[pt] O objetivo deste trabalho é apresentar alguns resultados referentes ao estudo da sensibilidade da reposta impulsional de sistemas lineares, causais, a tempo discreto e monovariáveis a aproximações nos coeficientes das equações a diferenças finitas que os representam. São estudados primeiramente sistemas variantes no tempo representados por matrizes de estado nas formas canônicas diagonal e de Jordan, sendo analisado o caso invariante como uma particularização. Tais formas canônicas permitem obter diretamente a sensibilidade da resposta impulsional do sistema em relação aos autovalores, que são, no caso de invariância, os pólos do mesmo. A seguir são tratados sistemas variantes no tempo com equações de diferenças finitas de forma qualquer, explorando-se funções de dependência entre os diversos coeficientes. Todo o estudo é baseado em técnicas do domínio do tempo e álgebra matricial. A impossibilidade de se trabalhar de modo simples no domínio da freqüência com sistemas variantes, fez com que este não fosse utilizado nem nos casas particulares da classe mais geral dos sistemas variantes. / [en] The objective of this work is to present some results on the sensitivity of the weighting sequence (impulse response) of linear, causal, monovariable, discrete-time systems to approximations of the coefficients of the difference equations that model them. The first part of the work is devoted to systems represented in canonical representations diagonal and Jordan forms; the time-invariant case is studied as a particularization. These canonical forms allow the sensitivity to be determined as a function of the model eigenvalues and, in the time-invariant case, of the poles of the transfer function. The second part addresses systems represented in general forms. The whole work is based on time-domain techniques. Frequency-domain techniques were not used due to the fact that they are more difficult than in the time-invariant case.

A modelagem da estrutura de dependência é de grande importância em todos os ramos da economia onde há incerteza. Ela é um elemento crucial na análise de risco e para a tomada de decisão sob incerteza. As cópulas oferecem aos agentes que se deparam com este problema um poderoso e flexível instrumento para modelar a estrutura de dependência entre variáveis aleatórias e que é preferível ao instrumento tradicional baseado na correlação linear. Neste estudo, nós analisamos a dinâmica temporal da estrutura de dependência entre índices de mercados financeiros internacionais e propomos um novo procedimento para capturar a estrutura de dependência ao longo do tempo. Adicionalmente, estudamos alguns fatos estilizados sobre índices de mercados financeiros como a relação entre volume-volatilidade e retorno-volatilidade. / Modelling dependence is of key importance to all economic fields in which uncertainty plays a large role. It is a crucial element of risk analysis and decision making under uncertainty. Copulas offer economic agents facing uncertainty a powerful and flexible tool to model dependence between random variables and often are preferable to the traditional, correlation-based approach. In this work we analyze the time dynamics of the dependence structure between broad stock market indices and propose a novel procedure to capture dependence structure over time. Additionally, we study some stylized facts about stock market indexes such as volume-volatility and return-volatility relations.

A modelagem da estrutura de dependência é de grande importância em todos os ramos da economia onde há incerteza. Ela é um elemento crucial na análise de risco e para a tomada de decisão sob incerteza. As cópulas oferecem aos agentes que se deparam com este problema um poderoso e flexível instrumento para modelar a estrutura de dependência entre variáveis aleatórias e que é preferível ao instrumento tradicional baseado na correlação linear. Neste estudo, nós analisamos a dinâmica temporal da estrutura de dependência entre índices de mercados financeiros internacionais e propomos um novo procedimento para capturar a estrutura de dependência ao longo do tempo. Adicionalmente, estudamos alguns fatos estilizados sobre índices de mercados financeiros como a relação entre volume-volatilidade e retorno-volatilidade. / Modelling dependence is of key importance to all economic fields in which uncertainty plays a large role. It is a crucial element of risk analysis and decision making under uncertainty. Copulas offer economic agents facing uncertainty a powerful and flexible tool to model dependence between random variables and often are preferable to the traditional, correlation-based approach. In this work we analyze the time dynamics of the dependence structure between broad stock market indices and propose a novel procedure to capture dependence structure over time. Additionally, we study some stylized facts about stock market indexes such as volume-volatility and return-volatility relations.

