The work presented in this dissertation can be grouped around two major themes. The first theme relates to the asset allocation and the second theme relates to risk management. In Chapter Three, we investigate the dynamics of foreign exchange and stock returns based on an extended version of Sentana and Wadhwani (1992) model. This study is mainly driven by the wish to explain two major stylized facts that puzzled the older models. We find evidence to support that only intertemporal variation in the foreign exchange risk premium can be explained by time¡Vvarying covariance priced risk factors. Furthermore, we also find that the first order autocorrelation of both foreign exchange and stock market returns in Taiwan is negatively related to the level of conditional volatility and covariance. This time-varying nature of the serial correlation pattern is consistent with our model where some traders follow feedback strategies. The three nested asset pricing models with four models of conditional second moments are strongly rejected. We conclude that our extended Sentana and Wadhwani model is more adequate in explaining the dynamics of foreign exchange and stock markets. In Chapter Four, we investigate the risk management of futures market and spot market returns. There is widespread evidence that the volatility of stock returns display an asymmetric response to good and bad news. This paper attempted and found the asymmetric behavior co-existence in spot as well as future markets. By using the Asymmetric Dynamic Model (ADC) proposed by Kroner and Ng (1998), we estimated the conditional covariance matrix asymmetric and calculated dynamic optimal hedge ratios. With the help of that asymmetric model, our ¡§out of sample¡¨ dynamic hedging strategy out-performed that of normally dynamic hedging strategies. However, while taking the transaction costs into consideration, the performance was even worse than that of the static strategy.

Precision orbit determination (POD) plays a vital role in the success of space-borne laser altimetry missions, such as ICESat (Ice, Cloud, and Land Elevation Satellite). Although current ICESat POD processing standards are achieving remarkable accuracy, new time-varying geopotential models derived from the GRACE (Gravity Recovery And Climate Experiment) mission were investigated as candidates to improve POD performance for the planned ICESat-2 mission. The objective of this research is to examine the effect of these time-varying geopotential models -- which include models of non-tidal atmospheric and ocean variability, seasonal variability caused by water mass motion, and secular variations caused by present-day ice-melt and glacial isostatic adjustment -- on ICESat POD. The quality of the POD solutions produced with the new geopotential models was quantified by examining the usual orbit quality tests -- DDHL (double-differenced high-low) and SLR (satellite laser ranging) observation residuals and orbit overlaps. Although the solutions produced in every test case indicated consistency and high accuracy of 1-2 cm, these metrics were rather insensitive to the small changes in the POD solutions induced by the new geopotential models, and were incapable of identifying any statistically significant improvements in the POD. However, examination of geographically correlated radial orbit perturbations showed that the radial orbit differences exhibited significant variability on the order of several millimeters, and were coherent with the temporal variability of the models implemented. Since radial orbit errors directly relate to the scientific quantities of interest in the ICESat mission -- the altimetry measurements and derived ice-sheet surface elevations -- this result is of obvious importance. The most notable effects included an annual radial orbit variation of up to 4 mm over the Amazon region induced by implementing the GRACE Annual model, and a secular variation of radial orbit differences over Greenland when the GRACE Trend model was applied. The effect of radial orbit error on ice-sheet altimetry was quantified by examining the mean geographically correlated radial orbit differences. Since the ice sheet elevation rates computed by ICESat scientists are on the order of tens of centimeters per year, it was concluded that, although the radial orbit perturbations are readily observable, with magnitudes on the order of a few millimeters they are too small to have a significant impact on the altimetry science. However, depending on the scientific objectives and radial orbit accuracy requirements set for ICESat-2, these effects may be important, and the use of time-varying geopotential models in ICESat-2 POD may be beneficial. / text

