Thèses sur le sujet « Continuous-time stochastic models »
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1
Parra, Rojas César. « Intrinsic fluctuations in discrete and continuous time models ». Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/intrinsic-fluctuations-in-discrete-and-continuous-time-models(d7006a2b-1496-44f2-8423-1f2fa72be1a5).html.
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This thesis explores the stochastic features of models of ecological systems in discrete and in continuous time. Our interest lies in models formulated at the microscale, from which a mesoscopic description can be derived. The stochasticity present in the models, constructed in this way, is intrinsic to the systems under consideration and stems from their finite size. We start by exploring a susceptible-infectious-recovered model for epidemic spread on a network. We are interested in the case where the connectivity, or degree, of the individuals is characterised by a very broad, or heterogeneous, distribution, and in the effects of stochasticity on the dynamics, which may depart wildly from that of a homogeneous population. The model at the mesoscale corresponds to a system of stochastic differential equations with a very large number of degrees of freedom which can be reduced to a two-dimensional model in its deterministic limit. We show how this reduction can be carried over to the stochastic case by exploiting a time-scale separation in the deterministic system and carrying out a fast-variable elimination. We use simulations to show that the temporal behaviour of the epidemic obtained from the reduced stochastic model yields reasonably good agreement with the microscopic model under the condition that the maximum allowed degree that individuals can have is not too close to the population size. This is illustrated using time series, phase diagrams and the distribution of epidemic sizes. The general mesoscopic theory used in continuous-time models has only very recently been developed for discrete-time systems in one variable. Here, we explore this one-dimensional theory and find that, in contrast to the continuous-time case, large jumps can occur between successive iterates of the process, and this translates at the mesoscale into the need for specifying `boundary' conditions everywhere outside of the system. We discuss these and how to implement them in the stochastic difference equation in order to obtain results which are consistent with the microscopic model. We then extend the theoretical framework to make it applicable to systems containing an arbitrary number of degrees of freedom. In addition, we extend a number of analytical results from the one-dimensional stochastic difference equation to arbitrary dimension, for the distribution of fluctuations around fixed points, cycles and quasi-periodic attractors of the corresponding deterministic map. We also derive new expressions, describing the autocorrelation functions of the fluctuations, as well as their power spectrum. From the latter, we characterise the appearance of noise-induced oscillations in systems of dimension greater than one, which have been previously observed in continuous-time systems and are known as quasi-cycles. Finally, we explore the ability of intrinsic noise to induce chaotic behaviour in the system for parameter values for which the deterministic map presents a non-chaotic attractor; we find that this is possible for periodic, but not for quasi-periodic, states.
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Elerian, Ola. « Simulation estimation of continuous-time models with applications to finance ». Thesis, University of Oxford, 1999. https://ora.ox.ac.uk/objects/uuid:9538382d-5524-416a-8a95-1b820dd795e1.
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Over recent years, we have witnessed a rapid development in the body of economic theory with applications to finance. It has had great success in finding theoretical explanations to economic phenomena. Typically, theories are employed that are defined by mathematical models. Finance in particular has drawn upon and developed the theory of stochastic differential equations. These produce elegant and tractable frameworks which help us to better understand the world. To directly apply such theories, the models must be assessed and their parameters estimated. Implementation requires the estimation of the model's elements using statistical techniques. These fit the model to the observed data. Unfortunately, existing statistical methods do not work satisfactorily when applied to many financial models. These methods, when applied to complex models often yield inaccurate results. Consequently, simpler analytical models are often preferred, but these are typically unrealistic representations of the underlying process, given the stylised facts reported in the literature. In practical applications, data is observed at discrete intervals and a discretisation is typically used to approximate the continuous-time model. This can lead to biased estimates, since the true underlying model is assumed continuous. This thesis develops new methods to estimate these types of models, with the objective of obtaining more accurate estimates of the underlying parameters present. The methods are applicable to general models. As the solution to the true continuous process is rarely known for these applications, the methods developed rely on building an Euler-Maruyama approximate model and using simulation techniques to obtain the distribution of the unknown quantities of interest. We propose to simulate the missing paths between the observed data points to reduce the bias from the approximate model. Alternatively, one could use a more sophisticated scheme to discretise the process. Unfortunately, their implementation with simulation methods require us to simulate from the density and evaluate the density at any given point. This has until now only been possible for the Euler-Maruyama scheme. One contribution of the thesis is to show the existence of a closed form solution from use of the higher order Milstein scheme. The likelihood based method is implemented within the Bayesian paradigm, as in the context of these models, Bayesian methods are often analytically easier. Concerning the estimation methodology, emphasis is placed on simulation efficiency; design and implementation of the method directly affects the accuracy and stability of the results. In conjunction with estimation, it is important to provide inference and diagnostic procedures. Meaningful information from simulation results must be extracted and summarised. This necessitates developing techniques to evaluate the plausibility and hence the fit of a particular model for a given dataset. An important aspect of model evaluation concerns the ability to compare model fit across a range of possible alternatives. The advantage with the Bayesian framework is that it allows comparison across non-nested models. The aim of the thesis is thus to provide an efficient estimation method for these continuous-time models, that can be used to conduct meaningful inference, with their performance being assessed through the use of diagnostic tools.
