Stochastic modelling of financial time series with memory and multifractal scaling

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.

On the affinity of Chuaria–Tawuia complex : a multidisciplinary study

In this study, biometric and structural engineering tool have been used to examine a possible relationship within Chuaria–Tawuia complex and micro-FTIR (Fourier Transform Infrared Spectroscopy) analyses to understand the biological affinity of Chuaria circularis Walcott, collected from the Mesoproterozoic Suket Shales of the Vindhyan Supergroup and the Neoproterozoic Halkal Shales of the Bhima Group of peninsular India. Biometric analyses of well preserved carbonized specimens show wide variation in morphology and uni-modal distribution. We believe and demonstrate to a reasonable extent that C. circularis most likely was a part of Tawuia-like cylindrical body of algal origin. Specimens with notch/cleft and overlapping preservation, mostly recorded in the size range of 3–5 mm, are of special interest. Five different models proposed earlier on the life cycle of C. circularis are discussed. A new model, termed as ‘Hybrid model’ based on present multidisciplinary study assessing cylindrical and spherical shapes suggesting variable cell wall strength and algal affinity is proposed. This model discusses and demonstrates varied geometrical morphologies assumed by Chuaria and Tawuia, and also shows the inter-relationship of Chuaria–Tawuia complex. Structural engineering tool (thin walled pressure vessel theory) was applied to investigate the implications of possible geometrical shapes (sphere and cylinder), membrane (cell wall) stresses and ambient pressure environment on morphologically similar C. circularis and Tawuia. The results suggest that membrane stresses developed on the structures similar to Chuaria–Tawuia complex were directly proportional to radius and inversely proportional to the thickness in both cases. In case of hollow cylindrical structure, the membrane stresses in circumferential direction (hoop stress) are twice of the longitudinal direction indicating that rupture or fragmentation in the body of Tawuia would have occurred due to hoop stress. It appears that notches and discontinuities seen in some of the specimens of Chuaria may be related to rupture suggesting their possible location in 3D Chuaria. The micro-FTIR spectra of C. circularis are characterized by both aliphatic and aromatic absorption bands. The aliphaticity is indicated by prominent alkyl group bands between 2800–3000 and 1300–1500 cm−1. The prominent absorption signals at 700–900 cm−1 (peaking at 875 and 860 cm−1) are due to aromatic CH out of plane deformation. A narrow, strong band is centred at 1540 cm−1 which could be COOH band. The presence of strong aliphatic bands in FTIR spectra suggests that the biogeopolymer of C. circularis is of aliphatic nature. The wall chemistry indicates the presence of ‘algaenan’—a biopolymer of algae.

Reconstruction of falsified computer logs for digital forensics investigations

Digital forensics investigations aim to find evidence that helps confirm or disprove a hypothesis about an alleged computer-based crime. However, the ease with which computer-literate criminals can falsify computer event logs makes the prosecutor's job highly challenging. Given a log which is suspected to have been falsified or tampered with, a prosecutor is obliged to provide a convincing explanation for how the log may have been created. Here we focus on showing how a suspect computer event log can be transformed into a hypothesised actual sequence of events, consistent with independent, trusted sources of event orderings. We present two algorithms which allow the effort involved in falsifying logs to be quantified, as a function of the number of `moves' required to transform the suspect log into the hypothesised one, thus allowing a prosecutor to assess the likelihood of a particular falsification scenario. The first algorithm always produces an optimal solution but, for reasons of efficiency, is suitable for short event logs only. To deal with the massive amount of data typically found in computer event logs, we also present a second heuristic algorithm which is considerably more efficient but may not always generate an optimal outcome.

Effects of switching time on output voltages of a multilevel inverter used in high frequency applications

Employing multilevel inverters is a proper solution to reduce harmonic content of output voltage and electromagnetic interference in high power electronic applications. In this paper, a new pulse width modulation method for multilevel inverters is proposed in which power devices’ on-off switching times have been considered. This method can be surveyed in order to analyse the effect of switching time on harmonic contents of output voltage in high frequency applications when a switching time is not negligible compared to a switching cycle. Fast Fourier transform calculation and analysis of output voltage waveforms and harmonic contents with regard to switching time variation are presented in this paper for a single phase (3, 5)-level inverters used in high voltage and high frequency converters. Mathematical analysis and MATLAB simulation results have been carried out to validate the proposed method.

