M.Sc. (Mathematical Statistics) / Stochastic Differential Equations (SDE’s) are commonly found in most of the modern finance used today. In this dissertation we use SDE’s to model a random phenomenon known as the short-term interest rate where the explanatory power of a particular short-term interest rate model is largely dependent on the description of the SDE to the real data. The challenge we face is that in most cases the transition density functions of these models are unknown and therefore, we need to find reliable and accurate alternative estimation techniques. In this dissertation, we discuss estimating techniques for discretely sampled continuous diffusion processes that do not require the true transition density function to be known. Moreover, the reader is introduced to the following techniques: (i) continuous time maximum likelihood estimation; (ii) discrete time maximum likelihood estimation; and (iii) estimating functions. We show through a Monte Carlo simulation study that the parameter estimates obtained from these techniques provide a good approximation to the estimates obtained from the true transition density. We also show that the bias in the mean reversion parameter can be reduced by implementing the jackknife bias reduction technique. Furthermore, the data analysis carried out on South-African interest rate data indicate strongly that single factor models do not explain the variability in the short-term interest rate. This may indicate the possibility of distinct jumps in the South-African interest rate market. Therefore, we leave the reader with the notion of incorporating jumps into a SDE framework.

In this thesis two collaborative localization techniques are studied: multidimensional scaling (MDS) and maximum likelihood estimator (MLE). A synthesis of a new location estimation method through a serial integration of these two techniques, such that an estimate is first obtained using MDS and then MLE is employed to fine-tune the MDS solution, was the subject of this research using various simulation and experimental studies. In the simulations, important issues including the effects of sensor node density, reference node density and different deployment strategies of reference nodes were addressed. In the experimental study, the path loss model of indoor environments is developed by determining the environment-specific parameters from the experimental measurement data. Then, the empirical path loss model is employed in the analysis and simulation study of the performance of collaborative localization techniques.

abstract: For the last 50 years, oscillator modeling in ranging systems has received considerable attention. Many components in a navigation system, such as the master oscillator driving the receiver system, as well the master oscillator in the transmitting system contribute significantly to timing errors. Algorithms in the navigation processor must be able to predict and compensate such errors to achieve a specified accuracy. While much work has been done on the fundamentals of these problems, the thinking on said problems has not progressed. On the hardware end, the designers of local oscillators focus on synthesized frequency and loop noise bandwidth. This does nothing to mitigate, or reduce frequency stability degradation in band. Similarly, there are not systematic methods to accommodate phase and frequency anomalies such as clock jumps. Phase locked loops are fundamentally control systems, and while control theory has had significant advancement over the last 30 years, the design of timekeeping sources has not advanced beyond classical control. On the software end, single or two state oscillator models are typically embedded in a Kalman Filter to alleviate time errors between the transmitter and receiver clock. Such models are appropriate for short term time accuracy, but insufficient for long term time accuracy. Additionally, flicker frequency noise may be present in oscillators, and it presents mathematical modeling complications. This work proposes novel H∞ control methods to address the shortcomings in the standard design of time-keeping phase locked loops. Such methods allow the designer to address frequency stability degradation as well as high phase/frequency dynamics. Additionally, finite-dimensional approximants of flicker frequency noise that are more representative of the truth system than the tradition Gauss Markov approach are derived. Last, to maintain timing accuracy in a wide variety of operating environments, novel Banks of Adaptive Extended Kalman Filters are used to address both stochastic and dynamic uncertainty. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2020

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Target tracking and trajectory prediction are state estimation applications. Popular state estimation techniques include the Kalman Filter (KF), Extended KF (EKF), Unscented KF (UKF), and the Particle Filter (PF). A limitation of these filters is that the model must be largely known; if this is violated, it may cause instability. A filter known as the Smooth Variable Structure Filter (SVSF) has been developed to address modeling errors. It is hypothesized that SVSFs will improve tracking and trajectory prediction performance due to their robustness against modeling uncertainties. To begin, two trajectory prediction algorithms for autonomous driving based on Interacting Multiple Model (IMM) estimation are developed. One combines the IMM and KF, called IMM-KF, and the other combines IMM with the Generalized Variable Boundary Layer - Smooth Variable Structure Filter (GVBL-SVSF), called IMM-GVBL-SVSF. The performance of both algorithms is comparatively analyzed using synthetic and real datasets. A comparison is made to machine learning strategies as well. Moreover, a general framework for SVSF formulation is proposed, putting a subset of SVSF variants under one umbrella. A strategy to combine nonlinear KFs with SVSFs is proposed, which results in six hybrid filters. Since a subset of SVSF variants can be discovered as special cases of these filters, the proposed framework puts these variants under one umbrella. The hybrid filters are applied to perform aircraft target tracking using synthetic radar measurements. Their performance is compared to the EKF, UKF, Cubature KF, PF, and other SVSFs. Furthermore, the covariance is reformulated for the Dynamic Second-Order Smooth Variable Structure Filter. A new PDAF is formulated that uses this covariance. An optimal filter that minimizes the trace of the covariance is also proposed. The new PDAF and the optimal filter are applied to perform aircraft tracking using synthetic radar data, and the performance is compared with other filters. / Thesis / Doctor of Philosophy (PhD) / This thesis proposes novel algorithms for state estimation, target tracking, and trajectory prediction. State estimation refers to estimating variables of a physical system (e.g. car, robot, airplane) that change over-time using sensor measurements. Examples of variables are position, velocity, and acceleration. These variables are state variables and the set of values together form the state. The state is the smallest set of variables that describe the past behavior of a system such that the system's future behavior can be predicted using these variables. The proposed state estimation methods are applied to perform target tracking. Target tracking involves estimating the state variables (e.g. position, velocity, acceleration) of moving objects detected by sensors such as radar, LIDAR, and camera. Trajectory prediction refers to estimating the future values of these variables in the next few seconds. This thesis also proposes trajectory prediction algorithms for autonomous driving, which utilize state estimation.