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Casas, Villalba Isabel. « Statistical inference in continuous-time models with short-range and/or long-range dependence ». University of Western Australia. School of Mathematics and Statistics, 2006. http://theses.library.uwa.edu.au/adt-WU2006.0133.
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The aim of this thesis is to estimate the volatility function of continuoustime stochastic models. The estimation of the volatility of the following wellknown international stock market indexes is presented as an application: Dow Jones Industrial Average, Standard and Poor’s 500, NIKKEI 225, CAC 40, DAX 30, FTSE 100 and IBEX 35. This estimation is studied from two different perspectives: a) assuming that the volatility of the stock market indexes displays shortrange dependence (SRD), and b) extending the previous model for processes with longrange dependence (LRD), intermediaterange dependence (IRD) or SRD. Under the efficient market hypothesis (EMH), the compatibility of the Vasicek, the CIR, the Anh and Gao, and the CKLS models with the stock market indexes is being tested. Nonparametric techniques are presented to test the affinity of these parametric volatility functions with the volatility observed from the data. Under the assumption of possible statistical patterns in the volatility process, a new estimation procedure based on the Whittle estimation is proposed. This procedure is theoretically and empirically proven. In addition, its application to the stock market indexes provides interesting results.
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Stelzer, Robert Josef. « Multivariate continuous time stochastic volatility models driven by a Lévy process ». kostenfrei, 2007. http://mediatum2.ub.tum.de/doc/624065/document.pdf.
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Tingström, Victor. « Sequential parameter and state learning in continuous time stochastic volatility models using the SMC² algorithm ». Thesis, KTH, Matematisk statistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-177104.
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In this Master’s thesis, joint sequential inference of both parameters and states of stochastic volatility models is carried out using the SMC2 algorithm found in SMC2: an efficient algorithm for sequential analysis of state-space models, Nicolas Chopin, Pierre E. Jacob, Omiros Papaspiliopoulos. The models under study are the continuous time s.v. models (i) Heston, (ii) Bates, and (iii) SVCJ, where inference is based on options prices. It is found that the SMC2 performs well for the simpler models (i) and (ii), wheras filtering in (iii) performs worse. Furthermore, it is found that the FFT option price evaluation is the most computationally demanding step, and it is suggested to explore other avenues of computation, such as GPGPU-based computing.I denna Masteruppsats estimeras sekventiellt parametrar och tillstånd i stokastiska volatilitetsmodeller nyttjandes SMC2 -algoritmen som återfinns i [1]. Modellerna som studeras är de kontinuerliga s.v.-modellerna (i) Heston, (ii) Bates och (iii) SVCJ, där inferens baseras på optionspriser. Vi finner att SMC2 presterar bra resultat för de enklare modellerna (i) och (ii) emedan filtrering för (iii) presterar sämre. Vi finner ytterligare att det beräkningsmässigt tyngsta steget är optionsprissättning nyttjandes FFT, därför föreslås det att undersöka andra beräkningssätt, såsom GPGPU-beräkning
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Witte, Hugh Douglas. « Markov chain Monte Carlo and data augmentation methods for continuous-time stochastic volatility models ». Diss., The University of Arizona, 1999. http://hdl.handle.net/10150/283976.
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In this paper we exploit some recent computational advances in Bayesian inference, coupled with data augmentation methods, to estimate and test continuous-time stochastic volatility models. We augment the observable data with a latent volatility process which governs the evolution of the data's volatility. The level of the latent process is estimated at finer increments than the data are observed in order to derive a consistent estimator of the variance over each time period the data are measured. The latent process follows a law of motion which has either a known transition density or an approximation to the transition density that is an explicit function of the parameters characterizing the stochastic differential equation. We analyze several models which differ with respect to both their drift and diffusion components. Our results suggest that for two size-based portfolios of U.S. common stocks, a model in which the volatility process is characterized by nonstationarity and constant elasticity of instantaneous variance (with respect to the level of the process) greater than 1 best describes the data. We show how to estimate the various models, undertake the model selection exercise, update posterior distributions of parameters and functions of interest in real time, and calculate smoothed estimates of within sample volatility and prediction of out-of-sample returns and volatility. One nice aspect of our approach is that no transformations of the data or the latent processes, such as subtracting out the mean return prior to estimation, or formulating the model in terms of the natural logarithm of volatility, are required.
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Malloch, Hamish Jr. « The valuation of options on traded accounts : continuous and discrete time models ». Thesis, The University of Sydney, 2010. http://hdl.handle.net/2123/7239.