Best basis-based intelligent machine fault diagnosis

The wavelet packet transform decomposes a signal into a set of bases for time–frequency analysis. This decomposition creates an opportunity for implementing distributed data mining where features are extracted from different wavelet packet bases and served as feature vectors for applications. This paper presents a novel approach for integrated machine fault diagnosis based on localised wavelet packet bases of vibration signals. The best basis is firstly determined according to its classification capability. Data mining is then applied to extract features and local decisions are drawn using Bayesian inference. A final conclusion is reached using a weighted average method in data fusion. A case study on rolling element bearing diagnosis shows that this approach can greatly improve the accuracy ofdiagno sis.

An old language for a new landscape

Because aesthetics can have a profound effect upon the human relationship to the non-human environment the importance of aesthetics to ecologically sustainable designed landscapes has been acknowledged. However, in recognition that the physical forms of designed landscapes are an expression of the social values of the time, some design professionals have called for a new aesthetic ― one that reflects these current ecological concerns. To address this, some authors have suggested various theoretical design frameworks upon which such an aesthetic could be based. Within these frameworks there is an underlying theme that the patterns and processes of natural systems have the potential to form a new aesthetic for landscape design —an aesthetic based on fractal rather than Euclidean geometry. Perry, Reeves and Sim (2008) have shown that it is possible to differentiate between different landscape forms by fractal analysis. However, this research also shows that individual scenes from within very different landscape forms can possess the same fractal properties. Early data, revealed by transforming landscape images from the spatial to the frequency domain, using the fast Fourier transform, suggest that fractal patterning can have a significant effect within the landscape. In fact, it may be argued that any landscape design that includes living processes will include some design element whose ultimate form can only be expressed through the mathematics of fractal geometry. This paper will present ongoing research into the potential role of fractal geometry as a basis for a new form language – a language that may articulate an aesthetic for landscape design that echoes our ecological awakening.

The osteogenic properties of CaP/silk composite scaffolds

The rationale for the present study was to develop porous CaP/silk composite scaffolds with a CaP-phase distribution and pore architecture better suited to facilitate osteogenic properties of human bone mesenchymal stromal cells (BMSCs) and in vivo bone formation abilities. This was achieved by first preparing CaP/silk hybrid powders which were then incorporated into silk to obtain uniform CaP/silk composite scaffolds, by means of a freeze-drying method. The composition, microstructure and mechanical properties of the CaP/silk composite scaffolds were ascertained by X-ray diffraction (XRD), Fourier transform infrared spectra (FTIR), scanning electron microscope (SEM) and a universal mechanical testing machine. BMSCs were cultured in these scaffolds and cell proliferation analyzed by confocal microscopy and MTS assay. Alkaline phosphatase (ALP) activity and osteogenic gene expression were assayed to determine if osteogenic differentiation had taken place. A calvarial defect model in SCID mice was used to determine the in vivo bone forming ability of the hybrid CaP/silk scaffolds. Our results showed that incorporating the hybrid CaP/silk powders into silk scaffolds improved both pore structure architecture and distribution of CaP powders in the composite scaffolds. By incorporating the CaP phase into silk scaffolds in vitro osteogenic differentiation of BMSCs was enhanced and there was increased in vivo cancellous bone formation. Here we report a method with which to prepare Ca/P composite scaffolds with a pore structure and Ca/P distribution better suited to facilitate BMSC differentiation and bone formation.