This thesis is comprised of three independent essays. One essay is in the field of macroeconomics and the other two are in time-series econometrics. The first essay, "Productivity and Business Investment over the Business Cycle", is co-authored with my co-supervisor Hashmat Khan. This essay documents a new stylized fact: the correlation between labour productivity and real business investment in the U.S. data switching from 0.54 to -0.1 in 1990. With the assistance of a bivariate VAR, we find that the response of investment to identified technology shocks has changed signs from positive to negative across two sub-periods: ranging from the time of the post-WWII era to the end of 1980s and from 1990 onwards, whereas the response to non-technology shocks has remained relatively unchanged. Also, the volatility of technology shocks declined less relative to the non-technology shocks. This raises the question of whether relatively more volatile technology shocks and the negative response of investment can together account for the decreased correlation. To answer this question, we consider a canonical DSGE model and simulate data under a variety of assumptions about the parameters representing structural features and volatility of shocks. The second and third essays are in time series econometrics and solely authored by myself. The second essay, however, focuses on the impact of ignoring structural breaks in the conditional volatility parameters on time-varying volatility parameters. The focal point of the third essay is on empirical relevance of structural breaks in time-varying volatility models and the forecasting gains of accommodating structural breaks in the unconditional variance. There are several ways in modeling time-varying volatility. One way is to use the autoregressive conditional heteroskedasticity (ARCH)/generalized ARCH (GARCH) class first introduced by Engle (1982) and Bollerslev (1986). One prominent model is Bollerslev (1986) GARCH model in which the conditional volatility is updated by its own residuals and its lags. This class of models is popular amongst practitioners in finance because they are able to capture stylized facts about asset returns such as fat tails and volatility clustering (Engle and Patton, 2001; Zivot, 2009) and require maximum likelihood methods for estimation. They also perform well in forecasting volatility. For example, Hansen and Lunde (2005) find that it is difficult to beat a simple GARCH(1,1) model in forecasting exchange rate volatility. Another way of modeling time-varying volatility is to use the class of stochastic volatility (SV) models including Taylor's (1986) autoregressive stochastic volatility (ARSV) model. With SV models, the conditional volatility is updated only by its own lags and increasingly used in macroeconomic modeling (i.e.Justiniano and Primiceri (2010)). Fernandez-Villaverde and Rubio-Ramirez (2010) claim that the stochastic volatility model fits better than the GARCH model and is easier to incorporate into DSGE models. However, Creal et al. (2013) recently introduced a new class of models called the generalized autoregressive score (GAS) models. With the GAS volatility framework, the conditional variance is updated by the scaled score of the model's density function instead of the squared residuals. According to Creal et al. (2013), GAS models are advantageous to use because updating the conditional variance using the score of the log-density instead of the second moments can improve a model's fit to data. They are also found to be less sensitive to other forms of misspecification such as outliers. As mentioned by Maddala and Kim (1998), structural breaks are considered to be one form of outliers. This raises the question about whether GAS volatility models are less sensitive to parameter non-constancy. This issue of ignoring structural breaks in the volatility parameters is important because neglecting breaks can cause the conditional variance to exhibit unit root behaviour in which the unconditional variance is undefined, implying that any shock to the variance will not gradually decline (Lamoureux and Lastrapes, 1990). The impact of ignoring parameter non-constancy is found in GARCH literature (see Lamoureux and Lastrapes, 1990; Hillebrand, 2005) and in SV literature (Psaradakis and Tzavalis, 1999; Kramer and Messow, 2012) in which the estimated persistence parameter overestimates its true value and approaches one. However, it has never been addressed in GAS literature until now. The second essay uses a simple Monte-Carlo simulation study to examine the impact of neglecting parameter non-constancy on the estimated persistence parameter of several GAS and non-GAS models of volatility. Five different volatility models are examined. Of these models, three --the GARCH(1,1), t-GAS(1,1), and Beta-t-EGARCH(1,1) models -- are GAS models, while the other two -- the t-GARCH(1,1) and EGARCH(1,1) models -- are not. Following Hillebrand (2005) who studied only the GARCH model, this essay examines the extent of how biased the estimated persistence parameter are by assessing impact of ignoring breaks on the mean value of the estimated persistence parameter. The impact of neglecting parameter non-constancy on the empirical sampling distributions and coverage probabilities for the estimated persistence parameters are also studied in this essay. For the latter, studying the effect on the coverage probabilities is important because a decrease in coverage probabilities is associated with an increase in Type I error. This study has implications for forecasting. If the size of an ignored break in parameters is small, then there may not be any gains in using forecast methods that accommodate breaks. Empirical evidence suggests that structural breaks are present in data on macro-financial variables such as oil prices and exchange rates. The potentially serious consequences of ignoring a break in GARCH parameters motivated Rapach and Strauss (2008) and Arouri et al. (2012) to study the empirical relevance of structural breaks in the context of GARCH models. However, the literature does not address the empirical relevance of structural breaks in the context of GAS models. The third and final essay contributes to this literature by extending Rapach and Strauss (2008) to include the t-GAS model and by comparing its performance to that of two non-GAS models, the t-GARCH and SV models. The empirical relevance of structural breaks in the models of volatility is assessed using a formal test by Dufour and Torres (1998) to determine how much the estimated parameters change over sub-periods. The in-sample performance of all the models is analyzed using both the weekly USD trade-weighted index between January 1973 and October 2016 and spot oil prices based on West Texas Intermediate between January 1986 and October 2016. The full sample is split into smaller subsamples by break dates chosen based on historical events and policy changes rather than formal tests. This is because commonly-used tests such as CUSUM suffer from low power (Smith, 2008; Xu, 2013). For each sub-period, all models are estimated using either oil or USD returns. The confidence intervals are constructed for the constant of the conditional parameter and the score parameter (or ARCH parameter in GARCH and t-GARCH models). Then Dufour and Torres's union-intersection test is applied to these confidence intervals to determine how much the estimated parameter change over sub-periods. If there is a set of values that intersects the confidence intervals of all sub-periods, then one can conclude that the parameters do not change that much. The out-of-sample performance of all time-varying volatility models are also assessed in the ability to forecast the mean and variance of oil and USD returns. Through this analysis, this essay also addresses whether using models that accommodate structural breaks in the unconditional variance of both GAS and non-GAS models will improve forecasts.