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In this thesis we are concerned with valuing options on traded accounts using both continuous and discrete time models. An option on a traded account is a zero strike call on the balance of a trading account which consists of a position of size $\theta$ in a risky asset (which we refer to as a stock) and the remaining wealth in a risk-free account. The choice of trading positions throughout the life of the option are made by the buyer, subject to constraints specified in the contract at the time of purchase. The specification of these trading constraints gives rise to some of the more well known examples including passport options and vacation options. At maturity, the option buyer is entitled to any positive wealth accumulated in the trading account whilst any losses are covered by the option seller. First, we examine the problem of valuing these options in continuous time. A review of some existing methods is presented, including a complete derivation of the pricing formula for the passport option and the option on a traded account following the methods proposed by Hyer et al. (1997) and Shreve and Vecer (2000), though we often use different techniques to those authors. We also present an alternative derivation for the value of a passport option using our own methodology which we believe is simpler than those currently available. Secondly, we consider the valuation problem in a discrete time setting by looking at one specific discrete time model, the binomial tree. This is a new contribution to the literature as binomial models for these options have not been previously examined. Using this approach, the greatest difficulty is the determination of an optimal trading strategy which is required to price this class of option. We show that in general, binomial models and continuous time models do not have the same trading strategy, and in fact that the analytic determination of the trading strategy for an option on a traded account may in fact be impossible to obtain. We then turn to passport options, where we are able to derive an analytic optimal strategy which in this case is identical to that used in the continuous time models, thus the problem of valuing passport options is reduced to the same computational burdens as a binomial valuation without recombining branches. Lastly, we examine some numerical methods which could be used to value options on traded accounts with binomial models. Our problem is shown to be an NP-hard convex maximisation which we convert into both an l1-norm convex maximisation and an indefinite quadratic program. Whilst we present algorithms which are guaranteed to obtain the optimal solution, they are also known to be inefficient and thus inappropriate for any likely application beyond a few time steps. We conclude by summarising our results and give directions for future research in this area.
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Tribastone, Mirco. « Scalable analysis of stochastic process algebra models ». Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4629.
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The performance modelling of large-scale systems using discrete-state approaches is fundamentally hampered by the well-known problem of state-space explosion, which causes exponential growth of the reachable state space as a function of the number of the components which constitute the model. Because they are mapped onto continuous-time Markov chains (CTMCs), models described in the stochastic process algebra PEPA are no exception. This thesis presents a deterministic continuous-state semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying mathematics for the performance evaluation. This is suitable for models consisting of large numbers of replicated components, as the ODE problem size is insensitive to the actual population levels of the system under study. Furthermore, the ODE is given an interpretation as the fluid limit of a properly defined CTMC model when the initial population levels go to infinity. This framework allows the use of existing results which give error bounds to assess the quality of the differential approximation. The computation of performance indices such as throughput, utilisation, and average response time are interpreted deterministically as functions of the ODE solution and are related to corresponding reward structures in the Markovian setting. The differential interpretation of PEPA provides a framework that is conceptually analogous to established approximation methods in queueing networks based on meanvalue analysis, as both approaches aim at reducing the computational cost of the analysis by providing estimates for the expected values of the performance metrics of interest. The relationship between these two techniques is examined in more detail in a comparison between PEPA and the Layered Queueing Network (LQN) model. General patterns of translation of LQN elements into corresponding PEPA components are applied to a substantial case study of a distributed computer system. This model is analysed using stochastic simulation to gauge the soundness of the translation. Furthermore, it is subjected to a series of numerical tests to compare execution runtimes and accuracy of the PEPA differential analysis against the LQN mean-value approximation method. Finally, this thesis discusses the major elements concerning the development of a software toolkit, the PEPA Eclipse Plug-in, which offers a comprehensive modelling environment for PEPA, including modules for static analysis, explicit state-space exploration, numerical solution of the steady-state equilibrium of the Markov chain, stochastic simulation, the differential analysis approach herein presented, and a graphical framework for model editing and visualisation of performance evaluation results.
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Lo, Chia Chun. « Application of continuous time Markov chain models : option pricing, term structure of interest rates and stochastic filtering ». Thesis, University of Essex, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.496255.
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Murray, Lawrence. « Bayesian learning of continuous time dynamical systems with applications in functional magnetic resonance imaging ». Thesis, University of Edinburgh, 2009. http://hdl.handle.net/1842/4157.
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Temporal phenomena in a range of disciplines are more naturally modelled in continuous-time than coerced into a discrete-time formulation. Differential systems form the mainstay of such modelling, in fields from physics to economics, geoscience to neuroscience. While powerful, these are fundamentally limited by their determinism. For the purposes of probabilistic inference, their extension to stochastic differential equations permits a continuous injection of noise and uncertainty into the system, the model, and its observation. This thesis considers Bayesian filtering for state and parameter estimation in general non-linear, non-Gaussian systems using these stochastic differential models. It identifies a number of challenges in this setting over and above those of discrete time, most notably the absence of a closed form transition density. These are addressed via a synergy of diverse work in numerical integration, particle filtering and high performance distributed computing, engineering novel solutions for this class of model. In an area where the default solution is linear discretisation, the first major contribution is the introduction of higher-order numerical schemes, particularly stochastic Runge-Kutta, for more efficient simulation of the system dynamics. Improved runtime performance is demonstrated on a number of problems, and compatibility of these integrators with conventional particle filtering and smoothing schemes discussed. Finding compatibility for the smoothing problem most lacking, the major theoretical contribution of the work is the introduction of two novel particle methods, the kernel forward-backward and kernel two-filter smoothers. By harnessing kernel density approximations in an importance sampling framework, these attain cancellation of the intractable transition density, ensuring applicability in continuous time. The use of kernel estimators is particularly amenable to parallelisation, and provides broader support for smooth densities than a sample-based representation alone, helping alleviate the well known issue of degeneracy in particle smoothers. Implementation of the methods for large-scale problems on high performance computing architectures is provided. Achieving improved temporal and spatial complexity, highly favourable runtime comparisons against conventional techniques are presented. Finally, attention turns to real world problems in the domain of Functional Magnetic Resonance Imaging (fMRI), first constructing a biologically motivated stochastic differential model of the neural and hemodynamic activity underlying the observed signal in fMRI. This model and the methodological advances of the work culminate in application to the deconvolution and effective connectivity problems in this domain.