Lam Suet-man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 111-117). / Abstracts in English and Chinese. / ACKNOWOLEDGMENTS --- p.iii / LIST OF TABLES --- p.iv / LIST OF ILLUSTRATIONS --- p.vi / CHAPTER / Chapter ONE --- INTRODUCTION --- p.1 / Chapter TWO --- REVIEW OF THE LITERATURE --- p.6 / Parametric Models / Nonparametric Estimation Techniques / Chapter THREE --- METHODOLOGY --- p.21 / Parametric Models / Nonparametric Models / Chapter FOUR --- DATA DESCRIPTION --- p.33 / Chapter FIVE --- EMPIRICAL FINDINGS --- p.39 / Estimation Results / Evaluation of Model Performance / Out-of-sample Forecast Evaluation / Chapter SIX --- CONCLUSION --- p.58 / TABLES --- p.62 / ILLUSTRATIONS --- p.97 / APPENDIX --- p.107 / BIBOGRAPHY --- p.111

This thesis consists of three parts: a genetic fuzzy trading model for stock trading, incremental intraday information for financial time series forecasting, and intraday effects in conditional variance estimation. Part A investigates a genetic fuzzy trading model for stock trading. This part contributes to use a fuzzy trading model to eliminate undesirable discontinuities, incorporate vague trading rules into the trading model and use genetic algorithm to select an optimal trading ruleset. Technical indicators are used to monitor the stock price movement and assist practitioners to set up trading rules to make buy-sell decision. Although some trading rules have a clear buy-sell signal, the signals are always detected with 'hard' logical. These trigger the undesirable discontinuities due to the jumps of the Boolean variables that may occur for small changes of the technical indicator. Some trading rules are vague and conflicting. They are difficult to incorporate into the trading system while they possess significant market information. Various performance comparisons such as total return, maximum drawdown and profit-loss ratios among different trading strategies were examined. Genetic fuzzy trading model always gave moderate performance. Part B studies and contributes to the literature that focuses on the forecasting of daily financial time series using intraday information. Conventional daily forecast always focuses on the use of lagged daily information up to the last market close while neglecting intraday information from the last market close to current time. Such intraday information are referred to incremental intraday information. They can improve prediction accuracy not only at a particular instant but also with the intraday time when an appropriate predictor is derived from such information. These are demonstrated in two forecasting examples, predictions of daily high and range-based volatility, using linear regression and Neural Network forecasters. Neural Network forecaster possesses a stronger causal effect of incremental intraday information on the predictand. Predictability can be estimated by a correlation without conducting any forecast. Part C explores intraday effects in conditional variance estimation. This contributes to the literature that focuses on conditional variance estimation with the intraday effects. Conventional GARCH volatility is formulated with an additive-error mean equation for daily return and an autoregressive moving-average specification for its conditional variance. However, the intra-daily information doesn't include in the conditional variance while it should has implication on the daily variance. Using Engle's multiplicative-error model formulation, range-based volatility is proposed as an intraday proxy for several GARCH frameworks. The impact of significant changes in intraday data is reflected in the MEM-GARCH variance. For some frameworks, it is possible to use lagged values of range-based volatility to delay the intraday effects in the conditional variance equation. / Ng, Hoi Shing Raymond. / Adviser: Kai-Pui Lam. / Source: Dissertation Abstracts International, Volume: 72-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 107-114). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