Advances in machine condition monitoring technologies are driven by the rise in complexity of modern machines and the increased demand for product reliability. Condition monitoring research tends to focus on the development of signal processing algorithms that are sensitive to machine faults, robust under time-varying operating conditions, and informative regarding the nature and extent of machine faults. A significant challenge remains for monitoring the condition of machines that are subject to time-varying operating conditions. The here presented work is concerned with the development of cost effective condition monitoring algorithms. It is investigated how empirical models (including probability density distributions and regression functions) may be used to extract diagnostic information from machine response signals that have been generated under fluctuating operating conditions. The proposed methodology is investigated on a number of case studies, including gearboxes, alternator end windings, and haul roads. It is shown how empirical models for machine condition monitoring may generally be implemented according to one of two basic approaches. The two approaches are referred to as discrepancy analysis and waveform reconstruction. Discrepancy analysis is concerned with the comparison of a novel signal to a reference model. The reference model is sufficiently expressive to represent vibration response as measured on a healthy machine over a range of operating conditions. The novel signal is compared to the reference model in such a manner that a discrepancy signal transform is obtained. A discrepancy signal is sensitive to faults, robust to time-varying operating conditions, and inherently simple. As such it may further beWaveform reconstruction implements a regression function to model machine response as a function of different state space variables. The regression function may subsequently be exploited to extract diagnostic information. The machine response may for instance be reconstructed at a specified steady state operating condition. This renders the signal wide-sense stationary so that Fourier analysis may be applied. analysed in order to extract periodicities and magnitudes as diagnostic markers. / Dissertation (MEng)--University of Pretoria, 2013. / gm2014 / Electrical, Electronic and Computer Engineering / unrestricted

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The thesis focuses on the social web and on the analysis of social networks with particular emphasis on their temporal aspects. Social networks are represented here by Time Varying Graphs (TVG), a general model for dynamic graphs borrowed from distributed computing. In the first part of the thesis we focus on the temporal aspects of social networks. We develop various temporal centrality measures for TVGs including betweenness, closeness, and eigenvector centralities, which are well known in the context of static graphs. Unfortunately the computational complexities of these temporal centrality metrics are not comparable with their static counterparts. For example, the computation of betweenness becomes intractable in the dynamic setting. For this reason, approximation techniques will also be considered. We apply these temporal measures to two very different datasets, one in the context of knowledge mobilization in a small community of university researchers, the other in the context of Facebook commenting activities among a large number of web users. In both settings, we perform a temporal analysis so to understand the importance of the temporal factors in the dynamics of those networks and to detect nodes that act as “accelerators”. In the second part of the thesis, we focus on a more standard static graph representation. We conduct a propagation study on YouTube datasets to understand and compare the propagation dynamics of two different types of users: subscribers and friends. Finally, we conclude the thesis with the proposal of a general framework to present, in a comprehensive model, the influence of the social web on e-commerce decision making.