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Arastuie, Makan. « Generative Models of Link Formation and Community Detection in Continuous-Time Dynamic Networks ». University of Toledo / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1596718772873086.
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Robacker, Thomas C. « Comparison of Two Parameter Estimation Techniques for Stochastic Models ». Digital Commons @ East Tennessee State University, 2015. https://dc.etsu.edu/etd/2567.
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Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a new method, the MCR method, which is unique to stochastic models and provides significantly better estimates and smaller confidence intervals for parameter values. Initial analysis of the new MCR method indicates that this method might be a viable method for parameter estimation for continuous time Markov chain models.
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Allahyani, Seham. « Contributions to filtering under randomly delayed observations and additive-multiplicative noise ». Thesis, Brunel University, 2017. http://bura.brunel.ac.uk/handle/2438/16297.
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This thesis deals with the estimation of unobserved variables or states from a time series of noisy observations. Approximate minimum variance filters for a class of discrete time systems with both additive and multiplicative noise, where the measurement might be delayed randomly by one or more sample times, are investigated. The delayed observations are modelled by up to N sample times by using N Bernoulli random variables with values of 0 or 1. We seek to minimize variance over a class of filters which are linear in the current measurement (although potentially nonlinear in past measurements) and present a closed-form solution. An interpretation of the multiplicative noise in both transition and measurement equations in terms of filtering under additive noise and stochastic perturbations in the parameters of the state space system is also provided. This filtering algorithm extends to the case when the system has continuous time state dynamics and discrete time state measurements. The Euler scheme is used to transform the process into a discrete time state space system in which the state dynamics have a smaller sampling time than the measurement sampling time. The number of sample times by which the observation is delayed is considered to be uncertain and a fraction of the measurement sample time. The same problem is considered for nonlinear state space models of discrete time systems, where the measurement might be delayed randomly by one sample time. The linearisation error is modelled as an additional source of noise which is multiplicative in nature. The algorithms developed are demonstrated throughout with simulated examples.
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Junuthula, Ruthwik Reddy. « Modeling, Evaluation and Analysis of Dynamic Networks for Social Network Analysis ». University of Toledo / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1544819215833249.
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Chen, Fengwei. « Contributions à l'identification de modèles à temps continu à partir de données échantillonnées à pas variable ». Thesis, Université de Lorraine, 2014. http://www.theses.fr/2014LORR0149/document.
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Cette thèse traite de l’identification de systèmes dynamiques à partir de données échantillonnées à pas variable. Ce type de données est souvent rencontré dans les domaines biomédical, environnemental, dans le cas des systèmes mécaniques où un échantillonnage angulaire est réalisé ou lorsque les données transitent sur un réseau. L’identification directe de modèles à temps continu est l’approche à privilégier lorsque les données disponibles sont échantillonnées à pas variable ; les paramètres des modèles à temps discret étant dépendants de la période d’échantillonnage. Dans une première partie, un estimateur optimal de type variable instrumentale est développé pour estimer les paramètres d’un modèle Box-Jenkins à temps continu. Ce dernier est itératif et présente l’avantage de fournir des estimées non biaisées lorsque le bruit de mesure est coloré et sa convergence est peu sensible au choix du vecteur de paramètres initial. Une difficulté majeure dans le cas où les données sont échantillonnées à pas variable concerne l’estimation de modèles de bruit de type AR et ARMA à temps continu (CAR et CARMA). Plusieurs estimateurs pour les modèles CAR et CARMA s’appuyant sur l’algorithme Espérance-Maximisation (EM) sont développés puis inclus dans l’estimateur complet de variable instrumentale optimale. Une version étendue au cas de l’identification en boucle fermée est également développée. Dans la deuxième partie de la thèse, un estimateur robuste pour l'identification de systèmes à retard est proposé. Cette classe de systèmes est très largement rencontrée en pratique et les méthodes disponibles ne peuvent pas traiter le cas de données échantillonnées à pas variable. Le retard n’est pas contraint à être un multiple de la période d’échantillonnage, contrairement à l’hypothèse traditionnelle dans le cas de modèles à temps discret. L’estimateur développé est de type bootstrap et combine la méthode de variable instrumentale itérative pour les paramètres de la fonction de transfert avec un algorithme numérique de type gradient pour estimer le retard. Un filtrage de type passe-bas est introduit pour élargir la région de convergence pour l’estimation du retard. Tous les estimateurs proposés sont inclus dans la boîte à outils logicielle CONTSID pour Matlab et sont évalués à l’aide de simulation de Monte-CarloThe output of a system is always corrupted by additive noise, therefore it is more practical to develop estimation algorithms that are capable of handling noisy data. The effect of white additive noise has been widely studied, while a colored additive noise attracts less attention, especially