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.

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.

Sequential decision fusion for controlled detection errors

Information fusion in biometrics has received considerable attention. The architecture proposed here is based on the sequential integration of multi-instance and multi-sample fusion schemes. This method is analytically shown to improve the performance and allow a controlled trade-off between false alarms and false rejects when the classifier decisions are statistically independent. Equations developed for detection error rates are experimentally evaluated by considering the proposed architecture for text dependent speaker verification using HMM based digit dependent speaker models. The tuning of parameters, n classifiers and m attempts/samples, is investigated and the resultant detection error trade-off performance is evaluated on individual digits. Results show that performance improvement can be achieved even for weaker classifiers (FRR-19.6%, FAR-16.7%). The architectures investigated apply to speaker verification from spoken digit strings such as credit card numbers in telephone or VOIP or internet based applications.

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.

To err (on the road) is human? An on-road study of driver errors

Human error, its causes and consequences, and the ways in which it can be prevented, remain of great interest to road safety practitioners. This paper presents the findings derived from an on-road study of driver errors in which 25 participants drove a pre-determined route using MUARC's On-Road Test Vehicle (ORTeV). In-vehicle observers recorded the different errors made, and a range of other data was collected, including driver verbal protocols, forward, cockpit and driver video, and vehicle data (speed, braking, steering wheel angle, lane tracking etc). Participants also completed a post trial cognitive task analysis interview. The drivers tested made a range of different errors, with speeding violations, both intentional and unintentional, being the most common. Further more detailed analysis of a sub-set of specific error types indicates that driver errors have various causes, including failures in the wider road 'system' such as poor roadway design, infrastructure failures and unclear road rules. In closing, a range of potential error prevention strategies, including intelligent speed adaptation and road infrastructure design, are discussed.

Real-time performance modelling of a sustained attention to response task

Vigilance declines when exposed to highly predictable and uneventful tasks. Monotonous tasks provide little cognitive and motor stimulation and contribute to human errors. This paper aims to model and detect vigilance decline in real time through participant’s reaction times during a monotonous task. A lab-based experiment adapting the Sustained Attention to Response Task (SART) is conducted to quantify the effect of monotony on overall performance. Then relevant parameters are used to build a model detecting hypovigilance throughout the experiment. The accuracy of different mathematical models are compared to detect in real-time – minute by minute - the lapses in vigilance during the task. We show that monotonous tasks can lead to an average decline in performance of 45%. Furthermore, vigilance modelling enables to detect vigilance decline through reaction times with an accuracy of 72% and a 29% false alarm rate. Bayesian models are identified as a better model to detect lapses in vigilance as compared to Neural Networks and Generalised Linear Mixed Models. This modelling could be used as a framework to detect vigilance decline of any human performing monotonous tasks.

The effects of cognitive ageing on the use of complex interfaces

This paper discusses an experiment investigating the effects of cognitive ageing and prior-experience with technology on using complex interfaces intuitively. Overall 37 participants, between the ages of 18 to 83, participated in this study. All participants were assessed for their cognitive abilities and prior-experience with technology. It was anticipated that the Central Executive function (a component of Working Memory) would emerge as one of the important cognitive functions in using complex interfaces. This was found to be the case with the strongest negative correlation occurring between sustained attention (one of the functions of the Central Executive), the time to complete the task and number of errors made by the participants.

Modular transactional memory

Software transactional memory has the potential to greatly simplify development of concurrent software, by supporting safe composition of concurrent shared-state abstractions. However, STM semantics are defined in terms of low-level reads and writes on individual memory locations, so implementations are unable to take advantage of the properties of user-defined abstractions. Consequently, the performance of transactions over some structures can be disappointing. ----- ----- We present Modular Transactional Memory, our framework which allows programmers to extend STM with concurrency control algorithms tailored to the data structures they use in concurrent programs. We describe our implementation in Concurrent Haskell, and two example structures: a finite map which allows concurrent transactions to operate on disjoint sets of keys, and a non-deterministic channel which supports concurrent sources and sinks. ----- ----- Our approach is based on previous work by others on boosted and open-nested transactions, with one significant development: transactions are given types which denote the concurrency control algorithms they employ. Typed transactions offer a higher level of assurance for programmers reusing transactional code, and allow more flexible abstract concurrency control.