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.

Executive control of working memory in schizophrenia

There is considerable evidence that working memory impairment is a common feature of schizophrenia. The present study assessed working memory and executive function in 54 participants with schizophrenia, and a group of 54 normal controls matched to the patients on age, gender and estimated premorbid IQ, using traditional and newer measures of executive function and two dual tasks—Telephone Search with Counting and the Memory Span and Tracking Task. Results indicated that participants with schizophrenia were significantly impaired on all standardised measures of executive function with the exception of a composite measure of the Trail Making Test. Results for the dual task measures demonstrated that while the participants with schizophrenia were unimpaired on immediate digit span recall over a 2-min period, they recalled fewer digit strings and performed more poorly on a tracking task (box-crossing task) compared with controls. In addition, participants with schizophrenia performed more poorly on the tracking task when they were required to simultaneously recall digits strings than when they performed this task alone. Contrary to expectation, results of the telephone search task under dual conditions were not significantly different between groups. These results may reflect the insufficient complexity of the tone-counting task as an interference task. Overall, the present study showed that participants with schizophrenia appear to have a restricted impairment of their working memory system that is evident in tasks in which the visuospatial sketchpad slave system requires central executive control.

Heparan sulfate mediates the proliferation and differentiation of rat mesenchymal stem cells

The growth and differentiation of mesenchymal stem cells is controlled by various growth factors, the activities of which can be modulated by heparan sulfates. We have previously underscored the necessity of sulfated glycosaminoglycans for the FGF-2-stimulated differentiation of osteoprogenitor cells. Here we show that exogenous application of heparan sulfate to cultures of primary rat MSCs stimulates their proliferation leading to increased expression of osteogenic markers and enhanced bone nodule formation. FGF-2 can also increase the proliferation and osteogenic differentiation of rMSCs when applied exogenously during their linear growth. However, as opposed to exogenous HS, the continuous use of FGF-2 during in vitro differentiation completely blocked rMSC mineralization. Furthermore, we show that the effects of both FGF-2 and HS are mediated through FGF receptor 1 (FGFR1) and that inhibition of signaling through this receptor arrests cell growth resulting in the cells being unable to reach the critical density necessary to induce differentiation. Interestingly, blocking FGFR1 signaling in post-confluent osteogenic cultures significantly increased calcium deposition. Taken together our data clearly suggests that FGFR1 signaling plays an important role during osteogenic differentiation, firstly by stimulating cell growth that is closely followed by an inhibitory affect once the cells have reached confluence. It also underlines the importance of HS as a co-receptor for the signaling of endogenous FGF-2 and suggests that purified glycosaminoglycans may be attractive alternatives to growth factors for improved ex vivo growth and differentiation of MSCs.

