Дисертації з теми "Models of time"
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1
Billah, Baki 1965. "Model selection for time series forecasting models." Monash University, Dept. of Econometrics and Business Statistics, 2001. http://arrow.monash.edu.au/hdl/1959.1/8840.
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2
Ambler, Gareth. "Time varying-coefficient models." Thesis, University of Sussex, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321345.
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3
Jähnichen, Patrick. "Time Dynamic Topic Models." Doctoral thesis, Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-200796.
Повний текст джерелаАнотація:
Information extraction from large corpora can be a useful tool for many applications in industry and academia. For instance, political communication science has just recently begun to use the opportunities that come with the availability of massive amounts of information available through the Internet and the computational tools that natural language processing can provide. We give a linguistically motivated interpretation of topic modeling, a state-of-the-art algorithm for extracting latent semantic sets of words from large text corpora, and extend this interpretation to cover issues and issue-cycles as theoretical constructs coming from political communication science. We build on a dynamic topic model, a model whose semantic sets of words are allowed to evolve over time governed by a Brownian motion stochastic process and apply a new form of analysis to its result. Generally this analysis is based on the notion of volatility as in the rate of change of stocks or derivatives known from econometrics. We claim that the rate of change of sets of semantically related words can be interpreted as issue-cycles, the word sets as describing the underlying issue. Generalizing over the existing work, we introduce dynamic topic models that are driven by general (Brownian motion is a special case of our model) Gaussian processes, a family of stochastic processes defined by the function that determines their covariance structure. We use the above assumption and apply a certain class of covariance functions to allow for an appropriate rate of change in word sets while preserving the semantic relatedness among words. Applying our findings to a large newspaper data set, the New York Times Annotated corpus (all articles between 1987 and 2007), we are able to identify sub-topics in time, \\\\textit{time-localized topics} and find patterns in their behavior over time. However, we have to drop the assumption of semantic relatedness over all available time for any one topic. Time-localized topics are consistent in themselves but do not necessarily share semantic meaning between each other. They can, however, be interpreted to capture the notion of issues and their behavior that of issue-cycles.
4
Petersson, Mikael. "Perturbed discrete time stochastic models." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-128979.
Повний текст джерелаАнотація:
In this thesis, nonlinearly perturbed stochastic models in discrete time are considered. We give algorithms for construction of asymptotic expansions with respect to the perturbation parameter for various quantities of interest. In particular, asymptotic expansions are given for solutions of renewal equations, quasi-stationary distributions for semi-Markov processes, and ruin probabilities for risk processes.At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Manuscript. Paper 5: Manuscript. Paper 6: Manuscript.
5
Harrison, Martin. "Time in quality constrained models." Thesis, University of Southampton, 1987. https://eprints.soton.ac.uk/361656/.
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6
Ehlers, Ricardo Sandes. "Bayesian model discrimination for time series and state space models." Thesis, University of Surrey, 2002. http://epubs.surrey.ac.uk/843599/.
Повний текст джерелаАнотація:
In this thesis, a Bayesian approach is adopted to handle parameter estimation and model uncertainty in autoregressive moving average (ARMA) time series models and dynamic linear models (DLM). Bayesian model uncertainty is handled in a parametric fashion through the use of posterior model probabilities computed via Markov chain Monte Carlo (MCMC) simulation techniques. Attention is focused on reversible jump Markov chain Monte Carlo (RJMCMC) samplers, which can move between models of different dimensions, to address the problem of model order uncertainty and strategies for proposing efficient sampling schemes in autoregressive moving average time series models and dynamic linear models are developed. The general problem of assessing convergence of the sampler in a dimension-changing context is addressed by computing estimates of the probabilities of moving to higher and lower dimensional spaces. Graphical and numerical techniques are used to compare different updating schemes. The methodology is illustrated by applying it to both simulated and real data sets and the results for the Bayesian model selection and parameter estimation procedures are compared with the classical model selection criteria and maximum likelihood estimation.
7
Mroz, Magda [Verfasser]. "Time-varying copula models for financial time series / Magda Mroz." Ulm : Universität Ulm. Fakultät für Mathematik und Wirtschaftswissenschaften, 2012. http://d-nb.info/1027341578/34.
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8
Price, David Charles. "History matching hydromechanical models using time-lapse seismic time-shifts." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/21733/.
Повний текст джерелаАнотація:
Although time-lapse seismic data has been used to great success in the history matching of reservoir fluid properties (i.e. saturation in reservoir simulators), it has been used far less effectively for benchmarking geomechanical behaviour. The reason for this is twofold. Firstly, hydromechanical models are typically large, complex and highly nonlinear with considerably large runtimes. Secondly, isolating and extracting quantifiable mechanical information from seismic data is difficult. However, by not attempting to utilise numerical history matching techniques, are we making the most out of the geomechanical information stored in time-lapse seismic data? In this Thesis I have attempted to answer this question by conducting a synthetic history matching study. I generate a hydromechanical model of a typical high pressure high temperature production scenario in the North Sea and utilise seismic history matching in an attempt to constrain the properties of the overburden and improve the models predictive capabilities. The study focuses primarily on overburden calibration as overburden timeshifts are not complicated by fluid effects, as in the reservoir, and hence can be considered as a purely geomechanical effect. Also the matching process is attempted utilising only a small, feasible number of model perturbations. Before seismic history matching can be successfully attempted it is important to have an in depth working knowledge of the model behaviour. Therefore, I conduct a multi-method Global Sensitivity Analysis (GSA) on over 4000 model perturbations, to evaluate the potential geomechanical information content of seismic time-shifts. Specifically, which model parameters cause the majority of the variation to overburden time-shifts. The results show that the majority of the variation in modelled shifts can be attributed to the Young's Modulus and Biot coefficient. These parameters appear the most influential for both near-offset time-shifts and the time-shift offset behaviour. However, the Poisson's ratio also becomes influential when considering the time-shift offset behaviour at long offsets. The results of the GSA also highlight that the over-parametrisation of material properties in the model can lead to unnecessary complexity in the model space. The simplification of complex rock properties (i.e. simplification of nonlinear relationships to single constants) will not significantly affect model performance whilst making seismic history matching more achievable. A robust history matching study also requires the consideration of all forms of uncertainty. One of the main causes of uncertainty in the process is that of the relationship between effective stress and seismic velocity i.e. the rock physics model. I analyse a handful of the most popular rock physics models and assess their behaviour and stability when applied to a large dry core dataset of different lithologies. The results show that most models are robust, well constrained and do a suitably good job at fitting velocity-stress data taken from core samples in a laboratory environment. However, slight discrepancies between different model approximations for the same core sample can cause significantly different time-lapse velocity predictions. The results also show that models are difficult to parameterise without the availability of velocity-stress core data. Attempting to do so can lead to even greater discrepancies in their time-lapse velocity predictions. The results also support the current belief that the velocity-stress core data may not be a good representation of the velocity-stress dependence of the subsurface I utilise an iterative emulator based approach to history matching which makes it possible to perform a robust history match with a small number of model realisations. I utilise the results of the GSA to define the model parameters in which to focus the history match and also utilise the results of the rock physics model analysis to define suitable uncertainties. The results of the emulation process show it is possible to perform a successful history match utilising only a small number of model perturbations and to constrain the uncertainty in the most influential model parameters. The process is improved significantly when both near-offset time-shifts and the time-shift offset behaviour are considered simultaneously in the matching process. It becomes apparent that the matching process and hence final solution is limited by the number of model realisations, iterations and the extent of the available seismic data. The greater the number of realisations, the more accurate the emulators whilst the more seismic observations, the more data available in which to test predicted models. Also, it becomes increasingly clear that the uncertainty in rock physics modelling dominates the matching process. Taking into consideration it's uncertainty makes it extremely difficult to confidently constrain any properties of the hydromechanical model from time-lapse seismic data. It becomes increasingly apparent that there is a great need to improve our understanding of rock behaviour (i.e. rock physics) before the seismic history matching of mechanical behavior becomes suitably accurate and economically appealing.