for a continuous-time (CT) noise. Sampling issues of CT stochastic processes are reviewed in this thesis, several sampling schemes are presented. Estimation of a CT stochastic process is studied. An expectation-maximization-based (EM) method to CT autoregressive/autoregressive moving average model is developed, which gives accurate estimation over a large range of sampling interval. Estimation of CT Box-Jenkins models is also considered in this thesis, in which the noise part is modeled to improve the performance of plant model estimation. The proposed method for CT Box-Jenkins model identification is in a two-step and iterative framework. Two-step means the plant and noise models are estimated in a separate and alternate way, where in estimating each of them, the other is assumed to be fixed. More specifically, the plant is estimated by refined instrumental variable (RIV) method while the noise is estimated by EM algorithm. Iterative means that the proposed method repeats the estimation procedure several times until a optimal estimate is found. Many practical systems have inherent time-delay. The problem of identifying delayed systems are of great importance for analysis, prediction or control design. The presence of a unknown time-delay greatly complicates the parameter estimation problem, essentially because the model are not linear with respect to the time-delay. An approach to continuous-time model identification of time-delay systems, combining a numerical search algorithm for the delay with the RIV method for the dynamic has been developed in this thesis. In the proposed algorithm, the system parameters and time-delay are estimated reciprocally in a bootstrap manner. The time-delay is estimated by an adaptive gradient-based method, whereas the system parameters are estimated by the RIV method. Since numerical method is used in this algorithm, the bootstrap method is likely to converge to local optima, therefore a low-pass filter has been used to enlarge the convergence region for the time-delay. The performance of the proposed algorithms are evaluated by numerical examples
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Driver, Charles C. « Hierarchical Continuous Time Dynamic Modelling for Psychology and the Social Sciences ». Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/18927.
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Im Rahmen dieser Dissertation bemühe ich mich, den statistischen Ansatz der zeitkontinuierlichen dynamischen Modellierung, der die Rolle der Zeit explizit berücksichtigt, zu erweitern und praktisch anwendbar zu machen. Diese Dissertation ist so strukturiert, dass ich in Kapitel 1 die Natur dynamischer Modelle bespreche, verschiedene Ansätze zum Umgang mit mehreren Personen betrachte und ein zeitkontinuierliches dynamisches Modell mit Input-Effekten (wie Interventionen) und einem Gaußschen Messmodell detailliert darstelle. In Kapitel 2 beschreibe ich die Verwendung der Software ctsem für R, die als Teil dieser Dissertation entwickelt wurde und die Modellierung von Strukturgleichungen und Mixed-Effects über einen frequentistischen Schätzansatz realisiert. In Kapitel 3 stelle ich einen hierarchischen, komplett Random-Effects beinhaltenden Bayesschen Schätzansatz vor, unter dem sich Personen nicht nur in Interceptparametern, sondern in allen Charakteristika von Mess - und Prozessmodell unterscheiden können, wobei die Schätzung individueller Parameter trotzdem von den Daten aller Personen profitiert. Kapitel 4 beschreibt die Verwendung der Bayesschen Erweiterung der Software ctsem. In Kapitel 5} betrachte ich die Natur experimenteller Interventionen vor dem Hintergrund zeitkontinuierlicher dynamischer Modellierung und zeige Ansätze, die die Art und Weise adressieren, mit der Interventionen auf psychologische Prozesse über die Zeit wirken. Das berührt Fragen, wie: 'Nach welcher Zeit zeigt eine Intervention ihre maximale Wirkung', 'Wie ändert sich die Form des Effektes im Laufe der Zeit' und 'Für wen ist die Wirkung am stärksten oder dauert am längsten an'. Viele Bei-spiele, die sowohl frequentistische als auch bayessche Formen der Software ctsem verwenden, sind enthalten. Im letzten Kapitel fasse ich die Dissertation zusammen, zeige Limitationen der angebotenen Ansätze auf und stelle meine Gedanken zu möglichen zukünftigen Entwicklungen dar.With this dissertation I endeavor to extend, and make practically applicable for psychology, the statistical approach of continuous time dynamic modelling, in which the role of time is made explicit. The structure of this dissertation is such that in Chapter 1, I discuss the nature of dynamic models, consider various approaches to handling multiple subjects, and detail a continuous time dynamic model with input effects (such as interventions) and a Gaussian measurement model. In Chapter 2, I describe the usage of the ctsem software for R developed as part of this dissertation, which provides a frequentist, mixed effects, structural equation modelling approach to estimation. Chapter 3 details a hierarchical Bayesian, fully random effects approach to estimation, allowing for subjects to differ not only in intercept parameters but in all characteristics of the measurement and dynamic models -- while still benefiting from other subjects data for parameter estimation. Chapter 4 describes the usage of the Bayesian extension to the ctsem software. In Chapter 5 I consider the nature of experimental interventions in the continuous time dynamic modelling framework, and show approaches to address questions regarding the way interventions influence psychological processes over time, with questions such as 'how long does a treatment take to reach maximum effect', `how does the shape of the effect change over time', and 'for whom is the effect strongest, or longest lasting'. Many examples using both frequentist and Bayesian forms of the ctsem software are given. For the final chapter I summarise the dissertation, consider limitations of the approaches offered, and provide some thoughts on possible future developments.