Introduction: Clostridium difficile infection (CDI) is a common hospital-acquired infection and a financial burden on the healthcare system. There is a need to reduce its impact on patients and the entire health system. More accurate estimates of the financial impact of CDI will assist hospitals in creating better CDI reduction strategies with limited resources. Previous research has not sufficiently accounted for the skewed nature of hospital cost data, baseline patient mortality risk, and the time-varying nature of CDI. Objective: We conducted a retrospective cohort study to estimate the cost impact of hospital-acquired CDI from the hospital perspective, using a number of analytical approaches. Method: We used clinical and administrative data for inpatients treated at The Ottawa Hospital to construct an analytical data set. Our primary outcome was direct costs and our primary exposure was hospital-acquired CDI. We performed the following analyses: Ordinary least square regression and generalized linear regression as time-fixed methods, and Kaplan-Meier survival curve and Cox regression models as time-varying methods. Results: A total of 49,888 admissions were included in this study (mean (SD) age of 64.6 ± 17.8 years, median (IQR) baseline mortality risk of 0.04 (0.01-0.14)). 360 (0.73%) patients developed CDI. Estimates of incremental cost due to CDI were substantially higher when using time-fixed methods than time-varying methods. Using methods that appropriately account for the time-varying nature of the exposure, the estimated incremental cost due to CDI was $8,997 per patient. In contrast, estimates from time-fixed methods ranged from $49,150 to $55,962: about a six fold difference. Conclusion: Estimates of hospital costs are strongly influenced by the time-varying nature of CDI as well as baseline mortality risk. If studies do not account for these factors, it is likely that the impact of hospital-acquired CDI will be overestimated.

The primary purpose of this thesis was to investigate if the modern Phillips Curve is valid for ASEAN five (Indonesia, Malaysia, Thailand, Singapore and Philippines) countries using a time-varying approach in the form of an ARMA-GARCH model. The method enables us to investigate how the inflation volatility reacts to economic shocks and if its history can predict the conditional variance of inflation. This study also aimed to investigate whether financial liberalisation affects the conditional variance of inflation. Moreover, we introduce a new parameter into the Phillips Curve. We propose the inclusion of a globally decomposed financial spillover index to see how it affects the inflation dynamics. Examining the period between 1996-2020, using monthly data. We find weak results, and the Phillips Curve was only valid for Singapore. Our findings also suggest that the inflation volatility is highly time-varying, indicating the suitability of the ARMA-GARCH framework. Significant coefficients in the model allow forecasting the conditional variance of inflation. The results support the idea that financial liberalisation to be volatility augmenting in some countries, suggesting a negative relationship between the degree of financial integration and received spillover effects. The globally decomposed spillover indices demonstrated weak results. For further investigations, we, therefore, propose the usage of regionally decomposed spillover indices.

Vibration-based condition monitoring is a key and crucial element for asset longevity and to avoid unexpected financial compromise. Currently, data-driven methodologies often require significant investments into data acquisition and a large amount of operational data for both healthy and unhealthy cases. The acquisition of unhealthy fault data is often financially infeasible and the result is that most methods detailed in literature are not suitable for critical industrial applications. In this work, unsupervised latent variable models negate the requirement for asset fault data. These models operate by learning the representation of healthy data and utilise health indicators to track deviance from this representation. A variety of latent variable models are compared, namely: Principal Component Analysis, Variational Auto-Encoders and Generative Adversarial Network-based methods. This research investigated the relationship between time-series data and latent variable model design under the sensible notion of data interpretation, the influence of model complexity on result performance on different datasets and shows that the latent manifold, when untangled and traversed in a sensible manner, is indicative of damage. Three latent health indicators are proposed in this work and utilised in conjunction with a proposed temporal preservation approach. The performance is compared over the different models. It was found that these latent health indicators can augment standard health indicators and benefit model performance. This allows one to compare the performance of different latent variable models, an approach that has not been realised in previous work as the interpretation of the latent manifold and the manifold response to anomalous instances had not been explored. If all aspects of a latent variable model are systematically investigated and compared, different models can be analysed on a consistent platform. In the model analysis step, a latent variable model is used to evaluate the available data such that the health indicators used to infer the health state of an asset, are available for analysis and comparison. The datasets investigated in this work consist of stationary and time-varying operating conditions. The objective was to determine whether deep learning is comparable or on par with state-of-the-art signal processing techniques. The results showed that damage is detectable in both the input space and the latent space and can be trended to identify clear condition deviance points. This highlights that both spaces are indicative of damage when analysed in a sensible manner. A key take away from this work is that for data that contains impulsive components that manifest naturally and not due to the presence of a fault, the anomaly detection procedure may be limited by inherent assumptions made in model formulations concerning Gaussianity. This work illustrates how the latent manifold is useful for the detection of anomalous instances, how one must consider a variety of latent-variable model types and how subtle changes to data processing can benefit model performance analysis substantially. For vibration-based condition monitoring, latent variable models offer significant improvements in fault diagnostics and reduce the requirement for expert knowledge. This can ultimately improve asset longevity and the investment required from businesses in asset maintenance. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2020. / Eskom Power Plant Engineering Institute (EPPEI) / UP Postgraduate Bursary / Mechanical and Aeronautical Engineering / MEng (Mechanical Engineering) / Unrestricted