This thesis consists of four chapters. Chapter 1 focuses on theoretical results on high-order laplacian-based regularization in function estimation. We studied the iterated laplacian regularization in the context of supervised learning in order to achieve both nice theoretical properties (like thin-plate splines) and good performance over complex region (like soap film smoother). In Chapter 2, we propose an innovative static path-planning algorithm called m-A* within an environment full of obstacles. Theoretically we show that m-A* reduces the number of vertex. In the simulation study, our approach outperforms A* armed with standard L1 heuristic and stronger ones such as True-Distance heuristics (TDH), yielding faster query time, adequate usage of memory and reasonable preprocessing time. Chapter 3 proposes m-LPA* algorithm which extends the m-A* algorithm in the context of dynamic path-planning and achieves better performance compared to the benchmark: lifelong planning A* (LPA*) in terms of robustness and worst-case computational complexity. Employing the same beamlet graphical structure as m-A*, m-LPA* encodes the information of the environment in a hierarchical, multiscale fashion, and therefore it produces a more robust dynamic path-planning algorithm. Chapter 4 focuses on an approach for the prediction of spot electricity spikes via a combination of boosting and wavelet analysis. Extensive numerical experiments show that our approach improved the prediction accuracy compared to those results of support vector machine, thanks to the fact that the gradient boosting trees method inherits the good properties of decision trees such as robustness to the irrelevant covariates, fast computational capability and good interpretation.

The ability to implement Wide Area Monitoring and Control in power systems is developing into a need in order to prevent wide scale cascading outages. Monitoring of events in the power system provides a great deal of insight into the behaviour of the system. The research work presented in this thesis focussed on two tools that aid in monitoring: State Estimation and Synchronised Phasors provided by Phasor Measurement Units (PMU). State Estimation is essentially an on-line data processing scheme used to estimate the best possible state (i.e. voltage phasors) from a monitored set of measurements (active and reactive powers/voltage phasor measurements). The ever growing complexity and developments in the state of art calls for robust state estimators that converge accurately and rapidly. Newton’s method forms the basis for most of the solution approaches. For real-time application in modern power systems, the existing Newton-based state estimation algorithms are too fragile numerically. It is known that Newton’s algorithm may fail to converge if the initial nominal point is far from the optimal point. Sometimes Newton’s algorithm can converge to a local minima. Also Newton’s step can fail to be a descent direction if the gain matrix is nearly singular or ill-conditioned. This thesis proposes a new and more robust method that is based on linear programming and trust region techniques. The proposed formulation is suitable for Upper Bound Linear Programming. The formulation is first introduced and its convergence characteristics with the use of Upper Bound Linear Programming is studied. In the subsequent part, the solution to the same formulation is obtained using trust region algorithms. Proposed algorithms have been tested and compared with well known methods. The trust region method-based state estimator is found to be more reliable. This enhanced reliability justifies the additional time and computational effort required for its execution. One of the key elements in the synchrophasor based wide area monitoring is the Phasor Measurement Unit. Synchronized, real time, voltage phasor angle, phasor measurements over a distributed power network presents an excellent opportunity for major improvements in power system control and protection. Two of the most significant applications include state estimation and instability prediction. In recent years, there has been a significant research activity on the problem of finding the suitable number of PMUs and their optimal locations. For State Estimation, such procedures, which basically ensure observability based on network topology, are sufficient. However for instability prediction, it is very essential that the PMUs are located such that important/vulnerable buses are also directly monitored. In this thesis a method for optimal placement of PMUs, considering the vulnerable buses is developed. This method serves two purposes viz., identifying optimal locations for PMU (planning stage), and identifying the set PMUs to be closely monitored for instability prediction. The major issue is to identify the key buses when the angular and voltage stability prediction is taken into account. Integer Linear Programming technique with equality and inequality constraints is used to find out the optimal placement set. Further, various aspects of including the Phasor Measurements in state estimation algorithms are addressed. Studies are carried out on various sample test systems, an IEEE 30-bus system and real life Indian southern grid equivalents of 24-bus system, 72-bus system and 205-bus system.

To overcome the curse of dimensionality, dimension reduction is important and necessary for understanding the underlying phenomena in a variety of fields. Dimension reduction is the transformation of high-dimensional data into a meaningful representation in the low-dimensional space. It can be further classified into feature selection and feature extraction. In this thesis, which is composed of four projects, the first two focus on feature selection, and the last two concentrate on feature extraction. The content of the thesis is as follows. The first project presents several efficient methods for the sparse representation of a multiple measurement vector (MMV); some theoretical properties of the algorithms are also discussed. The second project introduces the NP-hardness problem for penalized likelihood estimators, including penalized least squares estimators, penalized least absolute deviation regression and penalized support vector machines. The third project focuses on the application of manifold learning in the analysis and prediction of 24-hour electricity price curves. The last project proposes a new hessian regularized nonlinear time-series model for prediction in time series.