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.

National guidelines for digital modelling

These National Guidelines and Case Studies for Digital Modelling are the outcomes from one of a number of Building Information Modelling (BIM)-related projects undertaken by the CRC for Construction Innovation. Since the CRC opened its doors in 2001, the industry has seen a rapid increase in interest in BIM, and widening adoption. These guidelines and case studies are thus very timely, as the industry moves to model-based working and starts to share models in a new context called integrated practice. Governments, both federal and state, and in New Zealand are starting to outline the role they might take, so that in contrast to the adoption of 2D CAD in the early 90s, we ensure that a national, industry-wide benefit results from this new paradigm of working. Section 1 of the guidelines give us an overview of BIM: how it affects our current mode of working, what we need to do to move to fully collaborative model-based facility development. The role of open standards such as IFC is described as a mechanism to support new processes, and make the extensive design and construction information available to asset operators and managers. Digital collaboration modes, types of models, levels of detail, object properties and model management complete this section. It will be relevant for owners, managers and project leaders as well as direct users of BIM. Section 2 provides recommendations and guides for key areas of model creation and development, and the move to simulation and performance measurement. These are the more practical parts of the guidelines developed for design professionals, BIM managers, technical staff and ‘in the field’ workers. The guidelines are supported by six case studies including a summary of lessons learnt about implementing BIM in Australian building projects. A key aspect of these publications is the identification of a number of important industry actions: the need for BIM-compatible product information and a national context for classifying product data; the need for an industry agreement and setting process-for-process definition; and finally, the need to ensure a national standard for sharing data between all of the participants in the facility-development process.

National guidelines for digital modelling : case studies

These National Guidelines and Case Studies for Digital Modelling are the outcomes from one of a number of Building Information Modelling (BIM)-related projects undertaken by the CRC for Construction Innovation. Since the CRC opened its doors in 2001, the industry has seen a rapid increase in interest in BIM, and widening adoption. These guidelines and case studies are thus very timely, as the industry moves to model-based working and starts to share models in a new context called integrated practice. Governments, both federal and state, and in New Zealand are starting to outline the role they might take, so that in contrast to the adoption of 2D CAD in the early 90s, we ensure that a national, industry-wide benefit results from this new paradigm of working. Section 1 of the guidelines give us an overview of BIM: how it affects our current mode of working, what we need to do to move to fully collaborative model-based facility development. The role of open standards such as IFC is described as a mechanism to support new processes, and make the extensive design and construction information available to asset operators and managers. Digital collaboration modes, types of models, levels of detail, object properties and model management complete this section. It will be relevant for owners, managers and project leaders as well as direct users of BIM. Section 2 provides recommendations and guides for key areas of model creation and development, and the move to simulation and performance measurement. These are the more practical parts of the guidelines developed for design professionals, BIM managers, technical staff and ‘in the field’ workers. The guidelines are supported by six case studies including a summary of lessons learnt about implementing BIM in Australian building projects. A key aspect of these publications is the identification of a number of important industry actions: the need for BIMcompatible product information and a national context for classifying product data; the need for an industry agreement and setting process-for-process definition; and finally, the need to ensure a national standard for sharing data between all of the participants in the facility-development process.

Improved GrabCut segmentation via GMM optimisation

Semi-automatic segmentation of still images has vast and varied practical applications. Recently, an approach "GrabCut" has managed to successfully build upon earlier approaches based on colour and gradient information in order to address the problem of efficient extraction of a foreground object in a complex environment. In this paper, we extend the GrabCut algorithm further by applying an unsupervised algorithm for modelling the Gaussian Mixtures that are used to define the foreground and background in the segmentation algorithm. We show examples where the optimisation of the GrabCut framework leads to further improvements in performance.

