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.

Trace, a novel and exegesis

Trace concerns writing-walking and walking-writing. The multiple voices of both novel and exegesis assemble a rhizomic map of a walk and create a never-entirely-certain wandering look upon a woman walking, rather than a single cocksure gaze. Trace explores the aesthetics of Western walking literature and the various nostalgias inherent in that tradition. Trace wonders how lost a character can become on a walk and whether a walk is itself a kind of becoming. In the undefined liminal space where the urban bleeds into the rural, Trace challenges the singular perspective of the dominating gaze with a wandering look, which aims to make an original contribution to both the walk in literature and to exegetical form.

Bootstrap approaches for estimation and confidence intervals of long term memory processes

In this work, we investigate an alternative bootstrap approach based on a result of Ramsey [F.L. Ramsey, Characterization of the partial autocorrelation function, Ann. Statist. 2 (1974), pp. 1296-1301] and on the Durbin-Levinson algorithm to obtain a surrogate series from linear Gaussian processes with long range dependence. We compare this bootstrap method with other existing procedures in a wide Monte Carlo experiment by estimating, parametrically and semi-parametrically, the memory parameter d. We consider Gaussian and non-Gaussian processes to prove the robustness of the method to deviations from normality. The approach is also useful to estimate confidence intervals for the memory parameter d by improving the coverage level of the interval.

Jack's Bay (the architecturalisation of memory)

Jack's Bay (the architecturalisation of memory) is a key work of the author's exhibition Lightsite, which toured Western Australian galleries from February 2006 to November 2007. It is a five-minute-long exposure photographic image captured inside a purpose-built, room-sized pinhole camera which is demountable and does not have a floor. The work depicts octogenarian Jack Morris, who for forty years held the professional salmon fishing license in the hamlet of Bremer Bay, on the SE coast of Western Australia. The pinhole camera-room is sited within sand dunes new Jack's now demolished beachside camp. Three generations of Jack's descendents stand outside the room - from his daughter to his great grand children. The light from this exterior landscape is 'projected' inside the camera-room and illuminates the interior scene which includes that part of the sand dune upon which the floorless room is erected, along with Jack who is sitting inside. The image evokes the temporality of light. Here, light itself is portrayed as the primary medium through which we both perceive and describe landscape. In this way it is through the agency of light that we construct our connectivity to landscape.

Fusionless scoliosis correction using shape memory alloy staples

Severe spinal deformity in young children is a formidable challenge for optimal treatment. Standard interventions for adolescents, such as spinal deformity correction and fusion, may not be appropriate for young patients with considerable growth remaining. Alternative surgical options that provide deformity correction and protect the growth remaining in the spine are needed to treat this group of patients 1, 2. One such method is the use of shape memory alloy staples. We report our experience to date using video-assisted thoracoscopic insertion of shape memory alloy staples. A retrospective review was conducted of 13 patients with scoliosis, aged 7 to 13 years, who underwent video-assisted thoracoscopic insertion of shape memory staples. In our experience, video-assisted thoracoscopic insertion of shape memory alloy staples is a safe procedure with no complications noted. It is a reliable method of providing curve stability, however the follow up results to date indicate that the effectiveness of the procedure is greater in younger patients.

Fuzzy associative memory for humanoid robot joint control

Traditional approaches to joint control required accurate modelling of the system dynamic of the plant in question. Fuzzy Associative Memory (FAM) control schemes allow adequate control without a model of the system to be controlled. This paper presents a FAM based joint controller implemented on a humanoid robot. An empirically tuned PI velocity control loop is augmented with this feed forward FAM, with considerable reduction in joint position error achieved online and with minimal additional computational overhead.

Mediatisation and institutions of public memory : digital storytelling and the apology

Institutions of public memory are increasingly undertaking co-creative media initiatives in which community members create content with the support of institutional expertise and resources. This paper discusses one such initiative: the State Library of Queensland’s ‘Responses to the Apology’, which used a collaborative digital storytelling methodology to co-produce seven short videos capturing individual responses to Prime Minister Kevin Rudd’s 2008 ‘Apology to Australia’s Indigenous Peoples’. In examining this program, we are interested not only in the juxtaposition of ‘ordinary’ responses to an ‘official’ event, but also in how the production and display of these stories might also demonstrate a larger mediatisation of public memory.

Influence of historic land use change on the biosphere-atmosphere-exchange of C and N trace gases in the humid, subtropical region of Queensland

Increases in atmospheric concentrations of the greenhouse gases (GHGs) carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O) due to human activities have been linked to climate change. GHG emissions from land use change and agriculture have been identified as significant contributors to both Australia’s and the global GHG budget. This is expected to increase over the coming decades as rates of agriculture intensification and land use change accelerate to support population growth and food production. Limited data exists on CO2, CH4 and N2O trace gas fluxes from subtropical or tropical soils and land uses. To develop effective mitigation strategies a full global warming potential (GWP) accounting methodology is required that includes emissions of the three primary greenhouse gases. Mitigation strategies that focus on one gas only can inadvertently increase emissions of another. For this reason, detailed inventories of GHGs from soils and vegetation under individual land uses are urgently required for subtropical Australia. This study aimed to quantify GHG emissions over two consecutive years from three major land uses; a well-established, unfertilized subtropical grass-legume pasture, a 30 year (lychee) orchard and a remnant subtropical Gallery rainforest, all located near Mooloolah, Queensland. GHG fluxes were measured using a combination of high resolution automated sampling, coarser spatial manual sampling and laboratory incubations. Comparison between the land uses revealed that land use change can have a substantial impact on the GWP on a landscape long after the deforestation event. The conversion of rainforest to agricultural land resulted in as much as a 17 fold increase in GWP, from 251 kg CO2 eq. ha-1 yr-1 in the rainforest to 889 kg CO2 eq. ha-1 yr-1 in the pasture to 2538 kg CO2 eq. ha-1 yr-1 in the lychee plantation. This increase resulted from altered N cycling and a reduction in the aerobic capacity of the soil in the pasture and lychee systems, enhancing denitrification and nitrification events, and reducing atmospheric CH4 uptake in the soil. High infiltration, drainage and subsequent soil aeration under the rainforest limited N2O loss, as well as promoting CH4 uptake of 11.2 g CH4-C ha-1 day-1. This was among the highest reported for rainforest systems, indicating that aerated subtropical rainforests can act as substantial sink of CH4. Interannual climatic variation resulted in significantly higher N2O emission from the pasture during 2008 (5.7 g N2O-N ha day) compared to 2007 (3.9 g N2O-N ha day), despite receiving nearly 500 mm less rainfall. Nitrous oxide emissions from the pasture were highest during the summer months and were highly episodic, related more to the magnitude and distribution of rain events rather than soil moisture alone. Mean N2O emissions from the lychee plantation increased from an average of 4.0 g N2O-N ha-1 day-1, to 19.8 g N2O-N ha-1 day-1 following a split application of N fertilizer (560 kg N ha-1, equivalent to 1 kg N tree-1). The timing of the split application was found to be critical to N2O emissions, with over twice as much lost following an application in spring (emission factor (EF): 1.79%) compared to autumn (EF: 0.91%). This was attributed to the hot and moist climatic conditions and a reduction in plant N uptake during the spring creating conditions conducive to N2O loss. These findings demonstrate that land use change in subtropical Australia can be a significant source of GHGs. Moreover, the study shows that modifying the timing of fertilizer application can be an efficient way of reducing GHG emissions from subtropical horticulture.