Structure–property relationships of silk-modified mesoporous bioglass scaffolds

Porous mesopore-bioglass (MBG) scaffolds have been proposed as a new class of bone regeneration materials due to their apatite-formation and drug-delivery properties; however, the material’s inherent brittleness and high degradation and surface instability are major disadvantages, which compromise its mechanical strength and cytocompatibility as a biological scaffold. Silk, on the other hand, is a native biomaterial and is well characterized with respect to biocompatibility and tensile strength. In this study we set out to investigate what effects blending silk with MBG had on the physiochemical, drug-delivery and biological properties of MBG scaffolds with a view to bone tissue engineering applications. Transmission electron microscopy (TEM), scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR) were the methods used to analyze the inner microstructure, pore size and morphology, and composition of MBG scaffolds, before and after addition of silk. The effect of silk modification on the mechanical property of MBG scaffolds was determined by testing the compressive strength of the scaffolds and also compressive strength after degradation over time. The drug-delivery potential was evaluated by the release of dexamethasone (DEX) from the scaffolds. Finally, the cytocompatibility of silk-modified scaffolds was investigated by the attachment, morphology, proliferation, differentiation and bone-relative gene expression of bone marrow stromal cells (BMSCs). The results showed that silk modification improved the uniformity and continuity of pore network of MBG scaffolds, and maintained high porosity (94%) and large-pore size (200–400 mm). There was a significant improvement in mechanical strength, mechanical stability, and control of burst release of DEX in silkmodified MBG scaffolds. Silk modification also appeared to provide a better environment for BMSC attachment, spreading, proliferation, and osteogenic differentiation on MBG scaffolds.

The encapsulation of gold nanoparticles using RAFT, ATRP and miniemulsion polymerisation techniques

The investigation into the encapsulation of gold nanoparticles (AuNPs) by poly(methyl methacrylate) (PMMA) was undertaken. This was performed by three polymerisation techniques including: grafting PMMA synthesised by reversible addition-fragmentation chain transfer (RAFT) polymerisation to AuNPs, grafting PMMA synthesised by atom transfer radical polymerisation (ATRP) from the surface of functionalised AuNPs and by encapsulation of AuNPs within PMMA latexes produced through photo-initiated oil-in-water (o/w) miniemulsion polymerisation. The grafting of RAFT PMMA to AuNPs was performed by the addition of the RAFT functionalised PMMA to citrate stabilised AuNPs. This was conducted with a range of PMMA of varying molecular weight distribution (MWD) as either the dithioester or thiol end-group functionalities. The RAFT PMMA polymers were characterised by gel permeation chromatography (GPC), ultraviolet-visible (UV-vis), Fourier transform infrared-attenuated total reflectance (FTIR-ATR), Fourier transform Raman (FT-Raman) and proton nuclear magnetic resonance (1H NMR) spectroscopies. The attachment of PMMA to AuNPs showed a tendency for AuNPs to associate with the PMMA structures formed, though significant aggregation occurred. Interestingly, thiol functionalised end-group PMMA showed very little aggregation of AuNPs. The spherical polymer-AuNP structures did not vary in size with variations in PMMA MWD. The PMMA-AuNP structures were characterised using scanning electron microscopy (SEM), transition electron microscopy (TEM), energy dispersive X-ray analysis (EDAX) and UV-vis spectroscopy. The surface confined ATRP grafting of PMMA from initiator functionalised AuNPs was polymerised in both homogeneous and heterogeneous media. 11,11’- dithiobis[1-(2-bromo-2-methylpropionyloxy)undecane] (DSBr) was used as the surface-confined initiator and was synthesised in a three step procedure from mercaptoundecanol (MUD). All compounds were characterised by 1H NMR, FTIR-ATR and Raman spectroscopies. The grafting in homogeneous media resulted in amorphous PMMA with significant AuNP aggregation. Individually grafted AuNPs were difficult to separate and characterise, though SEM, TEM, EDAX and UV-vis spectroscopy was used. The heterogeneous polymerisation did not produce grafted AuNPs as characterised by SEM and EDAX. The encapsulation of AuNPs within PMMA latexes through the process of photoinitiated miniemulsion polymerisation was successfully achieved. Initially, photoinitiated miniemulsion polymerisation was conducted as a viable low temperature method of miniemulsion initiation. This proved successful producing a stable PMMA with good conversion efficiency and narrow particle size distribution (PSD). This is the first report of such a system. The photo-initiated technique was further optimised and AuNPs were included into the miniemulsion. AuNP encapsulation was very effective, producing reproducible AuNP encapsulated PMMA latexes. Again, this is the first reported case of this. The latexes were characterised by TEM, SEM, GPC, gravimetric analysis and dynamic light scattering (DLS).