This thesis is an effort to develop generalized dynamic models for systems with time-varying time delays. Unlike the simple time-delay model characterized by a transportation lag in the case of a fixed time delay, time-varying delays exhibit quite different characteristics, making the development of easy to use models a difficult endeavor. First an algorithm is developed to predict the actual input-output behavior when the input signal is directly fed into a device that characterizes the time-varying delay. Input-output behaviour generated with this algorithm serves as the truth model for subsequent approximate model development. Simulation results for different classes of delay and different inputs were obtained using the truth model. The input functions were limited to steps, ramps and sinusoids. This limited class of inputs and delays defines the scope of this thesis and the results are to be interpreted as such. The methodology adopted to identify the basic underpinnings of models was system identification where input-output data came from the truth model. Models for the aforementioned classes of inputs and delays were then derived using elementary system identification tools. These models were then carefully analyzed to extract trends by changing the delay parameter. A satisfactory trend was observed in the case of linearly varying time delay. A generalized model for the linearly varying time delay with step and polynomial inputs was developed. An attempt was also made at developing a generalized model for sinusoidally time-varying time delays. This study proposes a model for linearly time-varying time delay, whose structure is not surprisingly also dependent on the class of inputs. It is shown that the derived model reduces to the well known model in the case of a fixed delay.

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In adaptive control the goal is to deal with systems that have unknown and/or time-varying parameters. Adaptive control techniques have been developed since 1950’s and most results were proven in the cases when the time-variations were non-existent or slow. However the results pertaining to systems with fast time-variations are still limited, in particular, when it comes to plants with unstable zero dynamics. In this work we adopt the controller design technique from the area of gain scheduling, where the time-varying parameter is assumed to be measurable. We propose the design of a nonlinear periodic controller, where in each period the state and parameter values are estimated and an appropriate stabilizing control signal is applied. It is shown that the closed loop system is stable under fast parameter variations with persistent jumps: the trajectory of the closed loop state in response to the initial condition is bounded by a decaying exponential plus a gain times the size of the noise. Our approach imposes several constraints on the plant; however, we show that there exists at least one interesting class of systems, which includes plants with unstable zero dynamics, that can be stabilized by our controller.

Every auditory event provides an information-rich signal to the brain. The signal constitutes perceptual attributes of pitch, loudness, timbre, and also, conceptual attributes like location, emotions, meaning, etc. In the present work we examine the timbre perception of time-varying signals in particular. While stationary signal timbre, by-itself is complex perceptually, the time-varying signal timbre introduces an evolving pattern, adding to its multi-dimensionality. To characterize timbre, we conduct psycho-acoustic perception tests with normal-hearing human subjects. We focus on time-varying synthetic speech signals(can be extended to music) because listeners are perceptually consistent with speech. Also, we can parametrically control the timbre and pitch glides using linear time-varying models. In order to quantify the timbre change in time-varying signals, we define the JND(Just noticeable difference) of timbre using diphthongs, synthesized using time-varying formant frequency model. The diphthong JND is defined as a two dimensional contour on the plane of percentage change of formant frequencies of terminal vowels. Thus, we simplify the perceptual probing to a lower dimensional space, i.e, 2-D even for a diphthong, which is multi-parametric. We also study the impact of pitch glide on the timbre JND of the diphthong. It is observed that timbre JND is influenced by the occurrence of pitch glide. Focusing on the magnitude of perceptual timbre change, we design a MUSHRA-like listening test using the vowel continuum in the formant-frequency space. We provide explicit anchors for reference: 0% and 100%, thus quantifying the perceptual timbre change on a 1-D scale. We also propose an objective measure of timbre change and observe that there is good correlation between the objective measure and subjective human responses of percentage timbre change. Using the above experimental methodology, we studied the influence of pitch shift on timbre perception and observed that the perceptual timbre change increases with change in pitch. We used vowels and diphthongs with 5 different types of pitch glides-(i) Constant pitch,(ii) 3-semitone linearly-up,(iii) 3 semitone linearly-down, (iv)V–like pitch glide and (v) hat-like pitch glide. The present study shows that timbre change can be measured on a 1-D scale if the perturbation is along one-dimension. We observe that for bright vowels(/a/and/i/), linearly decreasing pitch glide(dull pitch glide)causes more timbre change than linearly increasing pitch glide(bright pitch glide).For dull vowels(/u/),it is vice-versa. To summarize, in congruent pitch glides cause more perceptual timbre change than congruent pitch glides.(Congruent pitch glide implies bright pitch glide in bright vowel or dull pitch glide in dull vowel and in congruent pitch glide implies bright pitch glide in dull vowel or dull pitch glide in bright vowel.) Experiments with quadratic pitch glides show that the decay portion of pitch glide affects timbre perception more than the attack portion in short duration signals with less or no sustained part. In case of time-varying timbre, bright diphthongs show patterns similar to bright vowels. Also, for bright diphthongs(/ai/), perceived timbre change is most with decreasing pitch glide(dull pitch glide). We also observed that listeners perceive more timbre change in constant pitch than in pitch glides, congruent with the timbre or pitch glides with quadratic changes. The main conclusion of this study is that pitch and timbre do interact and in congruent pitch glides cause more timbre change than congruent pitch glides. In the case of quadratic pitch glides, listener perception of vowels is influenced by the decay than the attack in pitch glide in short duration signals. In the case of time-varying timbre also, in congruent pitch glides cause the most timbre change, followed by constant pitch glide. For congruent pitch glides and quadratic pitch glides in time-varying timbre, the listeners perceive lesser timbre change than otherwise.

