dans les géométries confinées, nous observons une dépression des températures de transition, un élargissement du domaine de stabilité de la phase colonnaire et l'ouverture d'une hystérèse amplifiée dans les pores de plus petite taille. Un ordre orientationnel très élevé a été trouvé dans les phases colonnaires bulk par la RMN du solide et la structure des systèmes confinés colonnaires, dominée par une distribution radiale avec un ancrage homéotrope a été déterminée. La dynamique moléculaire a été étudiée par diffusion quasiélastique de neutrons. Elle est affectée par le confinement : la dynamique de grande amplitude est fortement ralentie, tandis que la dynamique rapide locale devient régie par une distribution très large de temps caractéristiques. / The aim of this work is to conduct fundamental and experimental studies of the physical properties of columnar discotic liquid crystal (CDLCs) confined in highly ordered porous templates at the nanoscale. CDLC molecule of planar shape, consist in rigid polyaromatic nuclei surrounded by functionalizable flexible aliphatic chains, and are capable of self-assembly in columns, thereby promoting overlap of their π electron orbitals. This makes these materials real candidates for applications in molecular electronics and photovoltaics due to the possibility of migration of the charge carriers along their columns. However, these applications require a good control of the parameters affecting the alignment mechanisms in the columnar phases of large single domains, preferably at room temperature. A very promising approach to optimize the diffusion lengths of charge carriers has been recently proposed, based on the formation of oriented CDLC nanowires by self-assembly in so-called "templates". However, structural and dynamical proprieties and confinement effects are still scarce, and could be a real scientific lock to their implementation. Our study is focused on commercial CDLCs (HPT) and Py4CEH which are confined in porous alumina and porous silicon membranes with pore diameters of c.a. tens of nm. The phase diagram was first studied by DSC and more deeply characterized by neutron scattering. In confined geometries, we observe a depression of the phase transition temperatures, a broadening of the columnar phase stability domain and an opening of hysteresis loops amplified by smaller pore size. A high orientational order was found in the bulk columnar phases by solid-state NMR, and the structure of confined columnar systems, dominated by a radial distribution with homeotropic anchoring was observed. The molecular dynamics was studied by quasielastic neutron scattering. It is affected by confinement: large lengthscale motions are massively slowed down, whereas the rapid and local dynamics becomes submitted to large distributions of correlation times.

Metal halide perovskites have attracted considerable attention as excellent candidates for application in solar cells. Despite their excellent performance, photovoltaic devices based on perovskite absorber’s wide-scale integration into industrial application is limited by their chemical and electrical instabilities. The central topic of this thesis is therefore to investigate thermodynamic aspects of point defects and the conduction mechanisms along with their implications for current–voltage characteristics i.e.,hysteresis in the solar cells. By application of three different methods, impedance spectroscopy, deep level transient spectroscopy and sweep rate dependent current–voltage characteristics as function of temperature, we show that understanding the fundamental aspects of mobile ionic defects in the material as well as the distribution of these defects in the device is essential for improving the stability and the device performance. We show that halide vacancy-interstitial pairs are present in all investigated perovskite compositions and these defects can lead to a significant reduction in the power conversion efficiency of perovskite solar cells. / Metallhalogenid-Perowskite haben erhebliche Aufmerksamkeit als hervorragende Kandidaten für die Anwendung in Solarzellen. Trotz ihrer ausgezeichneten Leistung ist die breite Integration von photovoltaischen Geräten auf der Grundlage von Perowskit-Absorbern in die industrielle Anwendung durch ihre chemische und elektrische Instabilität begrenzt. Das zentrale Thema dieser Arbeit ist daher die Untersuchung der thermodynamischen Aspekte von Punktdefekten und der Leitungsmechanismen sowie deren Auswirkungen auf die Strom-Spannungs-Charakteristik, i.e., die Hysterese in den Solarzellen. Durch die Anwendung von drei verschiedenen Methoden, der Impedanzspektroskopie, der Transientenspektroskopie auf tiefer Ebene und der Sweep-Rate-abhängigen Strom-Spannungs-Charakteristik als Funktion der Temperatur, zeigen wir, dass das Verständnis der grundlegenden Aspekte der mobilen ionischen Defekte im Material sowie der Verteilung dieser Defekte in der Vorrichtung für die Verbesserung der Stabilität und der Leistung der Vorrichtung von wesentlicher Bedeutung ist. Wir zeigen, dass Halogenid-Vakanz-Zwischengitter-Paare in allen untersuchten Perowskit-Zusammensetzungen vorhanden sind und dass diese Defekte zu einer signiőkanten Verringerung der Energieumwandlungseffizienz von Perowskit-Solarzellen führen können.

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