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.

Ovine Enzootic Abortion (OEA): a comparison of antibody responses in vaccinated and naturally-infected swiss sheep over a two year period

Background Prevention and control of ovine enzootic abortion (OEA) can be achieved by application of a live vaccine. In this study, five sheep flocks with different vaccination and infection status were serologically tested using a competitive enzyme-linked immunosorbent assay (cELISA) specific for Chlamydophila (Cp.) abortus over a two-year time period. Results Sheep in Flock A with recent OEA history had high antibody values after vaccination similar to Flock C with natural Cp. abortus infections. In contrast, OEA serology negative sheep (Flock E) showed individual animal-specific immunoreactions after vaccination. Antibody levels of vaccinated ewes in Flock B ranged from negative to positive two and three years after vaccination, respectively. Positive antibody values in the negative control Flock D (without OEA or vaccination) are probably due to asymptomatic intestinal infections with Cp. abortus. Excretion of the attenuated strain of Cp. abortus used in the live vaccine through the eye was not observed in vaccinated animals of Flock E. Conclusion The findings of our study indicate that, using serology, no distinction can be made between vaccinated and naturally infected sheep. As a result, confirmation of a negative OEA status in vaccinated animals by serology cannot be determined.

Overview of the ShARe/CLEF eHealth Evaluation Lab 2014

This paper reports on the 2nd ShARe/CLEFeHealth evaluation lab which continues our evaluation resource building activities for the medical domain. In this lab we focus on patients' information needs as opposed to the more common campaign focus of the specialised information needs of physicians and other healthcare workers. The usage scenario of the lab is to ease patients and next-of-kins' ease in understanding eHealth information, in particular clinical reports. The 1st ShARe/CLEFeHealth evaluation lab was held in 2013. This lab consisted of three tasks. Task 1 focused on named entity recognition and normalization of disorders; Task 2 on normalization of acronyms/abbreviations; and Task 3 on information retrieval to address questions patients may have when reading clinical reports. This year's lab introduces a new challenge in Task 1 on visual-interactive search and exploration of eHealth data. Its aim is to help patients (or their next-of-kin) in readability issues related to their hospital discharge documents and related information search on the Internet. Task 2 then continues the information extraction work of the 2013 lab, specifically focusing on disorder attribute identification and normalization from clinical text. Finally, this year's Task 3 further extends the 2013 information retrieval task, by cleaning the 2013 document collection and introducing a new query generation method and multilingual queries. De-identified clinical reports used by the three tasks were from US intensive care and originated from the MIMIC II database. Other text documents for Tasks 1 and 3 were from the Internet and originated from the Khresmoi project. Task 2 annotations originated from the ShARe annotations. For Tasks 1 and 3, new annotations, queries, and relevance assessments were created. 50, 79, and 91 people registered their interest in Tasks 1, 2, and 3, respectively. 24 unique teams participated with 1, 10, and 14 teams in Tasks 1, 2 and 3, respectively. The teams were from Africa, Asia, Canada, Europe, and North America. The Task 1 submission, reviewed by 5 expert peers, related to the task evaluation category of Effective use of interaction and targeted the needs of both expert and novice users. The best system had an Accuracy of 0.868 in Task 2a, an F1-score of 0.576 in Task 2b, and Precision at 10 (P@10) of 0.756 in Task 3. The results demonstrate the substantial community interest and capabilities of these systems in making clinical reports easier to understand for patients. The organisers have made data and tools available for future research and development.