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.

Pre-experimental familiarization increases hippocampal activity for both targets and lures in recognition memory: An fMRI study

In the present study, items pre-exposed in a familiarization series were included in a list discrimination task to manipulate memory strength. At test, participants were required to discriminate strong targets and strong lures from weak targets and new lures. This resulted in a concordant pattern of increased "old" responses to strong targets and lures. Model estimates attributed this pattern to either equivalent increases in memory strength across the two types of items (unequal variance signal detection model) or equivalent increases in both familiarity and recollection (dual process signal detection [DPSD] model). Hippocampal activity associated with strong targets and lures showed equivalent increases compared with missed items. This remained the case when analyses were restricted to high-confidence responses considered by the DPSD model to reflect predominantly recollection. A similar pattern of activity was observed in parahippocampal cortex for high-confidence responses. The present results are incompatible with "noncriterial" or "false" recollection being reflected solely in inflated DPSD familiarity estimates and support a positive correlation between hippocampal activity and memory strength irrespective of the accuracy of list discrimination, consistent with the unequal variance signal detection model account.

Attention and memory bias for body image and health related information using an Emotional Stroop task in a non-clinical sample

It has been proposed that body image disturbance is a form of cognitive bias wherein schemas for self-relevant information guide the selective processing of appearancerelated information in the environment. This threatening information receives disproportionately more attention and memory, as measured by an Emotional Stroop and incidental recall task. The aim of this thesis was to expand the literature on cognitive processing biases in non-clinical males and females by incorporating a number of significant methodological refinements. To achieve this aim, three phases of research were conducted. The initial two phases of research provided preliminary data to inform the development of the main study. Phase One was a qualitative exploration of body image concerns amongst males and females recruited through the general community and from a university. Seventeen participants (eight male; nine female) provided information on their body image and what factors they saw as positively and negatively impacting on their self evaluations. The importance of self esteem, mood, health and fitness, and recognition of the social ideal were identified as key themes. These themes were incorporated as psycho-social measures and Stroop word stimuli in subsequent phases of the research. Phase Two involved the selection and testing of stimuli to be used in the Emotional Stroop task. Six experimental categories of words were developed that reflected a broad range of health and body image concerns for males and females. These categories were high and low calorie food words, positive and negative appearance words, negative emotion words, and physical activity words. Phase Three addressed the central aim of the project by examining cognitive biases for body image information in empirically defined sub-groups. A National sample of males (N = 55) and females (N = 144), recruited from the general community and universities, completed an Emotional Stroop task, incidental memory test, and a collection of psycho-social questionnaires. Sub-groups of body image disturbance were sought using a cluster analysis, which identified three sub-groups in males (Normal, Dissatisfied, and Athletic) and four sub-groups in females (Normal, Health Conscious, Dissatisfied, and Symptomatic). No differences were noted between the groups in selective attention, although time taken to colour name the words was associated with some of the psycho-social variables. Memory biases found across the whole sample for negative emotion, low calorie food, and negative appearance words were interpreted as reflecting the current focus on health and stigma against being unattractive. Collectively these results have expanded our understanding of processing biases in the general community by demonstrating that the processing biases are found within non-clinical samples and that not all processing biases are associated with negative functionality

Situated case-based reasoning as a constructive memory model for design reasoning

This paper describes an extended case-based reasoning model that addresses the notion of situatedness in designing through constructive memory. The model is illustrated through an application for predicting the corrosion rate for a specific material on a specific building.

Measuring episodic memory: A novel approach with an indefinite number of alternative forms

Both clinical practice and clinical research settings can require successive administrations of a memory test, particularly when following the trajectory of suspected memory decline in older adults. However, relatively few verbal episodic memory tests have alternative forms. We set out to create a broad based memory test to allow for the use of an essentially unlimited number of alternative forms. Four tasks for inclusion in such a test were developed. These tasks varied the requirement for recall as opposed to recognition, the need to form an association between unrelated words, and the need to discriminate the most recent list from earlier lists, all of which proved useful. A total of 115 participants completed the battery of tests and were used to show that the test could differentiate between older and younger adults; a sub-sample of 73 participants completed alternative forms of the tests to determine test-retest reliability and the amount of learning to learn.

Event-related potential (ERP) correlates of impaired visuospatial memory in schizophrenia

Previous studies have reported that patients with schizophrenia demonstrate impaired performance during working memory (WM) tasks. The current study aimed to determine whether WM impairments in schizophrenia are accompanied by reduced slow wave (SW) activity during on-line maintenance of mnemonic information. Event-related potentials were obtained from patients with schizophrenia and well controls as they performed a visuospatial delayed response task. On 50% of trials, a distractor stimulus was introduced during the delay. Compared with controls, patients with schizophrenia produced less SW memory negativity, particularly over the right hemisphere, together with reduced frontal enhancement of SW memory negativity in response to distraction. The results indicate that patients with schizophrenia generate less maintenance phase neuronal activity during WM performance, especially under conditions of distraction.

Working memory correlates of three symptom clusters in schizophrenia

Examined whether discrete working memory deficits underlie positive, negative and disorganised symptoms of schizophrenia. 52 outpatients (mean age 37.5 yrs) with schizophrenia were studied using items drawn from the Positive and Negative Syndrome Scale (PANSS). Linear regression and correlational analyses were conducted to examine whether symptom dimension scores were related to performance on several tests of working memory function. Severity of negative symptoms correlated with reduced production of words during a verbal fluency task, impaired ability to hold letter and number sequences on-line and manipulate them simultaneously, reduced performance during a dual task, and compromised visuospatial working memory under distraction-free conditions. Severity of disorganisation symptoms correlated with impaired visuospatial working memory under conditions of distraction, failure of inhibition during a verbal fluency task, perseverative responding on a test of set-shifting ability, and impaired ability to judge the veracity of simple declarative statements. The present study provides evidence that the positive, negative and disorganised symptom dimensions of the PANSS constitute independent clusters, associated with unique patterns of working memory impairment.

Eye-movements and visual imagery : a working memory approach to the treatment of post-traumatic stress disorder

It has been claimed that the symptoms of post-traumatic stress disorder (PTSD) can be ameliorated by eye-movement desensitization-reprocessing therapy (EMD-R), a procedure that involves the individual making saccadic eye-movements while imagining the traumatic event. We hypothesized that these eye-movements reduce the vividness of distressing images by disrupting the function of the visuospatial sketchpad (VSSP) of working memory, and that by doing so they reduce the intensity of the emotion associated with the image. This hypothesis was tested by asking non-PTSD participants to form images of neutral and negative pictures under dual task conditions. Their images were less vivid with concurrent eye-movements and with a concurrent spatial tapping task that did not involve eye-movements. In the first three experiments, these secondary tasks did not consistently affect participants' emotional responses to the images. However, Expt 4 used personal recollections as stimuli for the imagery task, and demonstrated a significant reduction in emotional response under the same dual task conditions. These results suggest that, if EMD-R works, it does so by reducing the vividness and emotiveness of traumatic images via the VSSP of working memory. Other visuospatial tasks may also be of therapeutic value.

Quantum memory

New models of human cognition inspired by quantum theory could underpin information technologies that are better aligned with howwe recall information.

‘Capitalism’ as False Consciousness

The assertion on which this paper is based is that Capitalism has been superseded by Corporatism. I put forward an argument as to why Marxist scholars can and should abandon the idea that Capitalism still exists based on Marx’s approach to understanding political economy. Further, I argue that Marx’s method can be deployed to better understand and change the corporatist system in which we are currently living first by understanding what it means to be “labour” in a system governed by complex structures of debt.

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.