9
Wedi, Nils Peter. "Time-dependent boundaries in numerical models." Diss., lmu, 2005. http://nbn-resolving.de/urn:nbn:de:bvb:19-31420.
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10
Sjolander, Morne Rowan. "Time series models for paired comparisons." Thesis, Nelson Mandela Metropolitan University, 2011. http://hdl.handle.net/10948/d1012858.
Повний текст джерелаАнотація:
The method of paired comparisons is seen as a technique used to rank a set of objects with respect to an abstract or immeasurable property. To do this, the objects get to be compared two at a time. The results are input into a model, resulting in numbers known as weights being assigned to the objects. The weights are then used to rank the objects. The method of paired comparisons was first used for psychometric investigations. Various other applications of the method are also present, for example economic applications, and applications in sports statistics. This study involves taking paired comparison models and making them time-dependent. Not much research has been done in this area. Three new time series models for paired comparisons are created. Simulations are done to support the evidence obtained, and theoretical as well as practical examples are given to illustrate the results and to verify the efficiency of the new models. A literature study is given on the method of paired comparisons, as well as on the areas in which we apply our models. Our first two time series models for paired comparisons are the Linear-Trend Bradley- Terry Model and the Sinusoidal Bradley-Terry Model. We use the maximum likelihood approach to solve these models. We test our models using exact and randomly simulated data for various time periods and various numbers of objects. We adapt the Linear-Trend Bradley-Terry Model and received our third time series model for paired comparisons, the Log Linear-Trend Bradley-Terry Model. The daily maximum and minimum temperatures were received for Port Elizabeth, Uitenhage and Coega for 2005 until 2009. To evaluate the performance of the Linear-Trend Bradley-Terry Model and the Sinusoidal Bradley-Terry Model on estimating missing temperature data, we artificially remove observations of temperature from Coega’s temperature dataset for 2006 until 2008, and use various forms of these models to estimate the missing data points. The exchange rates for 2005 until 2008 between the following currencies: the Rand, Dollar, Euro, Pound and Yen, were obtained and various forms of our Log Linear-Trend Bradley-Terry Model are used to forecast the exchange rate for one day ahead for each month in 2006 until 2008. One of the features of this study is that we apply our time series models for paired comparisons to areas which comprise non-standard paired comparisons; and we want to encourage the use of the method of paired comparisons in a broader sense than what it is traditionally used for. The results of this study can be used in various other areas, like for example, in sports statistics, to rank the strength of sports players and predict their future scores; in Physics, to calculate weather risks of electricity generation, particularly risks related to nuclear power plants, and so forth, as well as in many other areas. It is hoped that this research will open the door to much more research in combining time series analysis with the method of paired comparisons.
11
Lupi, Claudio. "Models of nonstationary economic time series." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321600.
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12
Fleischman, Joyce D. "Mental models for time displayed tasks." Thesis, Monterey, California. Naval Postgraduate School, 1988. http://hdl.handle.net/10945/23301.
Повний текст джерелаАнотація:
The study described in this thesis attempts to determine whether there is a mental model for time-ordered tasks. The results of this study may be used to assist in the design of cockpit display formats for the Intelligent Air Attack System (IAAS) in the F/A-18, A-6 or other Navy and Air Force tactical aircraft, and may be applicable to telecommunications systems as well. Basic human factors engineering concepts and the characteristics of IAAS and of the Naval Telecommunications System are described. The approach and methodology for determining whether there is a consistent mental model for time-ordered tasks is discussed, and the results of a survey are presented. Based on this survey, it was determined that mental models for time-ordered tasks are not always the same, but instead are task-dependent. Schedules are most logically presented in a calendar-like format. For telecommunications related tasks, a front-to-back format is recommended. For time-ordered events in an aircraft cockpit, a top-to-bottom display order was preferred by a majority of study participants, but aviators preferred a left-to-right presentation. Theses. (SDW)
13
Karanasos, Menelaos. "Essays on financial time series models." Thesis, Birkbeck (University of London), 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.286252.
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14
Jones, Margaret. "Point prediction in survival time models." Thesis, University of Newcastle Upon Tyne, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340616.
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15
McGarry, Joanne S. "Seasonality in continuous time econometric models." Thesis, University of Essex, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.313064.