Thermal requirements, field mortality and population phenology modelling of Paropsis atomaria Olivier, an emergent pest in subtropical hardwood plantations

Paropsis atomaria is a recently emerged pest of eucalypt plantations in subtropical Australia. Its broad host range of at least 20 eucalypt species and wide geographical distribution provides it the potential to become a serious forestry pest both within Australia and, if accidentally introduced, overseas. Although populations of P. atomaria are genetically similar throughout its range, population dynamics differ between regions. Here, we determine temperature-dependent developmental requirements using beetles sourced from temperate and subtropical zones by calculating lower temperature thresholds, temperature-induced mortality, and day-degree requirements. We combine these data with field mortality estimates of immature life stages to produce a cohort-based model, ParopSys, using DYMEX™ that accurately predicts the timing, duration, and relative abundance of life stages in the field and number of generations in a spring–autumn (September–May) field season. Voltinism was identified as a seasonally plastic trait dependent upon environmental conditions, with two generations observed and predicted in the Australian Capital Territory, and up to four in Queensland. Lower temperature thresholds for development ranged between 4 and 9 °C, and overall development rates did not differ according to beetle origin. Total immature development time (egg–adult) was approximately 769.2 ± S.E. 127.8 DD above a lower temperature threshold of 6.4 ± S.E. 2.6 °C. ParopSys provides a basic tool enabling forest managers to use the number of generations and seasonal fluctuations in abundance of damaging life stages to estimate the pest risk of P. atomaria prior to plantation establishment, and predict the occurrence and duration of damaging life stages in the field. Additionally, by using local climatic data the pest potential of P. atomaria can be estimated to predict the risk of it establishing if accidentally introduced overseas. Improvements to ParopSys’ capability and complexity can be made as more biological data become available.

Context-Based Modelling of Interferometric Signals for the Assessment of Tear-Film Suface Quality

Modelling of interferometric signals related to tear film surface quality is considered. In the context of tear film surface quality estimation in normal healthy eyes, two clinical parameters are of interest: the build-up time, and the average interblink surface quality. The former is closely related to the signal derivative while the latter to the signal itself. Polynomial signal models, chosen for a particular set of noisy interferometric measurements, can be optimally selected, in some sense, with a range of information criteria such as AIC, MDL, Cp, and CME. Those criteria, however, do not always guarantee that the true derivative of the signal is accurately represented and they often overestimate it. Here, a practical method for judicious selection of model order in a polynomial fitting to a signal is proposed so that the derivative of the signal is adequately represented. The paper highlights the importance of context-based signal modelling in model order selection.

Setting hospital infection control policy : a decision-making framework incorporating health economics and healthcare epidemiology

