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.

Epithelial-mesenchymal transition and mesenchymal-epithelial transition are essential for the acquisition of stem cell properties in hTERT-immortalised oral epithelial cells

BACKGROUND INFORMATION: Evidence has shown that mesenchymal-epithelial transition (MET) and epithelial-mesenchymal transition (EMT) are linked to stem cell properties. We currently lack a model showing how the occurrence of MET and EMT in immortalised cells influences the maintenance of stem cell properties. Thus, we established a project aiming to investigate the roles of EMT and MET in the acquisition of stem cell properties in immortalised oral epithelial cells. RESULTS: In this study, a retroviral transfection vector (pLXSN-hTERT) was used to immortalise oral epithelial cells by insertion of the hTERT gene (hTERT(+)-oral mucosal epithelial cell line [OME]). The protein and RNA expression of EMT transcriptional factors (Snail, Slug and Twist), their downstream markers (E-cadherin and N-cadherin) and embryonic stem cell markers (OCT4, Nanog and Sox2) were studied by reverse transcription PCR and Western blots in these cells. Some EMT markers were detected at both mRNA and protein levels. Adipocytes and bone cells were noted in the multi-differentiation assay, showing that the immortal cells underwent EMT. The differentiation assay for hTERT(+)-OME cells revealed the recovery of epithelial phenotypes, implicating the presence of MET. The stem cell properties were confirmed by the detection of appropriate markers. Altered expression of alpha-tubulin and gamma-tubulin in both two-dimensional-cultured (without serum) and three-dimensional-cultured hTERT(+)-OME spheroids indicated the re-programming of cytoskeleton proteins which is attributed to MET processes in hTERT(+)-OME cells. CONCLUSIONS: EMT and MET are essential for hTERT-immortalised cells to maintain their epithelial stem cell properties.

The grapes of wrath: The Coonawarra dispute, geographical indications and international trade

The famous wine region of Coonawarra in South Australia has been promoted as ’Australia's other Red Centre', emphasizing its terra rossa soil and its cabernet sauvignon. In his atlas of the wine regions of Australia, John Beeston comments upon the rich and contested history of the region: ’Coonawarra is certainly the most famous cabernet sauvignon region in Australia, and some would argue, the most renowned wine region in Australia per se'. A reporter, Penelope Debelle, captures a sense of the legal conflict over the parameters of the boundaries of Coonawarra: ’Behind the name Coonawarra, an inglorious contest is being waged that pits the romance of South Australia's terra rossa cool-climate wine region against the cold commercial reality of the label.'This Chapter tells the story behind the Coonawarra litigation, addressing the parties to the dispute; the legal and historical context of the case; and the immediate impact case, as well as its lingering significance. It considers the ’Coonawarra' case as, very literally, a landmark in Australian jurisprudence in respect of intellectual property. This chapter engages in the methodology of ’legal storytelling'. In the field of new historicism, the use of anecdotes - petite histoire - has been seen as a useful way of challenging grand historical narratives. Joel Fineman has observed that the anecdote is ’the literary form or genre that uniquely refers to the real.' This chapter has three parts. Part 1 outlines the European Community - Australia Wine Agreement 1994, and the operation of the Australian Wine and Brandy Corporation Act 1980 (Cth). Part 2 considers the various stages of the dispute over the Coonawarra region - moving from the decision of the Geographical Indications Committee, to the ruling of the Administrative Appeals Tribunal; and the conclusive decision of the Full Court of the Federal Court of Australia. Part 3 examines the implications of the Coonawarra litigation for other wine regions of Australia - most notably, the King Valley in Victoria; but also the Hunter Valley in the New South Wales; and the Margaret River in Western Australia. The conclusion considers the ramifications of the European Community-Australia Wine Agreement 2007, which has been initialed by both sides.