Over the past several decades our understanding and meticulous characterization of the transient and spatial properties of materials evolved rapidly. The results present an exciting field for discovery, and craft materials to control and reshape light that we are just beginning to fathom. State-of-the-art nano-deposition processes, for example, can be utilized to build stratified waveguides made of thin dielectric layers, which put together result in a material with effective abnormal dispersion. Moreover, materials once deemed well known are revealing astonishing properties, v.gr. chalcogenide glasses undergo an atomic reconfiguration when illuminated with electrons or photons, this ensues in a temporal modification of its permittivity and permeability which could be used to build new Photonic Integrated Circuits.. This work revolves around the characterization and model of heterogeneous and time-varying materials and their applications, revisits Maxwell's equations in the context of nonlinear space- and time-varying media, and based on it introduces a numerical scheme that can be used to model waves in this kind of media. Finally some interesting applications for light confinement and beam transformations are shown.

Survival models are used in analysing time-to-event data. This type of data is very common in medical research. The Cox proportional hazard model is commonly used in analysing time-to-event data. However, this model is based on the proportional hazard (PH) assumption. Violation of this assumption often leads to biased results and inferences. Once non-proportionality is established, there is a need to consider time-varying effects of the covariates. Several models have been developed that relax the proportionality assumption making it possible to analyse data with time-varying effects of both baseline and time-updated covariates. I present various approaches for handling time-varying covariates and time-varying effects in time-to-event models. They include the extended Cox model which handles exogenous time-dependent covariates using the counting process formulation introduced by cite{andersen1982cox}. Andersen and Gill accounts for time varying covariates by each individual having multiple observations with the total-at-risk follow up for each individual being further divided into smaller time intervals. The joint models for the longitudinal and time-to-event processes and its extensions (parametrization and multivariate joint models) were used as it handles endogenous time-varying covariates appropriately. Another is the Aalen model, an additive model which accounts for time-varying effects. However, there are situations where all the covariates of interest do not have time-varying effects. Hence, the semi-parametric additive model can be used. In conclusion, comparisons are made on the results of all the fitted models and it shows that choice of a particular model to fit is influenced by the aim and objectives of fitting the model. In 2002, an AntiRetroviral Treatment (ART) service was established in the Cape Town township of Gugulethu, South Africa. These models will be applied to an HIV/AIDS observational dataset obtained from all patients who initiated ART within the programme between September 2002 and June 2007.