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16
BLANK, FRANCES FISCHBERG. "FACTOR MODELS WITH TIME-VARYING BETAS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2014. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=24569@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Diversos estudos envolvendo modelos de fatores para apreçamento de ativos contestam a validade do CAPM. Ao longo do tempo, para explicar as chamadas anomalias dos retornos das ações, os trabalhos se voltaram tanto para a busca de novos fatores de risco – os modelos multifatores – bem como para o tratamento dinâmico das sensibilidades relacionadas aos fatores de risco – os modelos condicionais de apreçamento de ativos. Os modelos condicionais, de um ou mais fatores, explicitam o valor esperado do retorno de um ativo de forma condicional a um conjunto de informação disponível no período anterior. As sensibilidades aos fatores de risco, os betas, são estimados como parâmetros dinâmicos a partir de diferentes abordagens na literatura. Nesta tese, o objetivo é o estudo de modelos condicionais na forma espaço-estado, em que os betas seguem processos estocásticos e são estimados a partir do filtro de Kalman, de forma a verificar o ganho na capacidade explicativa dos modelos. Dois estudos empíricos são realizados, um para o CAPM condicional no mercado brasileiro e outro para o modelo de três fatores condicional de Fama e French no mercado norte-americano. De modo geral, os resultados ao se considerar a variação temporal das sensibilidades aos fatores são melhores do que os obtidos a partir dos modelos incondicionais correspondentes, tanto no que se refere ao ajuste aos dados quanto à redução proporcionada nos erros de apreçamento.
The validity of CAPM is contested by several studies based on factor models. During the last decades, aiming to explain the known financial anomalies of stock returns, two major lines of research emerged: the use of asset pricing models that allow for multiple sources of risk – the multifactor models – as well as the dynamic approach to model the sensitivities of returns in respect to the risk factors – the conditional models. The conditional models, based on one or more risk factors, explicit the expected return conditional to the information set available in the previous period. The factor sensitivities, or the betas, are estimated as dynamic parameters according to different approaches in the literature. The main objective in this thesis is to study conditional pricing models based on state-space approach. The betas dynamics are described as stochastic processes and estimated through the Kalman filter in order to verify the models ability to explain the returns and related financial anomalies, such as size and value effects. Two empirical applications are presented: one for Conditional CAPM in the Brazilian stock market and another for Conditional Fama and French (1993) three-factor model in the American stock market. In both cases, time-varying sensitivities treatment provides better model adjustment as well as smaller pricing errors compared to correspondent unconditional models.
17
Mashikian, Paul Stephan. "Multiresolution models of financial time series." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/43483.
Повний текст джерелаАнотація:
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (leaves 89-92).
by Paul Stephan Mashikian.
M.Eng.
18
Bracegirdle, C. I. "Inference in Bayesian time-series models." Thesis, University College London (University of London), 2013. http://discovery.ucl.ac.uk/1383529/.
Повний текст джерелаАнотація:
Time series-data accompanied with a sequential ordering-occur and evolve all around us. Analysing time series is the problem of trying to discern and describe a pattern in the sequential data that develops in a logical way as the series continues, and the study of sequential data has occurred for a long period across a vast array of fields, including signal processing, bioinformatics, and finance-to name but a few. Classical approaches are based on estimating the parameters of temporal evolution of the process according to an assumed model. In econometrics literature, the field is focussed on parameter estimation of linear (regression) models with a number of extensions. In this thesis, I take a Bayesian probabilistic modelling approach in discrete time, and focus on novel inference schemes. Fundamentally, Bayesian analysis replaces parameter estimates by quantifying uncertainty in the value, and probabilistic inference is used to update the uncertainty based on what is observed in practice. I make three central contributions. First, I discuss a class of latent Markov model which allows a Bayesian approach to internal process resets, and show how inference in such a model can be performed efficiently, before extending the model to a tractable class of switching time series models. Second, I show how inference in linear-Gaussian latent models can be extended to allow a Bayesian approach to variance, and develop a corresponding variance-resetting model, the heteroskedastic linear-dynamical system. Third, I turn my attention to cointegration-a headline topic in finance-and describe a novel estimation scheme implied by Bayesian analysis, which I show to be empirically superior to the classical approach. I offer example applications throughout and conclude with a discussion.
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Fernandes, Cristiano Augusto Coelho. "Non-Gaussian structural time series models." Thesis, London School of Economics and Political Science (University of London), 1991. http://etheses.lse.ac.uk/1208/.
Повний текст джерелаАнотація:
This thesis aims to develop a class of state space models for non-Gaussian time series. Our models are based on distributions of the exponential family, such as the Poisson, the negative-binomial, the binomial and the gamma. In these distributions the mean is allowed to change over time through a mechanism which mimics a random walk. By adopting a closed sampling analysis we are able to derive finite dimensional filters, similar to the Kalman filter. These are then used to construct the likelihood function and to make forecasts of future observations. In fact for all the specifications here considered we have been able to show that the predictions give rise to schemes based on an exponentially weighted moving average (EWMA). The models may be extended to include explanatory variables via the kind of link functions that appear in GLIM models. This enables nonstochastic slope and seasonal components to be included. The Poisson, negative binomial and bivariate Poisson models are illustrated by considering applications to real data. Monte Carlo experiments are also conducted in order to investigate properties of maximum likelihood estimators and power studies of a post sample predictive test developed for the Poisson model.
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Elshamy, Wesam Samy. "Continuous-time infinite dynamic topic models." Diss., Kansas State University, 2012. http://hdl.handle.net/2097/15176.
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Doctor of PhilosophyDepartment of Computing and Information Sciences
William Henry Hsu
Topic models are probabilistic models for discovering topical themes in collections of documents. In real world applications, these models provide us with the means of organizing what would otherwise be unstructured collections. They can help us cluster a huge collection into different topics or find a subset of the collection that resembles the topical theme found in an article at hand. The first wave of topic models developed were able to discover the prevailing topics in a big collection of documents spanning a period of time. It was later realized that these time-invariant models were not capable of modeling 1) the time varying number of topics they discover and 2) the time changing structure of these topics. Few models were developed to address this two deficiencies. The online-hierarchical Dirichlet process models the documents with a time varying number of topics. It varies the structure of the topics over time as well. However, it relies on document order, not timestamps to evolve the model over time. The continuous-time dynamic topic model evolves topic structure in continuous-time. However, it uses a fixed number of topics over time. In this dissertation, I present a model, the continuous-time infinite dynamic topic model, that combines the advantages of these two models 1) the online-hierarchical Dirichlet process, and 2) the continuous-time dynamic topic model. More specifically, the model I present is a probabilistic topic model that does the following: 1) it changes the number of topics over continuous time, and 2) it changes the topic structure over continuous-time. I compared the model I developed with the two other models with different setting values. The results obtained were favorable to my model and showed the need for having a model that has a continuous-time varying number of topics and topic structure.
