Using monthly returns to model conditional heteroscedasticity

This empirical study examines the extent of non-linearity in a multivariate model of monthly financial series. To capture the conditional heteroscedasticity in the series, both the GARCH(1,1) and GARCH(1,1)-in-mean models are employed. The conditional errors are assumed to follow the normal and Student-t distributions. The non-linearity in the residuals of a standard OLS regression are also assessed. It is found that the OLS residuals as well as conditional errors of the GARCH models exhibit strong non-linearity. Under the Student density, the extent of non-linearity in the GARCH conditional errors was generally similar to those of the standard OLS. The GARCH-in-mean regression generated the worse out-of-sample forecasts.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

High stability interleaved fibre Michelson interferometer for on-line precision displacement measurements

A self-reference fiber Michelson interferometer measurement system, which employs fiber Bragg gratings (FBGs) as in-fiber reflective mirrors and interleaves together two fiber Michelson interferometers that share the common-interferometric-optical path, is presented. One of the fiber interferometers is used to stabilise the system by the use of an electronic feedback loop to compensate the influences resulting from the environmental disturbances, while the other one is used to perform the measurement task. The influences resulting from the environmental disturbances have been eliminated by the compensating action of the electronic feedback loop, this makes the system suitable for on-line precision measurement. By means of the homodyne phase-tracking technique, the linearity of the measurement results of displacement measurements has been very high.

Resistance heating of steel conductors of circular cross-section

The object of this thesis is to develop a method for calculating the losses developed in steel conductors of circular cross-section and at temperatures below 100oC, by the direct passage of a sinusoidally alternating current. Three cases are considered. 1. Isolated solid or tubular conductor. 2. Concentric arrangement of tube and solid return conductor. 3. Concentric arrangement of two tubes. These cases find applications in process temperature maintenance of pipelines, resistance heating of bars and design of bus-bars. The problems associated with the non-linearity of steel are examined. Resistance heating of bars and methods of surface heating of pipelines are briefly described. Magnetic-linear solutions based on Maxwell's equations are critically examined and conditions under which various formulae apply investigated. The conditions under which a tube is electrically equivalent to a solid conductor and to a semi-infinite plate are derived. Existing solutions for the calculation of losses in isolated steel conductors of circular cross-section are reviewed, evaluated and compared. Two methods of solution are developed for the three cases considered. The first is based on the magnetic-linear solutions and offers an alternative to the available methods which are not universal. The second solution extends the existing B/H step-function approximation method to small diameter conductors and to tubes in isolation or in a concentric arrangement. A comprehensive experimental investigation is presented for cases 1 and 2 above which confirms the validity of the proposed methods of solution. These are further supported by experimental results reported in the literature. Good agreement is obtained between measured and calculated loss values for surface field strengths beyond the linear part of the d.c. magnetisation characteristic. It is also shown that there is a difference in the electrical behaviour of a small diameter conductor or thin tube under resistance or induction heating conditions.

Multi-topic information filtering with a single user profile

In Information Filtering (IF) a user may be interested in several topics in parallel. But IF systems have been built on representational models derived from Information Retrieval and Text Categorization, which assume independence between terms. The linearity of these models results in user profiles that can only represent one topic of interest. We present a methodology that takes into account term dependencies to construct a single profile representation for multiple topics, in the form of a hierarchical term network. We also introduce a series of non-linear functions for evaluating documents against the profile. Initial experiments produced positive results.

Distributed temperature sensing using a chirped fibre Bragg grating

A fully distributed temperature sensor consisting of a chirped fibre Bragg grating has been demonstrated. By fitting a numerical model of the grating response including temperature change, position and width of localized heating applied to the grating, we achieve measurements of these parameters to within 2.2 K, 149 µm and 306 µm of applied values, respectively. Assuming that deviation from linearity is accounted for in making measurement, much higher precision is achievable and the standard deviations for these measurements are 0.6 K, 28.5 µm and 56.0 µm, respectively.