The majority of current smokers in the United States want to quit smoking; however, long-term abstinence rates do not improve beyond 30%, despite the availability of effective pharmaco-behavioral treatments and increased outreach of awareness programs on quitting benefits. One of the reasons is non-adherence to pharmacological treatment. Pharmacological treatments are developed to alleviate withdrawal symptoms experienced during a quit attempt. However, without continued treatment adherence, especially in the first few weeks of a quit attempt (when withdrawal symptoms fluctuate the most), the chances of relapse peak. Thus, adherence to pharmacological treatments must be improved to sustain long-term smoking abstinence. Moreover, smoking cessation is a complex and time-varying process. Therefore, the time-varying causal structure of adherence and smoking cessation must be studied carefully.The time-varying mechanisms underlying the smoking cessation process can be captured efficiently through intensive longitudinal data and quantified through appropriate methods. Mediation analysis is an efficient tool for studying such mechanisms. However, despite the time-varying nature of the data, existing approaches for assessing mediation provide overall average (in)direct effects over time and omit describing the temporal characteristic of the dynamic effect. This dissertation research aims to develop a new approach to estimating time-varying causal (in)direct effects of pharmacological treatments on daily smoking cessation outcome(s) mediated via daily treatment adherence. Additionally, it is hypothesized that adherence is influenced by daily stress events related to social contextual factors, not treatment-induced. The purpose of this research is to derive time-varying causal (in)direct effects. A local polynomial regression-based approach integrated with the mediational g-formula was proposed as a possible solution. Furthermore, since no other studies have studied time-specific mediation effects using a potential outcomes framework-based method, the performance of the proposed method was tested using two simulation studies. Finally, the optimum analytical approach (based on the findings from the simulation studies) was applied to answer the substantive research questions on smoking cessation using empirical data from a smoking cessation clinical trial. This dissertation is divided into six chapters. A brief overview of the chapters is as follows: Chapter 1 provides a comprehensive background and rationale for the methodological and substantive research that motivated this work. The chapter concludes with the three specific aims addressed in this research and a summary of the next steps. In Chapter 2, the longitudinal causal frameworks and the assumptions required to interpret the estimated time-varying (in)direct effects as causal are described in detail. These frameworks were further used in Chapters 3 and 4 for the two simulation studies that evaluated the performance of the proposed new approach. The simulation study in Chapter 3 evaluates the time-varying (in)direct effects in a longitudinal study in the absence of exposure-induced time-varying confounding of a mediator-outcome pathway. Four outcome scenarios with a binary exposure, a binary mediator, and a time-varying binary confounder of the mediator-outcome pathway were examined: 1) continuous outcome, 2) rare binary outcome, 3) common binary outcome, and 4) count outcome that is not zero-inflated. Two types of path-specific causal estimands are identifiable for these scenarios. The findings suggest good performance of the proposed analytical approach in producing accurate effect estimates (reduced bias and reasonable coverage) of these estimands for all the outcome scenarios. The simulation study in Chapter 4 evaluates the time-varying (in)direct effects in a longitudinal study in the presence of exposure-induced time-varying confounding of a mediator-outcome pathway. A zero-inflated count outcome scenario with a binary exposure, a binary mediator, and a time-varying binary confounder of the mediator-outcome pathway was examined. Four types of path-specific causal estimands are identifiable for this scenario, and the findings suggest good performance of the proposed analytical approach in producing accurate effect estimates. Chapter 5 uses the Wisconsin Smokers Health Study II data to assess the mechanisms via which pharmacological smoking cessation treatments affect the cessation-related outcome(s) in the presence of time-varying confounding that is not exposure induced. We found that individuals randomized to Nicotine Patch only group have better smoking cessation outcome(s) compared to individuals on Varenicline or combination Nicotine Replacement Therapy. This is due to better adherence among Nicotine Patch-only users. Finally, Chapter 6 presents the concluding remarks, including key findings from the three studies, limitations, and recommendations for future research. / Epidemiology