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MacDonald, Iain L. "Time series models for discrete data." Doctoral thesis, University of Cape Town, 1992. http://hdl.handle.net/11427/26105.
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Azzouzi, Mehdi. "Hidden state models for time series." Thesis, Aston University, 1999. http://publications.aston.ac.uk/10605/.
Повний текст джерелаАнотація:
Amongst all the objectives in the study of time series, uncovering the dynamic law of its generation is probably the most important. When the underlying dynamics are not available, time series modelling consists of developing a model which best explains a sequence of observations. In this thesis, we consider hidden space models for analysing and describing time series. We first provide an introduction to the principal concepts of hidden state models and draw an analogy between hidden Markov models and state space models. Central ideas such as hidden state inference or parameter estimation are reviewed in detail. A key part of multivariate time series analysis is identifying the delay between different variables. We present a novel approach for time delay estimating in a non-stationary environment. The technique makes use of hidden Markov models and we demonstrate its application for estimating a crucial parameter in the oil industry. We then focus on hybrid models that we call dynamical local models. These models combine and generalise hidden Markov models and state space models. Probabilistic inference is unfortunately computationally intractable and we show how to make use of variational techniques for approximating the posterior distribution over the hidden state variables. Experimental simulations on synthetic and real-world data demonstrate the application of dynamical local models for segmenting a time series into regimes and providing predictive distributions.
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Xiong, Yimin. "Time series clustering using ARMA models /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?COMP%202004%20XIONG.
Повний текст джерелаАнотація:
Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004.Includes bibliographical references (leaves 49-55). Also available in electronic version. Access restricted to campus users.
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Dupré, la Tour Tom. "Nonlinear models for neurophysiological time series." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLT018/document.
Повний текст джерелаАнотація:
Dans les séries temporelles neurophysiologiques, on observe de fortes oscillations neuronales, et les outils d'analyse sont donc naturellement centrés sur le filtrage à bande étroite.Puisque cette approche est trop réductrice, nous proposons de nouvelles méthodes pour représenter ces signaux.Nous centrons tout d'abord notre étude sur le couplage phase-amplitude (PAC), dans lequel une bande haute fréquence est modulée en amplitude par la phase d'une oscillation neuronale plus lente.Nous proposons de capturer ce couplage dans un modèle probabiliste appelé modèle autoregressif piloté (DAR). Cette modélisation permet une sélection de modèle efficace grâce à la mesure de vraisemblance, ce qui constitue un apport majeur à l'estimation du PAC.%Nous présentons différentes paramétrisations des modèles DAR et leurs algorithmes d'inférence rapides, et discutons de leur stabilité.Puis nous montrons comment utiliser les modèles DAR pour l'analyse du PAC, et démontrons l'avantage de l'approche par modélisation avec trois jeux de donnée.Puis nous explorons plusieurs extensions à ces modèles, pour estimer le signal pilote à partir des données, le PAC sur des signaux multivariés, ou encore des champs réceptifs spectro-temporels.Enfin, nous proposons aussi d'adapter les modèles de codage parcimonieux convolutionnels pour les séries temporelles neurophysiologiques, en les étendant à des distributions à queues lourdes et à des décompositions multivariées. Nous développons des algorithmes d'inférence efficaces pour chaque formulations, et montrons que l'on obtient de riches représentations de façon non-superviséeIn neurophysiological time series, strong neural oscillations are observed in the mammalian brain, and the natural processing tools are thus centered on narrow-band linear filtering.As this approach is too reductive, we propose new methods to represent these signals.We first focus on the study of phase-amplitude coupling (PAC), which consists in an amplitude modulation of a high frequency band, time-locked with a specific phase of a slow neural oscillation.We propose to use driven autoregressive models (DAR), to capture PAC in a probabilistic model. Giving a proper model to the signal enables model selection by using the likelihood of the model, which constitutes a major improvement in PAC estimation.%We first present different parametrization of DAR models, with fast inference algorithms and stability discussions.Then, we present how to use DAR models for PAC analysis, demonstrating the advantage of the model-based approach on three empirical datasets.Then, we explore different extensions to DAR models, estimating the driving signal from the data, PAC in multivariate signals, or spectro-temporal receptive fields.Finally, we also propose to adapt convolutional sparse coding (CSC) models for neurophysiological time-series, extending them to heavy-tail noise distribution and multivariate decompositions. We develop efficient inference algorithms for each formulation, and show that we obtain rich unsupervised signal representations
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Lattimer, Alan Martin. "Model Reduction of Nonlinear Fire Dynamics Models." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/70870.
Повний текст джерелаАнотація:
Due to the complexity, multi-scale, and multi-physics nature of the mathematical models for fires, current numerical models require too much computational effort to be useful in design and real-time decision making, especially when dealing with fires over large domains. To reduce the computational time while retaining the complexity of the domain and physics, our research has focused on several reduced-order modeling techniques. Our contributions are improving wildland fire reduced-order models (ROMs), creating new ROM techniques for nonlinear systems, and preserving optimality when discretizing a continuous-time ROM. Currently, proper orthogonal decomposition (POD) is being used to reduce wildland fire-spread models with limited success. We use a technique known as the discrete empirical interpolation method (DEIM) to address the slowness due to the nonlinearity. We create new methods to reduce nonlinear models, such as the Burgers' equation, that perform better than POD over a wider range of input conditions. Further, these ROMs can often be constructed without needing to capture full-order solutions a priori. This significantly reduces the off-line costs associated with creating the ROM. Finally, we investigate methods of time-discretization that preserve the optimality conditions in a certain norm associated with the input to output mapping of a dynamical system. In particular, we are able to show that the Crank-Nicholson method preserves the optimality conditions, but other single-step methods do not. We further clarify the need for these discrete-time ROMs to match at infinity in order to ensure local optimality.Ph. D.
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Yu, Fu. "On statistical analysis of vehicle time-headways using mixed distribution models." Thesis, University of Dundee, 2014. https://discovery.dundee.ac.uk/en/studentTheses/d101df63-b7db-45b6-8a03-365b64345e6b.