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.

Short-term electricity demand and gas price forecasts using wavelet transforms and adaptive models

This paper presents some forecasting techniques for energy demand and price prediction, one day ahead. These techniques combine wavelet transform (WT) with fixed and adaptive machine learning/time series models (multi-layer perceptron (MLP), radial basis functions, linear regression, or GARCH). To create an adaptive model, we use an extended Kalman filter or particle filter to update the parameters continuously on the test set. The adaptive GARCH model is a new contribution, broadening the applicability of GARCH methods. We empirically compared two approaches of combining the WT with prediction models: multicomponent forecasts and direct forecasts. These techniques are applied to large sets of real data (both stationary and non-stationary) from the UK energy markets, so as to provide comparative results that are statistically stronger than those previously reported. The results showed that the forecasting accuracy is significantly improved by using the WT and adaptive models. The best models on the electricity demand/gas price forecast are the adaptive MLP/GARCH with the multicomponent forecast; their MSEs are 0.02314 and 0.15384 respectively.

Novel glucose sensor based on enzymeimmobilized 81° tilted fiber grating

We demonstrate a novel glucose sensor based on an optical fiber grating with an excessively tilted index fringe structure and its surface modified by glucose oxidase (GOD). The aminopropyltriethoxysilane (APTES) was utilized as binding site for the subsequent GOD immobilization. Confocal microscopy and fluorescence microscope were used to provide the assessment of the effectiveness in modifying the fiber surface. The resonance wavelength of the sensor exhibited red-shift after the binding of the APTES and GOD to the fiber surface and also in the glucose detection process. The red-shift of the resonance wavelength showed a good linear response to the glucose concentration with a sensitivity of 0.298nm(mg/ml)-1 in the very low concentration range of 0.0∼3.0mg/ml. Compared to the previously reported glucose sensor based on the GOD-immobilized long period grating (LPG), the 81° tilted fiber grating (81°-TFG) based sensor has shown a lower thermal cross-talk effect, better linearity and higher Q-factor in sensing response. In addition, its sensitivity for glucose concentration can be further improved by increasing the grating length and/or choosing a higher-order cladding mode for detection. Potentially, the proposed techniques based on 81°-TFG can be developed as sensitive, label free and micro-structural sensors for applications in food safety, disease diagnosis, clinical analysis and environmental monitoring.

Computer-aided categorisation and quantification of connectives in English and Arabic (based on newspaper text corpora).

This study presents a detailed contrastive description of the textual functioning of connectives in English and Arabic. Particular emphasis is placed on the organisational force of connectives and their role in sustaining cohesion. The description is intended as a contribution for a better understanding of the variations in the dominant tendencies for text organisation in each language. The findings are expected to be utilised for pedagogical purposes, particularly in improving EFL teaching of writing at the undergraduate level. The study is based on an empirical investigation of the phenomenon of connectivity and, for optimal efficiency, employs computer-aided procedures, particularly those adopted in corpus linguistics, for investigatory purposes. One important methodological requirement is the establishment of two comparable and statistically adequate corpora, also the design of software and the use of existing packages and to achieve the basic analysis. Each corpus comprises ca 250,000 words of newspaper material sampled in accordance to a specific set of criteria and assembled in machine readable form prior to the computer-assisted analysis. A suite of programmes have been written in SPITBOL to accomplish a variety of analytical tasks, and in particular to perform a battery of measurements intended to quantify the textual functioning of connectives in each corpus. Concordances and some word lists are produced by using OCP. Results of these researches confirm the existence of fundamental differences in text organisation in Arabic in comparison to English. This manifests itself in the way textual operations of grouping and sequencing are performed and in the intensity of the textual role of connectives in imposing linearity and continuity and in maintaining overall stability. Furthermore, computation of connective functionality and range of operationality has identified fundamental differences in the way favourable choices for text organisation are made and implemented.