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Horký, Miroslav. « Modely hromadné obsluhy ». Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-232033.
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The master’s thesis solves models of queueing systems, which use the property of Markov chains. The queueing system is a system, where the objects enter into this system in random moments and require the service. This thesis solves specifically such models of queueing systems, in which the intervals between the objects incomings and service time have exponential distribution. In the theoretical part of the master’s thesis I deal with the topics stochastic process, queueing theory, classification of models and description of the models having Markovian property. In the practical part I describe realization and function of the program, which solves simulation of chosen model M/M/m. At the end I compare results which were calculated in analytic way and by simulation of the model M/M/m.
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Albertyn, Martin. « Generic simulation modelling of stochastic continuous systems ». Thesis, Pretoria : [s.n.], 2004. http://upetd.up.ac.za/thesis/available/etd-05242005-112442.
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Rýzner, Zdeněk. « Využití teorie hromadné obsluhy při návrhu a optimalizaci paketových sítí ». Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2011. http://www.nusl.cz/ntk/nusl-219285.
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This master's thesis deals with queueing theory and its application in designing node models in packet-switched network. There are described general principles of designing queueing theory models and its mathematical background. Further simulator of packet delay in network was created. This application implements two described models - M/M/1 and M/G/1. Application can be used for simulating network nodes and obtaining basic network characteristics like packet delay or packet loss. Next, lab exercise was created, in that exercise students familiarize themselves with basic concepts of queueing theory and examine both analytical and simulation approach to solving queueing systems.
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Yuan, Di. « Essays on continuous time diffusion models ». Thesis, 2013. http://hdl.handle.net/2440/83807.
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During the past few decades, continuous time diffusion models have become an integral part of financial economics. Especially, in certain core areas in finance, such as interest rate, asset pricing, option pricing, portfolio selection and volatility modelling, continuous time diffusion models have proved to be a very attractive way to conduct research and gain economic intuition. This thesis makes three main contributions to the field of continuous time diffusion models. First, we propose regime-switching Heston, GARCH, and CEV stochastic volatility models where all parameters are allowed to vary depending on the state of the economy. Then we apply these models to describe the dynamics of S&P 500 and VIX. We find strong evidence of regime shifts for all models. The CEV model is statistically preferred to other two nested models in explaining dynamics of data. Second, because the true transition density functions of regime-switching stochastic volatility models are unknown, the standard maximum likelihood estimation cannot be conducted. We first conduct the maximum likelihood estimation with closed-form likelihood expansions for regime-switching continuous time stochastic volatility models. Third, to approximate a continuous time diffusion process, researchers often use the Euler approximation in the literature. Theoretically, the smaller the discretization interval is, the more accurate the Euler approximation is expected to be. However, even when the discretization interval is too small, the accuracy of the Euler approximation can get worse because of the roundoff error and random number generator bias. A variety of univariate and multivariate diffusion models from the literature are considered. We use the solution of a diffusion process when it is available and usable as a benchmark. The Milstein approximation is also adopted to compare the accuracy of the Euler approximation. Depending on the problem of interest, different criteria are used to measure accuracy of approximation. The percentage error and strong convergence can be examined when a good approximation of sample path of a diffusion model is required. The weak convergence is preferred for the cases where approximation of moments of the process matters. In our Monte Carlo simulation studies of diverse diffusion models, we measure accuracy of the Euler approximation not only by using those criteria but also by looking at end point of the approximation. The simulation results show that an appropriate discretization interval must be picked for different diffusion models when applying the Euler approximation.Thesis (Ph.D.) -- University of Adelaide, School of Economics, 2013
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Lin, Liang-Ching, et 林良靖. « Goodness-of-fit test for Continuous Time Stochastic Volatility Models ». Thesis, 2013. http://ndltd.ncl.edu.tw/handle/86397692008041741207.