Повний текст джерелаАнотація:
For decades, vehicle time-headway distribution models have been studied by many researchers and traffic engineers. A good time-headway model can be beneficial to traffic studies and management in many aspects; e.g. with a better understanding of road traffic patterns and road user behaviour, the researchers or engineers can give better estimations and predictions under certain road traffic conditions and hence make better decisions on traffic management and control. The models also help us to implement high-quality microscopic traffic simulation studies to seek good solutions to traffic problems with minimal interruption of the real traffic environment and minimum costs. Compared within previously studied models, the mixed (SPM and GQM) mod- els, especially using the gamma or lognormal distributions to describe followers headways, are probably the most recognized ones by researchers in statistical stud- ies of headway data. These mixed models are reported with good fitting results indicated by goodness-of-fit tests, and some of them are better than others in com- putational costs. The gamma-SPM and gamma-GQM models are often reported to have similar fitting qualities, and they often out-perform the lognormal-GQM model in terms of computational costs. A lognormal-SPM model cannot be formed analytically as no explicit Laplace transform is available with the lognormal dis- tribution. The major downsides of using mixed models are the difficulties and more flexibilities in fitting process as they have more parameters than those single models, and this sometimes leads to unsuccessful fitting or unreasonable fitted pa- rameters despite their success in passing GoF tests. Furthermore, it is difficult to know the connections between model parameters and realistic traffic situations or environments, and these parameters have to be estimated using headway samples. Hence, it is almost impossible to explain any traffic phenomena with the param- eters of a model. Moreover, with the gamma distribution as the only common well-known followers headway model, it is hard to justify whether it has described the headway process appropriately. This creates a barrier for better understanding the process of how drivers would follow their preceding vehicles. This study firstly proposes a framework developed using MATLAB, which would help researchers in quick implementations of any headway distributions of interest. This framework uses common methods to manage and prepare headway samples to meet those requirements in data analysis. It also provides common structures and methods on implementing existing or new models, fitting models, testing their performance hence reporting results. This will simplify the development work involved in headway analysis, avoid unnecessary repetitions of work done by others and provide results in formats that are more comparable with those reported by others. Secondly, this study focuses on the implementation of existing mixed models, i.e. the gamma-SPM, gamma-GQM and lognormal-GQM, using the proposed framework. The lognormal-SPM is also tested for the first time, with the recently developed approximation method of Laplace transform available for lognormal distributions. The parameters of these mixed models are specially discussed, as means of restrictions to simplify the fitting process of these models. Three ways of parameter pre-determinations are attempted over gamma-SPM and gamma-GQM models. A couple of response-time (RT) distributions are focused on in the later part of this study. Two RT models, i.e. Ex-Gaussian (EMG) and inverse Gaussian (IVG) are used, for first time, as single models to describe headway data. The fitting performances are greatly comparable to the best known lognormal single model. Further extending this work, these two models are tested as followers headway distributions in both SPM and GQM mixed models. The test results have shown excellent fitting performance. These now bring researchers more alternatives to use mixed models in headway analysis, and this will help to compare the be- haviours of different models when they are used to describe followers headway data. Again, similar parameter restrictions are attempted for these new mixed models, and the results show well-acceptable performance, and also corrections on some unreasonable fittings caused by the over flexibilities using 4- or 5- parameter models.
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McDonald, Daniel J. "Generalization Error Bounds for Time Series." Research Showcase @ CMU, 2012. http://repository.cmu.edu/dissertations/184.
Повний текст джерелаАнотація:
In this thesis, I derive generalization error bounds — bounds on the expected inaccuracy of the predictions — for time series forecasting models. These bounds allow forecasters to select among competing models, and to declare that, with high probability, their chosen model will perform well — without making strong assumptions about the data generating process or appealing to asymptotic theory. Expanding upon results from statistical learning theory, I demonstrate how these techniques can help time series forecasters to choose models which behave well under uncertainty. I also show how to estimate the β-mixing coefficients for dependent data so that my results can be used empirically. I use the bound explicitly to evaluate different predictive models for the volatility of IBM stock and for a standard set of macroeconomic variables. Taken together my results show how to control the generalization error of time series models with fixed or growing memory.
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Kötter, Mirko. "Optimal investment in time inhomogeneous Poisson models." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=979754747.
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Kleinow, Torsten. "Testing continuous time models in financial markets." Doctoral thesis, [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=965412091.
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Haas, Markus. "Dynamic mixture models for financial time series /." Berlin : Pro Business, 2004. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=012999049&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Holan, Scott Harold. "Time series exponential models: theory and methods." Diss., Texas A&M University, 2004. http://hdl.handle.net/1969.1/431.
Повний текст джерелаАнотація:
The exponential model of Bloomfield (1973) is becoming increasingly important due to its recent applications to long memory time series. However, this model has received little consideration in the context of short memory time series. Furthermore, there has been very little attempt at using the EXP model as a model to analyze observed time series data. This dissertation research is largely focused on developing new methods to improve the utility and robustness of the EXP model. Specifically, a new nonparametric method of parameter estimation is developed using wavelets. The advantage of this method is that, for many spectra, the resulting parameter estimates are less susceptible to biases associated with methods of parameter estimation based directly on the raw periodogram. Additionally, several methods are developed for the validation of spectral models. These methods test the hypothesis that the estimated model provides a whitening transformation of the spectrum; this is equivalent to the time domain notion of producing a model whose residuals behave like the residuals of white noise. The results of simulation and real data analysis are presented to illustrate these methods.
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Breitner, Susanne. "Time-varying coefficient models and measurement error." Diss., lmu, 2007. http://nbn-resolving.de/urn:nbn:de:bvb:19-79772.
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Wohlrabe, Klaus. "Forecasting with mixed-frequency time series models." Diss., lmu, 2009. http://nbn-resolving.de/urn:nbn:de:bvb:19-96817.
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Maruta, Ichiro. "Studies on Identification of Constinuous-time Models." 京都大学 (Kyoto University), 2011. http://hdl.handle.net/2433/142133.
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Buchholz, Henrik. "Real-time visualization of 3D city models." Phd thesis, Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2007/1333/.
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McAdam, Taylor J. "Analysis of Time-Dependent Integrodifference Population Models." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/hmc_theses/44.