Characterisation of mesenchymal cells from osteophytes in osteoarthritis

Osteophytes form through the process of chondroid metamorphosis of fibrous tissue followed by endochondral ossification. Osteophytes have been found to consist of three different mesenchymal tissue regions including endochondral bone formation within cartilage residues, intra-membranous bone formation within fibrous tissue and bone formation within bone marrow spaces. All these features provide evidence of mesenchymal stem cells (MSC) involvement in osteophyte formation; nevertheless, it remains to be characterised. MSC from numerous mesenchymal tissues have been isolated but bone marrow remains the “ideal” due to the ease of ex vivo expansion and multilineage potential. However, the bone marrow stroma has a relatively low number of MSC, something that necessitates the need for long-term culture and extensive population doublings in order to obtain a sufficient number of cells for therapeutic applications. MSC in vitro have limited proliferative capacity and extensive passaging compromises differentiation potential. To overcome this barrier, tissue derived MSC are of strong interest for extensive study and characterisation, with a focus on their potential application in therapeutic tissue regeneration. To date, no MSC type cell has been isolated from osteophyte tissue, despite this tissue exhibiting all the hallmark features of a regenerative tissue. Therefore, this study aimed to isolate and characterise cells from osteophyte tissues in relation to their phenotype, differentiation potential, immuno-modulatory properties, proliferation, cellular ageing, longevity and chondrogenesis in in vitro defect model in comparison to patient matched bone marrow stromal cells (bMSC). Osteophyte derived cells were isolated from osteophyte tissue samples collected during knee replacement surgery. These cells were characterised by the expression of cell surface antigens, differentiation potential into mesenchymal lineages, growth kinetics and modulation of allo-immune responses. Multipotential stem cells were identified from all osteophyte samples namely osteophyte derived mesenchymal stem cells (oMSC). Extensively expanded cell cultures (passage 4 and 9 respectively) were used to confirm cytogenetic stability and study signs of cellular aging, telomere length and telomerase activity. Cultured cells at passage 4 were used to determine 84 pathway focused stem cell related gene expression profile. Micro mass pellets were cultured in chondrogenic differentiation media for 21 days for phenotypic and chondrogenic related gene expression. Secondly, cell pellets differentiated overnight were placed into articular cartilage defects and cultured for further 21 days in control medium and chondrogenic medium to study chondrogenesis and cell behaviour. The surface antigen expression of oMSC was consistent with that of mesenchymal stem cells, such as lacking the haematopoietic and common leukocyte markers (CD34, CD45) while expressing those related to adhesion (CD29, CD166, CD44) and stem cells (CD90, CD105, CD73). The proliferation capacity of oMSC in culture was superior to that of bMSC, and they readily differentiated into tissues of the mesenchymal lineages. oMSC also demonstrated the ability to suppress allogeneic T-cell proliferation, which was associated with the expression of tryptophan degrading enzyme indoleamine 2,3 dioxygenase (IDO). Cellular aging was more prominent in late passage bMSC than in oMSC. oMSC had longer telomere length in late passages compared with bMSC, although there was no significant difference in telomere lengths in the early passages in either cell type. Telomerase activity was detectable only in early passage oMSC and not in bMSC. In osteophyte tissues telomerase positive cells were found to be located peri vascularly and were Stro-1 positive. Eighty-four pathway-focused genes were investigated and only five genes (APC, CCND2, GJB2, NCAM and BMP2) were differentially expressed between bMSC and oMSC. Chondrogenically induced micro mass pellets of oMSC showed higher staining intensity for proteoglycans, aggrecan and collagen II. Differential expression of chondrogenic related genes showed up regulation of Aggrecan and Sox 9 in oMSC and collagen II in bMSC. The in vitro defect models of oMSC in control medium showed rounded and aggregated cells staining positively for proteoglycan and presence of some extracellular matrix. In contrast, defects with bMSC showed fragmentation and loss of cells, fibroblast-like cell morphology staining positively for proteoglycans. For defects maintained in chondrogenic medium, rounded, aggregated and proteoglycan positive cells were found in both oMSC and bMSC cultures. Extracellular matrix and cellular integration into newly formed matrix was evident only in oMSC defects. For analysis of chondrocyte hypertrophy, strong expression of type X collagen could be noticed in the pellet cultures and transplanted bMSC. In summary, this study demonstrated that osteophyte derived cells had similar properties to mesenchymal stem cells in the expression of antigen phenotype, differential potential and suppression of allo-immune response. Furthermore, when compared to bMSC, oMSC maintained a higher proliferative capacity due to a retained level of telomerase activity in vitro, which may account for the relatively longer telomeres delaying growth arrest by replicative senescence compared with bMSC. oMSC behaviour in defects supported chondrogenesis which implies that cells derived from regenerative tissue can be an alternative source of stem cells and have a potential clinical application for therapeutic stem cell based tissue regeneration.

Runx2 overexpression in bone marrow stromal cells accelerates bone formation in critically-sized femoral defects

The repair of large non-unions in long bones remains a significant clinical problem due to high failure rates and limited tissue availability for auto- and allografts. Many cell-based strategies for healing bone defects deliver bone marrow stromal cells to the defect site to take advantage of the inherent osteogenic capacity of this cell type. However, many factors, including donor age and ex vivo expansion of the cells, cause bone marrow stromal cells to lose their differentiation ability. To overcome these limitations, we have genetically engineered bone marrow stromal cells to constitutively overexpress the osteoblast specific transcription factor Runx2. In the present study, we examined Runx2-modified bone marrow stromal cells, delivered via poly(caprolactone) scaffolds loaded with type I collagen meshes, in critically-sized segmental defects in rats compared to unmodified cells, cell-free scaffolds and empty defects. Runx2 expression in bone marrow stromal cells accelerated healing of critically-sized defects compared to unmodified bone marrow stromal cells and defects receiving cell-free treatments. These findings provide an accelerated method for healing large bone defects which may reduce recovery time and the need for external fixation of critically-sized defects.

Enhancing in vivo vascularized bone formation by cobalt chloride-treated bone marrow stromal cells in a tissue engineered periosteum model

The periosteum plays an indispensable role in both bone formation and bone defect healing. In this study we constructed an artificial in vitro periosteum by incorporating osteogenic differentiated bone marrow stromal cells (BMSCs) and cobalt chloride (CoCl(2))-treated BMSCs. The engineered periostea were implanted both subcutaneously and into skull bone defects in SCID mice to investigate ectopic and orthotopic osteogenesis and vascularization. After two weeks in subcutaneous and four weeks in bone defect areas, the implanted constructs were assessed for ectopic and orthotopic osteogenesis and vascularization by micro-CT, histomorphometrical and immunohistochemical methods. The results showed that CoCl(2) pre-treated BMSCs induced higher degree of vascularization and enhanced osteogenesis within the implants in both ectopic and orthotopic areas. This study provided a novel approach using BMSCs sourced from the same patient for both osteogenic and pro-angiogenic purposes in constructing tissue engineered periosteum to enhance vascularized osteogenesis.