Texte intégralRésumé :
博士國立中山大學
應用數學系研究所
101
A goodness-of-fit test for stationary distributions of continuous time stochastic processes plays an important role in building up stochastic differential equation (SDE) models. In the first part of this dissertation, we propose two types of goodness-of-fit tests for continuous time stochastic volatility models (SVMs) based on discretely sampled observations. The first type of test is constructed by measuring deviations between the empirical and true characteristic functions obtained from the hypothesized stochastic volatility model. It is shown that under the null, the first proposed test statistics asymptotically follow a weighted sum of products of centered normal random variables. The second type of test is the Bickel-Rosenblatt test which is constructed by measuring integrated squared deviations between the nonparametric kernel density estimate from the observations and a parametric fit of the density. It is shown that under the null hypothesis, the Bickel-Rosenblatt test statistic is asymptotically normal. We also developed the Bickel-Rosenblatt test for the multivariate SVMs with a copula link. Its asymptotic null distribution is derived and bivariate examples are given. Simulation studies and real data analysis are conducted for both proposed tests. In the second part of this thesis, we consider inference for the SVMs with market microstructure noises which are often used to model high frequency financial data. Estimation of the integrated volatility is an important problem for high frequency financial data analysis. We consider the minimum variance unbiased estimator (MVUE) of the integrated volatility proposed by Lin (2007). The MVUE minimizes the finite sample variance in the class of unbiased estimators which are linear combinations of the sample autocovariance functions. The variance of the MVUE converges at a rate of Op(n−1/4). In particular, the MVUE achieves the maximum likelihood estimator efficiency for the constant volatility case. A recursive algorithm is developed to compute the optimal weights of the MVUE. Improved estimators of the microstructure noise variance and the quarticity are also proposed to facilitate the estimation procedure. Simulation results show our proposed estimator attains higher efficiency than state-of-the-art methods for the finite samples. Finally, a real data analysis is conducted for illustration. We also consider the goodness-of-fit test for the SVMs with microstructure noises. Moment estimators of the model parameters are proposed. A goodness-of-fit test based on the characteristic function is proposed. Simulation results of sizes and powers of the proposed test are given.
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Walker, James. « Bayesian Inference and Model Selection for Partially-Observed, Continuous-Time, Stochastic Epidemic Models ». Thesis, 2019. http://hdl.handle.net/2440/124703.
Texte intégralRésumé :
Emerging infectious diseases are an ongoing threat to the health of populations around the world. In response, countries such as the USA, UK and Australia, have outlined data collection protocols to surveil these novel diseases. One of the aims of these data collection protocols is to characterise the disease in terms of transmissibility and clinical severity in order to inform an appropriate public health response. This kind of data collection protocol is yet to be enacted in Australia, but such a protocol is likely to be tested during a seasonal in uenza ( u) outbreak in the next few years. However, it is important that methods for characterising these diseases are ready and well understood for when an epidemic disease emerges. The epidemic may only be characterised well if its dynamics are well described (by a model) and are accurately quanti ed (by precisely inferred model parameters). This thesis models epidemics and the data collection process as partially-observed continuous-time Markov chains and aims to choose between models and infer parameters using early outbreak data. It develops Bayesian methods to infer epidemic parameters from data on multiple small outbreaks, and outbreaks in a population of households. An exploratory analysis is conducted to assess the accuracy and precision of parameter estimates under di erent epidemic surveillance schemes, di erent models and di erent kinds of model misspeci cation. It describes a novel Bayesian model selection method and employs it to infer two important characteristics for understanding emerging epidemics: the shape of the infectious period distribution; and, the time of infectiousness relative to symptom onset. Lastly, this thesis outlines a method for jointly inferring model parameters and selecting between epidemic models. This new method is compared with an existing method on two epidemic models and is applied to a di cult model selection problem.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2020
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Stelzer, Robert [Verfasser]. « Multivariate continuous time stochastic volatility models driven by a Lévy process / Robert Josef Stelzer ». 2007. http://d-nb.info/986220337/34.
Texte intégral
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Varziri, M. Saeed. « Parameter estimation in nonlinear continuous-time dynamic models with modelling errors and process disturbances ». Thesis, 2008. http://hdl.handle.net/1974/1248.
Texte intégralRésumé :
Model-based control and process optimization technologies are becoming more commonly used by chemical engineers. These algorithms rely on fundamental or empirical models that are frequently described by systems of differential equations with unknown parameters. It is, therefore, very important for modellers of chemical engineering processes to have access to reliable and efficient tools for parameter estimation in dynamic models. The purpose of this thesis is to develop an efficient and easy-to-use parameter estimation algorithm that can address difficulties that frequently arise when estimating parameters in nonlinear continuous-time dynamic models of industrial processes.
The proposed algorithm has desirable numerical stability properties that stem from using piece-wise polynomial discretization schemes to transform the model differential equations into a set of algebraic equations. Consequently, parameters can be estimated by solving a nonlinear programming problem without requiring repeated numerical integration of the differential equations.
Possible modelling discrepancies and process disturbances are accounted for in the proposed algorithm, and estimates of the process disturbance intensities can be obtained along with estimates of model parameters and states. Theoretical approximate confidence interval expressions for the parameters are developed.