Повний текст джерелаАнотація:
The population dynamics of species with separate growth and dispersal stages can be described by a discrete-time, continuous-space integrodifference equation relating the population density at one time step to an integral expression involving the density at the previous time step. Prior research on this model has assumed that the equation governing the population dynamics remains fixed over time, however real environments are constantly in flux. We show that for time-varying models, there is a value Λ that can be computed to determine a sufficient condition for population survival. We also develop a framework for analyzing persistence of a population for which growth and dispersal behavior alternate predictably throughout time. Finally, we consider a number of time-varying models that include randomness.
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Liu, Zhao, and 劉釗. "On mixture double autoregressive time series models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/196465.
Повний текст джерелаАнотація:
Conditional heteroscedastic models are one important type of time series models which have been widely investigated and brought out continuously by scholars in time series analysis. Those models play an important role in depicting the characteristics of the real world phenomenon, e.g. the behaviour of _nancial market. This thesis proposes a mixture double autoregressive model by adopting the exibility of mixture models to the double autoregressive model, a novel conditional heteroscedastic model recently proposed by Ling (2004). Probabilistic properties including strict stationarity and higher order moments are derived for this new model and, to make it more exible, a logistic mixture double autoregressive model is further introduced to take into account the time varying mixing proportions. Inference tools including the maximum likelihood estimation, an EM algorithm for searching the estimator and an information criterion for model selection are carefully studied for the logistic mixture double autoregressive model. We notice that the shape changing characteristics of the multimodal conditional distributions is an important feature of this new type of model. The conditional heteroscedasticity of time series is also well depicted. Monte Carlo experiments give further support to these two new models, and the analysis of an empirical example based on our new models as well as other mainstream ones is also reported.published_or_final_version
Statistics and Actuarial Science
Master
Master of Philosophy
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Hallgren, Jonas. "Continuous time Graphical Models and Decomposition Sampling." Licentiate thesis, KTH, Matematisk statistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-159954.
Повний текст джерелаАнотація:
Two topics in temporal graphical probabilistic models are studied. The topics are treated in separate papers, both with applications in finance. The first paper study inference in dynamic Bayesian networks using Monte Carlo methods. A new method for sampling random variables is proposed. The method divides the sample space into subspaces. This allows the sampling to be done in parallel with independent and distinct sampling methods on the subspaces. The methodology is demonstrated on a volatility model and some toy examples with promising results. The second paper treats probabilistic graphical models in continuous time —a class of models with the ability to express causality. Tools for inference in these models are developed and employed in the design of a causality measure. The framework is used to analyze tick-by-tick data from the foreign exchange market.Två teman inom temporala grafiska modeller betraktas. De behandlas i separata artiklar, båda med tillämpningar inom finans. Den första artikeln studerar inferens i dynamiska Bayesianska nätverk med Monte Carlo-metoder. En ny metod för att simulera slumptal föreslås. Metoden delar upp tillståndsrummet i underrum. Detta gör att simuleringarna kan utföras parallellt med oberoende och distinkta simuleringstekniker på underrummen. Metodiken demonstreras på en volatilitesmodell och ett par leksaksmodeller med lovande resultat. Den andra artikeln behandlar probabilistiska grafiska modeller i kontinuerlig tid. Dessa modeller har förmåga att uttrycka kausalitet. Verktyg för inferens i dessa modeller utvecklas och används för att designa ett kausalitets-mått. Ramverket tillämpas genom att analysera tick-data från valutamarknaden.
QC 20150218
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Bryans, Jeremy William. "Denotational semantic models for real-time LOTOS." Thesis, University of Reading, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.360755.
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MELLEM, MARCELO TOURASSE NASSIM. "AUTOREGRESSIVE-NEURAL HYBRID MODELS FOR TIME SERIES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1997. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=14541@1.
Повний текст джерелаАнотація:
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOREste trabalho apresenta um modelo linear por partes chamado de modelo ARN. Trata-se de uma estrutura híbrida que envolve modelos autoregressivos e redes neurais. Este modelo é comparado com o modelo AR de coeficientes fixos e com a rede neural estática aplicada à previsão. Os resultados mostram que o ARN consegue identificar a estrutura não-linear dos dados simulados e que na maioria dos casos ele possui melhor habilidade preditiva do que os modelos supracitados.
In this thesis we develop a piece-wise linear model named ARN model. Our model has a hybrid structure which combines autoregressive models and neural networks. We compare our model to the fixed-coefficient AR model and to the prediction static neural network. Our results show that ARN is able to find the non-linear structure of simulated data and in most cases it performs better than the methods mentioned above.
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Parmar, Kiresh. "Time-delayed models of genetic regulatory networks." Thesis, University of Sussex, 2017. http://sro.sussex.ac.uk/id/eprint/70716/.
Повний текст джерелаАнотація:
In this thesis I have analysed several mathematical models, which represent the dynamics of genetic regulatory networks. Methods of bifurcation analysis and direct numerical simulations were employed to study the biological phenomena that can occur due to the presence of time delays, such as stable periodic oscillations induced by Hopf bifurcations. To highlight the biological implications of time-delayed systems, different models of genetic regulatory networks as relevant to the onset and development of cancer were studied in detail, as well as genetic regulatory networks which describe the effects of transcription factors in the immune system. A network of an oscillator coupled with a switch was explored, as systems such as these are prevalent in genetic regulatory networks. The effects of time delays on its oscillatory and bistable behaviour were then investigated, the results of which were compared with available results from the literature.
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Okonna, Ime Udo. "Time-delayed models of infectious diseases dynamics." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/73551/.
Повний текст джерелаАнотація:
This research work is on time-delayed models of infectious diseases dynamics. The dynamics of infectious diseases are studied in the presence of time delays representing temporary immunity or latency. We have designed and analysed time-delayed models with various parameters to simulate disease dynamics, in a view to gaining insight into the behaviour of a population in the presence of infectious diseases, and the reaction of the population to changes in the management procedure of such infections.
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Shakandli, Mohamed M. "State space models in medical time series." Thesis, University of Sheffield, 2018. http://etheses.whiterose.ac.uk/19306/.