Computer simulation of form-roll design

Changes in modern structural design have created a demand for products which are light but possess high strength. The objective is a reduction in fuel consumption and weight of materials to satisfy both economic and environmental criteria. Cold roll forming has the potential to fulfil this requirement. The bending process is controlled by the shape of the profile machined on the periphery of the rolls. A CNC lathe can machine complicated profiles to a high standard of precision, but the expertise of a numerical control programmer is required. A computer program was developed during this project, using the expert system concept, to calculate tool paths and consequently to expedite the procurement of the machine control tapes whilst removing the need for a skilled programmer. Codifying the expertise of a human and the encapsulation of knowledge within a computer memory, destroys the dependency on highly trained people whose services can be costly, inconsistent and unreliable. A successful cold roll forming operation, where the product is geometrically correct and free from visual defects, is not easy to attain. The geometry of the sheet after travelling through the rolling mill depends on the residual strains generated by the elastic-plastic deformation. Accurate evaluation of the residual strains can provide the basis for predicting the geometry of the section. A study of geometric and material non-linearity, yield criteria, material hardening and stress-strain relationships was undertaken in this research project. The finite element method was chosen to provide a mathematical model of the bending process and, to ensure an efficient manipulation of the large stiffness matrices, the frontal solution was applied. A series of experimental investigations provided data to compare with corresponding values obtained from the theoretical modelling. A computer simulation, capable of predicting that a design will be satisfactory prior to the manufacture of the rolls, would allow effort to be concentrated into devising an optimum design where costs are minimised.

Analysis of magnetoencephaoographic data as a nonlinear dynamical system

This thesis presents the results from an investigation into the merits of analysing Magnetoencephalographic (MEG) data in the context of dynamical systems theory. MEG is the study of both the methods for the measurement of minute magnetic flux variations at the scalp, resulting from neuro-electric activity in the neocortex, as well as the techniques required to process and extract useful information from these measurements. As a result of its unique mode of action - by directly measuring neuronal activity via the resulting magnetic field fluctuations - MEG possesses a number of useful qualities which could potentially make it a powerful addition to any brain researcher's arsenal. Unfortunately, MEG research has so far failed to fulfil its early promise, being hindered in its progress by a variety of factors. Conventionally, the analysis of MEG has been dominated by the search for activity in certain spectral bands - the so-called alpha, delta, beta, etc that are commonly referred to in both academic and lay publications. Other efforts have centred upon generating optimal fits of "equivalent current dipoles" that best explain the observed field distribution. Many of these approaches carry the implicit assumption that the dynamics which result in the observed time series are linear. This is despite a variety of reasons which suggest that nonlinearity might be present in MEG recordings. By using methods that allow for nonlinear dynamics, the research described in this thesis avoids these restrictive linearity assumptions. A crucial concept underpinning this project is the belief that MEG recordings are mere observations of the evolution of the true underlying state, which is unobservable and is assumed to reflect some abstract brain cognitive state. Further, we maintain that it is unreasonable to expect these processes to be adequately described in the traditional way: as a linear sum of a large number of frequency generators. One of the main objectives of this thesis will be to prove that much more effective and powerful analysis of MEG can be achieved if one were to assume the presence of both linear and nonlinear characteristics from the outset. Our position is that the combined action of a relatively small number of these generators, coupled with external and dynamic noise sources, is more than sufficient to account for the complexity observed in the MEG recordings. Another problem that has plagued MEG researchers is the extremely low signal to noise ratios that are obtained. As the magnetic flux variations resulting from actual cortical processes can be extremely minute, the measuring devices used in MEG are, necessarily, extremely sensitive. The unfortunate side-effect of this is that even commonplace phenomena such as the earth's geomagnetic field can easily swamp signals of interest. This problem is commonly addressed by averaging over a large number of recordings. However, this has a number of notable drawbacks. In particular, it is difficult to synchronise high frequency activity which might be of interest, and often these signals will be cancelled out by the averaging process. Other problems that have been encountered are high costs and low portability of state-of-the- art multichannel machines. The result of this is that the use of MEG has, hitherto, been restricted to large institutions which are able to afford the high costs associated with the procurement and maintenance of these machines. In this project, we seek to address these issues by working almost exclusively with single channel, unaveraged MEG data. We demonstrate the applicability of a variety of methods originating from the fields of signal processing, dynamical systems, information theory and neural networks, to the analysis of MEG data. It is noteworthy that while modern signal processing tools such as independent component analysis, topographic maps and latent variable modelling have enjoyed extensive success in a variety of research areas from financial time series modelling to the analysis of sun spot activity, their use in MEG analysis has thus far been extremely limited. It is hoped that this work will help to remedy this oversight.