Through a practical two-phase nylon reactor example, as well as several simulation studies using stirred tank reactors, it is shown that the proposed parameter estimation algorithm can address difficulties such as: different types of measured responses with different levels of measurement noise, measurements taken at irregularly-spaced sampling times, unknown initial conditions for some state variables, unmeasured state variables, and unknown disturbances that enter the process and influence its future behaviour.Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2008-06-20 16:34:44.586
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Thaba, Lethabo Jane. « Modelling the short term interest with stochastic differential equation in continuous time : linear versus non-linear mode ». Thesis, 2014. http://hdl.handle.net/10210/11137.
Texte intégralRésumé :
M.Com. (Financial Economics)Recently, there has been a growth in the bond market. This growth has brought with it an ever-increasing volume and range of interest rate depended derivative products known as interest rate derivatives. Amongst the variables used in pricing these derivative products is the short-term interest rate. A numbers of short-term interest rate models that are used to fit the short-term interest rate exist. Therefore, understanding the features characterised by various short-term interest rate models, and determining the best fitting models is crucial as this variable is fundamental in pricing interest rate derivatives, which further determine the decision making of economic agents. This dissertation examines various short-term interest rate models in continuous time in order to determine which model best fits the South African short-term interest rates. Both the linear and nonlinear short-term interest rate models were estimated. The methodology adopted in estimating the models was parametric approach using Quasi Maximum Likelihood Estimation (QMLE). The findings indicate that nonlinear models seem to fit the South African short-term interest rate data better than the linear models
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Long, Chu Hoang. « A parametric linear programming approach to continuous-time stochastic optimal control problems with binary variables : applications to bioeconomic models and marine reserves ». Phd thesis, 2009. http://hdl.handle.net/1885/150597.
Texte intégral
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Ho, Shih-Ju, et 賀世儒. « Optimal control for continuous-time stochastic T-S fuzzy model with stochastic uncertainty ». Thesis, 2008. http://ndltd.ncl.edu.tw/handle/49749805655657511193.
Texte intégral
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Jacewitz, Stefan A. « Essays on the Predictability and Volatility of Asset Returns ». 2009. http://hdl.handle.net/1969.1/ETD-TAMU-2009-08-859.
Texte intégralRésumé :
This dissertation collects two papers regarding the econometric and economic theory
and testing of the predictability of asset returns. It is widely accepted that stock
returns are not only predictable but highly so. This belief is due to an abundance
of existing empirical literature fi nding often overwhelming evidence in favor of predictability.
The common regressors used to test predictability (e.g., the dividend-price
ratio for stock returns) are very persistent and their innovations are highly correlated
with returns. Persistence when combined with a correlation between innovations in
the regressor and asset returns can cause substantial over-rejection of a true null hypothesis.
This result is both well documented and well known. On the other hand,
stochastic volatility is both broadly accepted as a part of return time series and largely
ignored by the existing econometric literature on the predictability of returns. The
severe e ffect that stochastic volatility can have on standard tests are demonstrated
here. These deleterious e ffects render standard tests invalid. However, this problem
can be easily corrected using a simple change of chronometer. When a return time
series is read in the usual way, at regular intervals of time (e.g., daily observations),
then the distribution of returns is highly non-normal and displays marked time heterogeneity.
If the return time series is, instead, read according to a clock based on
regular intervals of volatility, then returns will be independent and identically normally
distributed. This powerful result is utilized in a unique way in each chapter of
this dissertation. This time-deformation technique is combined with the Cauchy t-test and the newly introduced martingale estimation technique. This dissertation nds no
evidence of predictability in stock returns. Moreover, using martingale estimation,
the cause of the Forward Premium Anomaly may be more easily discerned.
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PATARA, FULVIO. « Multi-level meta-modeling architectures applied to eHealth ». Doctoral thesis, 2016. http://hdl.handle.net/2158/1041924.
Texte intégralRésumé :
Over the last decade, a growing digital universe of unstructured or semi- structured human-sourced information, structured process-mediated data, and well-structured machine-generated data, encourages the adoption of innovative forms of data modeling and information processing to enable enhanced insight, decision making, and process automation applied to a variety of different contexts. Healthcare comprises a notable domain of interest, where the availability of a large amount of information can be exploited to take relevant and tangible benefits in terms of efficiency of the care process, improved out- comes and reduced health system costs. However, due to the complex nature of clinical data, a number of challenges needs to be faced, mainly related on how data characterized by volume, variety, variability, velocity, and veracity can be effectively and efficiently modeled, and how these data can be exploited for increasing the domain knowledge and supporting decision-making processes.
The aim of this dissertation is to describe the crucial role played by soft- ware architectures in order to overcome challenges posed by the healthcare context. Specifically, this dissertation addresses the development and applicability of multi-level meta-modeling architectures to various scenarios of eHealth, where flexibility and changeability represent primary requirements. Meta-modeling principles are concretely exploited in the implementation of an adaptable patient-centric Electronic Health Record (EHR) system to face a number of challenging requirements, including: adaptability to different specialities and organizational contexts; run-time configurability by domain experts; interoperability of heterogeneous data produced by various sources and accessed by various actors; applicability of guideline recommendations for evaluating clinical practice compliance; applicability of Activity Recognition techniques for monitoring and classifying human activities in pervasive intelligent environments.