Повний текст джерелаАнотація:
This thesis concerns the set-up and application of a state space model to medical time series. Considering medical count time series (such as number of asthma patients or a number of sudden infant death syndrome recorded over time), we discuss and propose non-linear and non-Gaussian state space models, in particular dynamic generalized linear models (DGLMs). Sequential Monte Carlo methods, also known as particle filters are employed for tracking a posterior state distribution. We assess the proposed methodology by way of an extensive simulation experiment. In the first simulation study, we found that the results from the Liu and West particle filter algorithm have shown better performance over the Storvik particle filter algorithm in terms of precision of the estimation of hyper-parameters and accuracy of forecasting. Beside, the obtained results from the Liu and West particle filter algorithm are quite similar from the ones that were obtained by the MCMC. In addition, in the second simulation study, we found the Liu and West particle filter algorithm with the Poisson model still does better than the other proposed models, even if it is incorrectly specified. The Smith (1985) method for model diagnostics is used. The results obtained from simulation studies showed that this methodology was successful. Finally, we developed a Bayesian monitoring model for evaluating the performance of the fitted model in a sequential way by using the Bayes factors and nonparametric binomial control chart with proposed runs rules. The novelty of this approach is to exploit the results obtained from the PSR or INTPSR for the model diagnostics to calculate the values of the Bayes factors. We found that the proposed control procedure provided an effective way of detecting out-of-control signals of the process.
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Jones, Charles I. (Charles Irving). "Time series tests of endogenous growth models." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/12701.
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Johnson, Matthew James Ph D. Massachusetts Institute of Technology. "Bayesian time series models and scalable inference." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/89993.
Повний текст джерелаАнотація:
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 197-206).
With large and growing datasets and complex models, there is an increasing need for scalable Bayesian inference. We describe two lines of work to address this need. In the first part, we develop new algorithms for inference in hierarchical Bayesian time series models based on the hidden Markov model (HMM), hidden semi-Markov model (HSMM), and their Bayesian nonparametric extensions. The HMM is ubiquitous in Bayesian time series models, and it and its Bayesian nonparametric extension, the hierarchical Dirichlet process hidden Markov model (HDP-HMM), have been applied in many settings. HSMMs and HDP-HSMMs extend these dynamical models to provide state-specific duration modeling, but at the cost of increased computational complexity for inference, limiting their general applicability. A challenge with all such models is scaling inference to large datasets. We address these challenges in several ways. First, we develop classes of duration models for which HSMM message passing complexity scales only linearly in the observation sequence length. Second, we apply the stochastic variational inference (SVI) framework to develop scalable inference for the HMM, HSMM, and their nonparametric extensions. Third, we build on these ideas to define a new Bayesian nonparametric model that can capture dynamics at multiple timescales while still allowing efficient and scalable inference. In the second part of this thesis, we develop a theoretical framework to analyze a special case of a highly parallelizable sampling strategy we refer to as Hogwild Gibbs sampling. Thorough empirical work has shown that Hogwild Gibbs sampling works very well for inference in large latent Dirichlet allocation models (LDA), but there is little theory to understand when it may be effective in general. By studying Hogwild Gibbs applied to sampling from Gaussian distributions we develop analytical results as well as a deeper understanding of its behavior, including its convergence and correctness in some regimes.
by Matthew James Johnson.
Ph. D.
46
Kwan, Tan Hwee. "Robust estimation for structural time series models." Thesis, London School of Economics and Political Science (University of London), 1990. http://etheses.lse.ac.uk/2809/.
Повний текст джерелаАнотація:
This thesis aims at developing robust methods of estimation in order to draw valid inference from contaminated time series. We concentrate on additive and innovation outliers in structural time series models using a state space representation. The parameters of interest are the state, hyperparameters and coefficients of explanatory variables. Three main contributions evolve from the research. Firstly, a filter named the approximate Gaussian sum filter is proposed to cope with noisy disturbances in both the transition and measurement equations. Secondly, the Kalman filter is robustified by carrying over the M-estimation of scale for i.i.d observations to time-dependent data. Thirdly, robust regression techniques are implemented to modify the generalised least squares transformation procedure to deal with explanatory variables in time series models. All the above procedures are tested against standard non-robust estimation methods for time series by means of simulations. Two real examples are also included.
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Shaik, Taqui Hassan Ansari. "Automated development of process time estimating models." Thesis, De Montfort University, 2006. http://hdl.handle.net/2086/4111.
Повний текст джерелаАнотація:
This research has examined the cost estimating and cost modeling research literature and identified the benefits and limitations of existing practices. Particular emphasis has been placed on the methods available for developing cost models at the early stages of product and process development where data from which to develop models is scarce. Shortfalls in existing practices have been identified as well as potential methods of resolving these limitations. Of these methods Virtual Manufacturing appears to offer the greatest potential for resolving issues with lack of data availability by enabling such data to be generated. Detailed trials have, therefore, been undertaken to examine the effectiveness of Virtual Manufacturing in terms of its ability to generate valid data in the quantities required to ensure accurate cost models can be developed. In addition, the research has involved the use of Data Mining techniques to identify the cost estimating relationship's within the data output from the Virtual Manufacturing trials. Here the aim has been to investigate the potential use of Data Mining techniques to fully automate the data analysis stage of the cost model development process.
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Almarashi, Abdullah Maedh. "Statistical inference for Poisson time series models." Thesis, University of Strathclyde, 2014. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=23669.
Повний текст джерелаАнотація:
There are many nonlinear econometric models which are useful in analysis of financial time series. In this thesis, we consider two kinds of nonlinear autoregressive models for nonnegative integer-valued time series: threshold autoregressive models and Markov switching models, in which the conditional distribution given historical information is the Poisson distribution. The link between the conditional variance (i.e. the conditional mean for the Poisson distribution) and its past values as well as the observed values of the Poisson process may be different according to the threshold variable in threshold autoregressive models, and to an unobservable state variable in Markov switching models in different regimes. We give a condition on parameters under which the Poisson generalized threshold autoregressive heteroscedastic (PTGARCH) process can be approximated by a geometrically ergodic process. Under this condition, we discuss statistical inference (estimation and tests) for PTGARCH models, and give the asymptotic theory on the inference. The complete structure of the threshold autoregressive model is not exactly specific in economic theory for the most financial applications of the model. In particular, the number of regimes, the value of threshold and the delay parameter are often unknown and cannot be assumed known. Therefore, in this research, the performance of various information criteria for choosing the number of regimes, the threshold value and the delay parameters for different sample sizes is investigated. Tests for threshold nonlinearity are applied. The characteristics of Markovian switching Poisson generalized autoregressive hetero-scedastic (MS-PGARCH) models are given, and the maximum likelihood estimation of parameters is discussed. Simulation studies and applications to modelling financial counting time series are presented to support our methodology for both the PTGARCH model and the MS-PGARCH model.