Milk : students building mobile learning games in everyday places

This paper explores how mobile games can transform everyday places into dynamic learning spaces filled with information and inspiration. It discusses the motivation inherent in playing games and creating games for others, and how this stimulates an iterative process of creation and reflection and evokes a natural desire to engage in learning. The use of MiLK at the Adelaide Botanic Gardens is offered as a case in point. MiLK is an authoring tool that allows students and teachers to create and share SMS games for mobile phones. A group of South Australian high school students used MiLK to play a game, create their own games and play each other’s games during a day at the gardens. This paper details the learning processes involved in these activities and how the students reflected on their learning, conducted peer assessment, and engaged in a two-way discussion with their teacher about new technologies and their implications for learning. The paper concludes with a discussion of the needs and requirements of 21st Century learners and how MiLK can support constructivist and connectivist teaching methods that engage learners and may produce an appropriately skilled future workforce.

How can we exploit mobile data to customise learning based on a student’s environmental surroundings?

User-Based intelligent systems are already commonplace in a student’s online digital life. Each time they browse, search, buy, join, comment, play, travel, upload, download, a system collects, analyses and processes data in an effort to customise content and further improve services. This panel session will explore how intelligent systems, particularly those that gather data from mobile devices, can offer new possibilities to assist in the delivery of customised, personal and engaging learning experiences. The value of intelligent systems for education lies in their ability to formulate authentic and complex learner profiles that bring together and systematically integrate a student’s personal world with a formal curriculum framework. As we well know, a mobile device can collect data relating to a student’s interests (gathered from search history, applications and communications), location, surroundings and proximity to others (GPS, Bluetooth). However, what has been less explored is the opportunity for a mobile device to map the movements and activities of a student from moment to moment and over time. This longitudinal data provides a holistic profile of a student, their state and surroundings. Analysing this data may allow us to identify patterns that reveal a student’s learning processes; when and where they work best and for how long. Through revealing a student’s state and surroundings outside of schools hour, this longitudinal data may also highlight opportunities to transform a student’s everyday world into an inventory for learning, punctuating their surroundings with learning recommendations. This would in turn lead to new ways to acknowledge and validate and foster informal learning, making it legitimate within a formal curriculum.

Investigation of highly regulated promoters for the production of recombinant proteins in plants