Background: Reducing rates of healthcare acquired infection has been identified by the Australian Commission on Safety and Quality in Health Care as a national priority. One of the goals is the prevention of central venous catheter-related bloodstream infection (CR-BSI). At least 3,500 cases of CR-BSI occur annually in Australian hospitals, resulting in unnecessary deaths and costs to the healthcare system between $25.7 and $95.3 million. Two approaches to preventing these infections have been proposed: use of antimicrobial catheters (A-CVCs); or a catheter care and management ‘bundle’. Given finite healthcare budgets, decisions about the optimal infection control policy require consideration of the effectiveness and value for money of each approach. Objectives: The aim of this research is to use a rational economic framework to inform efficient infection control policy relating to the prevention of CR-BSI in the intensive care unit. It addresses three questions relating to decision-making in this area: 1. Is additional investment in activities aimed at preventing CR-BSI an efficient use of healthcare resources? 2. What is the optimal infection control strategy from amongst the two major approaches that have been proposed to prevent CR-BSI? 3. What uncertainty is there in this decision and can a research agenda to improve decision-making in this area be identified? Methods: A decision analytic model-based economic evaluation was undertaken to identify an efficient approach to preventing CR-BSI in Queensland Health intensive care units. A Markov model was developed in conjunction with a panel of clinical experts which described the epidemiology and prognosis of CR-BSI. The model was parameterised using data systematically identified from the published literature and extracted from routine databases. The quality of data used in the model and its validity to clinical experts and sensitivity to modelling assumptions was assessed. Two separate economic evaluations were conducted. The first evaluation compared all commercially available A-CVCs alongside uncoated catheters to identify which was cost-effective for routine use. The uncertainty in this decision was estimated along with the value of collecting further information to inform the decision. The second evaluation compared the use of A-CVCs to a catheter care bundle. We were unable to estimate the cost of the bundle because it is unclear what the full resource requirements are for its implementation, and what the value of these would be in an Australian context. As such we undertook a threshold analysis to identify the cost and effectiveness thresholds at which a hypothetical bundle would dominate the use of A-CVCs under various clinical scenarios. Results: In the first evaluation of A-CVCs, the findings from the baseline analysis, in which uncertainty is not considered, show that the use of any of the four A-CVCs will result in health gains accompanied by cost-savings. The MR catheters dominate the baseline analysis generating 1.64 QALYs and cost-savings of $130,289 per 1.000 catheters. With uncertainty, and based on current information, the MR catheters remain the optimal decision and return the highest average net monetary benefits ($948 per catheter) relative to all other catheter types. This conclusion was robust to all scenarios tested, however, the probability of error in this conclusion is high, 62% in the baseline scenario. Using a value of $40,000 per QALY, the expected value of perfect information associated with this decision is $7.3 million. An analysis of the expected value of perfect information for individual parameters suggests that it may be worthwhile for future research to focus on providing better estimates of the mortality attributable to CR-BSI and the effectiveness of both SPC and CH/SSD (int/ext) catheters. In the second evaluation of the catheter care bundle relative to A-CVCs, the results which do not consider uncertainty indicate that a bundle must achieve a relative risk of CR-BSI of at least 0.45 to be cost-effective relative to MR catheters. If the bundle can reduce rates of infection from 2.5% to effectively zero, it is cost-effective relative to MR catheters if national implementation costs are less than $2.6 million ($56,610 per ICU). If the bundle can achieve a relative risk of 0.34 (comparable to that reported in the literature) it is cost-effective, relative to MR catheters, if costs over an 18 month period are below $613,795 nationally ($13,343 per ICU). Once uncertainty in the decision is considered, the cost threshold for the bundle increases to $2.2 million. Therefore, if each of the 46 Level III ICUs could implement an 18 month catheter care bundle for less than $47,826 each, this approach would be cost effective relative to A-CVCs. However, the uncertainty is substantial and the probability of error in concluding that the bundle is the cost-effective approach at a cost of $2.2 million is 89%. Conclusions: This work highlights that infection control to prevent CR-BSI is an efficient use of healthcare resources in the Australian context. If there is no further investment in infection control, an opportunity cost is incurred, which is the potential for a more efficient healthcare system. Minocycline/rifampicin catheters are the optimal choice of antimicrobial catheter for routine use in Australian Level III ICUs, however, if a catheter care bundle implemented in Australia was as effective as those used in the large studies in the United States it would be preferred over the catheters if it was able to be implemented for less than $47,826 per Level III ICU. Uncertainty is very high in this decision and arises from multiple sources. There are likely greater costs to this uncertainty for A-CVCs, which may carry hidden costs, than there are for a catheter care bundle, which is more likely to provide indirect benefits to clinical practice and patient safety. Research into the mortality attributable to CR-BSI, the effectiveness of SPC and CH/SSD (int/ext) catheters and the cost and effectiveness of a catheter care bundle in Australia should be prioritised to reduce uncertainty in this decision. This thesis provides the economic evidence to inform one area of infection control, but there are many other infection control decisions for which information about the cost-effectiveness of competing interventions does not exist. This work highlights some of the challenges and benefits to generating and using economic evidence for infection control decision-making and provides support for commissioning more research into the cost-effectiveness of infection control.