Optical fibre sensors and their applications in the industrial weighing and aerospace industries

This thesis presents the design, fabrication and testing of novel grating based Optical Fibre Sensor (OFS) systems being interrogated using “off the shelf” interrogation systems, with the eventual development of marketable commercial systems at the forefront of the research. Both in the industrial weighing and aerospace industries, there has been a drive to investigate the feasibility of using optical fibre sensors being deployed where traditionally their electrical or mechanical counterparts would traditionally have been. Already, in the industrial weighing industry, commercial operators are deploying OFS-based Weigh-In-Motion (WIM) systems. Likewise, in the aerospace industry, OFS have been deployed to monitor such parameters as load history, impact detection, structural damage, overload detection, centre of gravity and the determination of blade shape. Based on the intrinsic properties of fibre Bragg gratings (FBGs) and Long Period Fibre Gratings (LPFGs), a number of novel OFS-based systems have been realised. Experimental work has shown that in the case of static industrial weighing, FBGs can be integrated with current commercial products and used to detect applied loads. The work has also shown that embedding FBGs in e-glass, to form a sensing patch, can result in said patches being bonded to rail track, forming the basis of an FBG-based WIM system. The results obtained have been sufficiently encouraging to the industrial partner that this work will be progressed beyond the scope of the work presented in this thesis. Likewise, and to the best of the author’s knowledge, a novel Bragg grating based systems for aircraft fuel parameter sensing has been presented. FBG-based pressure sensors have been shown to demonstrate good sensitivity, linearity and repeatability, whilst LPFG-based systems have demonstrated a far greater sensitivity when compared to FBGs, as well the advantage of being potentially able to detect causes of fuel adulteration based on their sensitivity to refractive index (RI). In the case of the LPFG-based system, considerable work remains to be done on the mechanical strengthening to improve its survivability in a live aircraft fuel tank environment. The FBG system has already been developed to an aerospace compliant prototype and is due to be tested at the fuel testing facility based at Airbus, Filton, UK. It is envisaged by the author that in both application areas, continued research in this area will lead to the eventual development of marketable commercial products.

Multi-level optimization of a fiber transmission system via nonlinearity management

linearity management is explored as a complete tool to obtain maximum transmission reach in a WDM fiber transmission system, making it possible to optimize multiple system parameters, including optimal dispersion pre-compensation, with fast simulations based on the continuous-wave approximation.

Implementation and characterization of liquid-level sensor based on a long-period fiber grating Mach-Zehnder interferometer

An optical liquid-level sensor (LLS) based on a long-period fiber grating (LPG) interferometer is proposed and experimentally demonstrated. Two identical 3-dB LPGs are fabricated to form an in-fiber Mach-Zehnder interferometer, and the fiber portion between two LPGs is exposed to the liquid as the sensing element. The sensitivity and measurement range of the sensors employing different orders of cladding modes are investigated both theoretically and experimentally. The experimental results show good linearity and large measurement range. One of the significant advantages of such a sensing structure is that the measurement level is not limited to the length of the LPG itself. Also, the measurement range and sensitivity of the proposed LLS can be readily tailored for a particular applications.