Plants have been identified as promising expression systems for the commercial production of recombinant proteins. Plant-based protein production or “biofarming” offers a number of advantages over traditional expression systems in terms of scale of production, the capacity for post-translation processing, providing a product free of contaminants and cost effectiveness. A number of pharmaceutically important and commercially valuable proteins, such as antibodies, biopharmaceuticals and industrial enzymes are currently being produced in plant expression systems. However, several challenges still remain to improve recombinant protein yield with no ill effect on the host plant. The ability for transgenic plants to produce foreign proteins at commercially viable levels can be directly related to the level and cell specificity of the selected promoter driving the transgene. The accumulation of recombinant proteins may be controlled by a tissue-specific, developmentally-regulated or chemically-inducible promoter such that expression of recombinant proteins can be spatially- or temporally- controlled. The strict control of gene expression is particularly useful for proteins that are considered toxic and whose expression is likely to have a detrimental effect on plant growth. To date, the most commonly used promoter in plant biotechnology is the cauliflower mosaic virus (CaMV) 35S promoter which is used to drive strong, constitutive transgene expression in most organs of transgenic plants. Of particular interest to researchers in the Centre for Tropical Crops and Biocommodities at QUT are tissue-specific promoters for the accumulation of foreign proteins in the roots, seeds and fruit of various plant species, including tobacco, banana and sugarcane. Therefore this Masters project aimed to isolate and characterise root- and seed-specific promoters for the control of genes encoding recombinant proteins in plant-based expression systems. Additionally, the effects of matching cognate terminators with their respective gene promoters were assessed. The Arabidopsis root promoters ARSK1 and EIR1 were selected from the literature based on their reported limited root expression profiles. Both promoters were analysed using the PlantCARE database to identify putative motifs or cis-acting elements that may be associated with this activity. A number of motifs were identified in the ARSK1 promoter region including, WUN (wound-inducible), MBS (MYB binding site), Skn-1, and a RY core element (seed-specific) and in the EIR1 promoter region including, Skn-1 (seed-specific), Box-W1 (fungal elicitor), Aux-RR core (auxin response) and ABRE (ABA response). However, no previously reported root-specific cis-acting elements were observed in either promoter region. To confirm root specificity, both promoters, and truncated versions, were fused to the GUS reporter gene and the expression cassette introduced into Arabidopsis via Agrobacterium-mediated transformation. Despite the reported tissue-specific nature of these promoters, both upstream regulatory regions directed constitutive GUS expression in all transgenic plants. Further, similar levels of GUS expression from the ARSK1 promoter were directed by the control CaMV 35S promoter. The truncated version of the EIR1 promoter (1.2 Kb) showed some differences in the level of GUS expression compared to the 2.2 Kb promoter. Therefore, this suggests an enhancer element is contained in the 2.2 Kb upstream region that increases transgene expression. The Arabidopsis seed-specific genes ATS1 and ATS3 were selected from the literature based on their seed-specific expression profiles and gene expression confirmed in this study as seed-specific by RT-PCR analysis. The selected promoter regions were analysed using the PlantCARE database in order to identify any putative cis elements. The seed-specific motifs GCN4 and Skn-1 were identified in both promoter regions that are associated with elevated expression levels in the endosperm. Additionaly, the seed-specific RY element and the ABRE were located in the ATS1 promoter. Both promoters were fused to the GUS reporter gene and used to transform Arabidopsis plants. GUS expression from the putative promoters was consitutive in all transgenic Arabidopsis tissue tested. Importantly, the positive control FAE1 seed-specific promoter also directed constitutive GUS expression throughout transgenic Arabidopsis plants. The constitutive nature seen in all of the promoters used in this study was not anticipated. While variations in promoter activity can be caused by a number of influencing factors, the variation in promoter activity observed here would imply a major contributing factor common to all plant expression cassettes tested. All promoter constructs generated in this study were based on the binary vector pCAMBIA2300. This vector contains the plant selection gene (NPTII) under the transcriptional control of the duplicated CaMV 35S promoter. This CaMV 35S promoter contains two enhancer domains that confer strong, constitutive expression of the selection gene and is located immediately upstream of the promoter-GUS fusion. During the course of this project, Yoo et al. (2005) reported that transgene expression is significantly affected when the expression cassette is located on the same T-DNA as the 35S enhancer. It was concluded, the trans-acting effects of the enhancer activate and control transgene expression causing irregular expression patterns. This phenomenon seems the most plausible reason for the constitutive expression profiles observed with the root- and seed-specific promoters assessed in this study. The expression from some promoters can be influenced by their cognate terminator sequences. Therefore, the Arabidopsis ARSK1, EIR1, ATS1 and ATS3 terminator sequences were isolated and incorporated into expression cassettes containing the GUS reporter gene under the control of their cognate promoters. Again, unrestricted GUS activity was displayed throughout transgenic plants transformed with these reporter gene fusions. As previously discussed constitutive GUS expression was most likely due to the trans-acting effect of the upstream CaMV 35S promoter in the selection cassette located on the same T-DNA. The results obtained in this study make it impossible to assess the influence matching terminators with their cognate promoters have on transgene expression profiles. The obvious future direction of research continuing from this study would be to transform pBIN-based promoter-GUS fusions (ie. constructs containing no CaMV 35S promoter driving the plant selection gene) into Arabidopsis in order to determine the true tissue specificity of these promoters and evaluate the effects of their cognate 3’ terminator sequences. Further, promoter truncations based around the cis-elements identified here may assist in determining whether these motifs are in fact involved in the overall activity of the promoter.