Stem cell–related gene expression in clonal populations of mesenchymal stromal cells from bone marrow

Decline in the frequency of potent mesenchymal stem cells (MSCs) has been implicated in ageing and degenerative diseases. Increasing the circulating stem cell population can lead to renewed recruitment of these potent cells at sites of damage. Therefore, identifying the ideal cells for ex vivo expansion will form a major pursuit of clinical applications. This study is a follow-up of previous work that demonstrated the occurrence of fast-growing multipotential cells from the bone marrow samples. To investigate the molecular processes involved in the existence of such varying populations, gene expression studies were performed between fast- and slow-growing clonal populations to identify potential genetic markers associated with stemness using the quantitative real-time polymerase chain reaction comprising a series of 84 genes related to stem cell pathways. A group of 10 genes were commonly overrepresented in the fast-growing stem cell clones. These included genes that encode proteins involved in the maintenance of embryonic and neural stem cell renewal (sex-determining region Y-box 2, notch homolog 1, and delta-like 3), proteins associated with chondrogenesis (aggrecan and collagen 2 A1), growth factors (bone morphogenetic protein 2 and insulin-like growth factor 1), an endodermal organogenesis protein (forkhead box a2), and proteins associated with cell-fate specification (fibroblast growth factor 2 and cell division cycle 2). Expression of diverse differentiation genes in MSC clones suggests that these commonly expressed genes may confer the maintenance of multipotentiality and self-renewal of MSCs.

Characterization of electron trapping in dye-sensitized solar cells by near-IR transmittance measurements

In situ near-IR transmittance measurements have been used to characterize the density of trapped electrons in dye-sensitized solar cells (DSCs). Measurements have been made under a range experimental conditions including during open circuit photovoltage decay and during recording of the IV characteristic. The optical cross section of electrons at 940 nm was determined by relating the IR absorbance to the density of trapped electrons measured by charge extraction. The value, σn = 5.4 × 10-18 cm2, was used to compare the trapped electron densities in illuminated DSCs under open and short circuit conditions in order to quantify the difference in the quasi Fermi level, nEF. It was found that nEF for the cells studied was 250 meV over wide range of illuminat on intensities. IR transmittance measurements have also been used to quantify shifts in conduction band energy associated with dye adsorption.

A comparison of different methods to determine diffusion length in dye-sensitized solar cells

A new steady state method for determination of the electron diffusion length in dye-sensitized solar cells (DSCs) is described and illustrated with data obtained using cells containing three different types of electrolyte. The method is based on using near-IR absorbance methods to establish pairs of illumination intensity for which the total number of trapped electrons is the same at open circuit (where all electrons are lost by interfacial electron transfer) as at short circuit (where the majority of electrons are collected at the contact). Electron diffusion length values obtained by this method are compared with values derived by intensity modulated methods and by impedance measurements under illumination. The results indicate that the values of electron diffusion length derived from the steady state measurements are consistently lower than the values obtained by the non steady-state methods. For all three electrolytes used in the study, the electron diffusion length was sufficiently high to guarantee electron collection efficiencies greater than 90%. Measurement of the trap distributions by near-IR absorption confirmed earlier observations of much higher electron trap densities for electrolytes containing Li+ ions. It is suggested that the electron trap distributions may not be intrinsic properties of the TiO2 nanoparticles, but may be associated with electron-ion interactions.

Novel ruthenium bipyridyl dyes with s-donor ligands and their application in dye-sensitized solar cells

Two series of novel ruthenium bipyridyl dyes incorporating sulfur-donor bidentate ligands with general formula \[Ru(R-bpy)2C2N2S2] and \[Ru(R-bpy)2(S2COEt)]\[NO3] (where R =H, CO2Et, CO2H; C2N2S2 = cyanodithioimidocarbonate and S2COEt = ethyl xanthogenate) have been synthesized and characterized spectroscopically, electrochemically and computationally. The acid derivatives in both series (C2N2S2 3 and S2COEt 6) were used as a photosensitizer in a dye-sensitized solar cell (DSSC) and the incident photo-to-current conversion efficiency (IPCE), overall efficiency (_) and kinetics of the dye/TiO2 system were investigated. It was found that 6 gave a higher efficiency cell than 3 despite the latter dye’s more favorable electronic properties, such as greater absorption range, higher molar extinction coefficient and large degree of delocalization of the HOMO. The transient absorption spectroscopy studies revealed that the recombination kinetics of 3 were unexpectedly fast, which was attributed to the terminal CN on the ligand binding to the TiO2, as evidenced by an absorption study of R =H and CO2Et dyes sensitized on TiO2, and hence leading to a lower efficiency DSSC.