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Song, Li. "Piecewise models for long memory time series." Paris 11, 2010. http://www.theses.fr/2010PA112128.
Повний текст джерелаАнотація:
De nombreux travaux existent sur les processus stationnaires à longue mémoire (LM) et sur les modèles présentant des changements structurels. Cependant, il y a relativement peu de travaux sur les processus à LM non stationnaires faisant intervenir des ruptures, et ceci sans doute car LM et changement structurel sont deux phénomènes qu'il est facile de confondre. Dans cette thèse, nous considérons un modèle paramétrique de séries chronologiques à LM et non stationnaires : le processus localement autorégressif à moyenne mobile fractionnairement intégrée (FARlMA). Dans ce modèle, le nombre et les positions des points de ruptures (PRs) peuvent varier entre deux régimes, de même que les ordres et les coefficients des différentes parties FARlMA. Nous proposons deux méthodes pour estimer les paramètres de ce modèle. La première consiste à optimiser un critère basé sur le principe de description de longueur minimum (MDL). Nous montrons que ce critère est meilleur que le critère d'information bayésien et qu'un critère existant dans la littérature et aussi basé sur le principe MOL. Comme l'espace paramétrique est de grande dimension, l'optimisation pratique de notre critère est une tâche difficile et nous proposons une mise en oeuvre basée sur un algorithme génétique. La seconde méthode s'applique au cas de séries très longues comme des données de trafic intemet par exemple. En effet dans ce cas, la minimisation d'un critère basé sur le principe MDL est quasi impossible en pratique. Pour ajuster le modèle, nous proposons une méthode basée sur les différences entre les estimations des paramètres des différents blocs de données. La méthode se décompose en quatre étapes. Dans l'étape 1, nous ajustons un modèle FARlMA stationnaire à la série complète. Des estimées locales des paramètres sont obtenues dans l'étape 2. Dans l'étape 3, pour tous les nombres possibles de PR, on sélectionne les intervalles contenant un PR, on estime les positions des PRs et on estime les paramètres de chaque bloc. Enfin, l'étape 4 concerne la sélection du nombre de PRs en utilisant la somme des carrés des résidus des différents blocs. On montre l'efficacité de nos deux méthodes d'estimation au moyen de simulations numériques et on étudie aussi le cas de séries réellesThere are many studies on stationary processes exhibiting long range dependence (LRD) and on piecewise models involving structural changes. But the literature on structural breaks in LRD models is relatively sparse because structural changes and LRD are easily confused. Some works consider the case where only some coefficients in a LRD model are allowed to change. Ln this thesis, we consider a non-stationary LRD parametric model, namely the piecewise fractional autoregressive integrated moving-average (FARlMA) model. It is a pure structural change model inwhich the nurnber and the locations of break points (BPs) as well as the ARMA orders and the corresponding coefficients are allowed to change between two regimes. Two methods are proposed to estimate the parameters of this model. The first one is to optimize a criterion based on the minimum description length (MDL) principle. We show that this criterion outperforms the Bayesian information criterion and another MDL based criterion proposed in the literature. Since the search space is huge, the practical optimization of our criterion is a complicated task and we design an automatic methodology based on a genetic algorithm. The second method is designed for very long time series, like Internet traffic data. Ln such cases, the minimisation of the criterion based on MDL is very difficult. We propose a method based on the differences between parameter estimations of different blocks of data to fit the piecewise FARIMA model. This method consists in a four-step procedure. Ln Step 1, we fit a stationary FARiMA model to the whole series. Local parameter estimates are obtained in Step 2. Ln Step 3, for all possible BP numbers, we select the intervals with a BP, we estimate the BP locations and we estimate the parameters of each stationary block. Lastly, Step 4 concerns the selection of the BP number using the sum of squared residuals of the different fitted piecewise models. The effectiveness of the two methods proposed in the thesis is shown by simulations and applications to real data are considered
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Liu, Yi. "Time-Varying Coefficient Models for Recurrent Events." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/97999.
Повний текст джерелаАнотація:
I have developed time-varying coefficient models for recurrent event data to evaluate the temporal profiles for recurrence rate and covariate effects. There are three major parts in this dissertation. The first two parts propose a mixed Poisson process model with gamma frailties for single type recurrent events. The third part proposes a Bayesian joint model based on multivariate log-normal frailties for multi-type recurrent events. In the first part, I propose an approach based on penalized B-splines to obtain smooth estimation for both time-varying coefficients and the log baseline intensity. An EM algorithm is developed for parameter estimation. One issue with this approach is that the estimating procedure is conditional on smoothing parameters, which have to be selected by cross-validation or optimizing certain performance criterion. The procedure can be computationally demanding with a large number of time-varying coefficients. To achieve objective estimation of smoothing parameters, I propose a mixed-model representation approach for penalized splines. Spline coefficients are treated as random effects and smoothing parameters are to be estimated as variance components. An EM algorithm embedded with penalized quasi-likelihood approximation is developed to estimate the model parameters. The third part proposes a Bayesian joint model with time-varying coefficients for multi-type recurrent events. Bayesian penalized splines are used to estimate time-varying coefficients and the log baseline intensity. One challenge in Bayesian penalized splines is that the smoothness of a spline fit is considerably sensitive to the subjective choice of hyperparameters. I establish a procedure to objectively determine the hyperparameters through a robust prior specification. A Markov chain Monte Carlo procedure based on Metropolis-adjusted Langevin algorithms is developed to sample from the high-dimensional distribution of spline coefficients. The procedure includes a joint sampling scheme to achieve better convergence and mixing properties. Simulation studies in the second and third part have confirmed satisfactory model performance in estimating time-varying coefficients under different curvature and event rate conditions. The models in the second and third part were applied to data from a commercial truck driver naturalistic driving study. The application results reveal that drivers with 7-hours-or-less sleep prior to a shift have a significantly higher intensity after 8 hours of on-duty driving and that their intensity remains higher after taking a break. In addition, the results also show drivers' self-selection on sleep time, total driving hours in a shift, and breaks. These applications provide crucial insight into the impact of sleep time on driving performance for commercial truck drivers and highlights the on-road safety implications of insufficient sleep and breaks while driving. This dissertation provides flexible and robust tools to evaluate the temporal profile of intensity for recurrent events.PHD