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Dissertations / Theses on the topic 'Time-series analysis Inference'
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Li, Yang, and 李杨. "Statistical inference for some econometric time series models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/195984.
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With the increasingly economic activities, people have more and more interest in econometric models. There are two mainstream econometric models which are very popular in recent decades. One is quantile autoregressive (QAR) model which allows varying-coefficients in linear time series and greatly promotes the ranges of regression research. The first topic of this thesis is to focus on the modeling of QAR model. We propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to QAR models, and introduce two valuable quantities, the quantile autocorrelation function (QACF) and the quantile partial autocorrelation function (QPACF). This allows us to extend the Box-Jenkins three-stage procedure (model identification, model parameter estimation, and model diagnostic checking) from classical autoregressive models to quantile autoregressive models. Specifically, the QPACF of an observed time series can be employed to identify the autoregressive order, while the QACF of residuals obtained from the model can be used to assess the model adequacy. We not only demonstrate the asymptotic properties of QCOR, QPCOR, QACF and PQACF, but also show the large sample results of the QAR estimates and the quantile version of the Ljung- Box test. Moreover, we obtain the bootstrap approximations to the distributions of parameter estimators and proposed measures. Simulation studies indicate that the proposed methods perform well in finite samples, and an empirical example is presented to illustrate the usefulness of QAR model.
The other important econometric model is autoregressive conditional duration (ACD) model which is developed with the purpose of depicting ultra high frequency (UHF) financial time series data. The second topic of this thesis is designed to incorporate ACD model with one of the extreme value distributions, i.e. Fréchet distribution. We apply the maximum likelihood estimation (MLE) to Fréchet ACD models and derive its generalized residuals for model adequacy checking. It is noteworthy that simulations show a relative greater sensitiveness in the linear parameters to sampling errors. This phenomenon successfully reflects the skewness of the Fréchet distribution and suggests a method to practitioners in proceeding model accuracy. Furthermore, we present the empirical sizes and powers for Box-Pierce, Ljung-Box and modified Box-Pierce statistics as comparisons of the proposed portmanteau statistic.
In addition to the Fréchet ACD, we also systematically analyze theWeibull ACD, where the Weibull distribution is the other nonnegative extreme value distribution. The last topic of the thesis explains the estimation and diagnostic checking the Weibull ACD model. By investigating the MLE in this model, there exhibits a slight sensitiveness in linear parameters. However, there is an obvious phenomenon on the trade-off between the skewness of Weibull distribution and the sampling error when the simulations are conducted. Moreover, the asymptotic properties are also studied for the generalized residuals and a goodness-of-fit test is employed to obtain a portmanteau statistic. Through the simulation results in size and power, it shows that Weibull ACD is superior to Fréchet ACD in specifying the wrong model. This is meaningful in practice.<br>published_or_final_version<br>Statistics and Actuarial Science<br>Doctoral<br>Doctor of Philosophy
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Kwok, Sai-man Simon. "Statistical inference of some financial time series models." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B36885654.
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黃鎮山 and Chun-shan Wong. "Statistical inference for some nonlinear time series models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31239444.
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Wong, Chun-shan. "Statistical inference for some nonlinear time series models /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20715316.
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Wang, Chao, and 王超. "Statistical inference for some discrete-valued time series." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B48329514.
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Some problems of' statistical inference for discrete-valued time series are investigated in this study. New statistical theories and methods are developed which may aid us in gaining more insight into the understanding of discrete-valued time series data.
The first part is concerned with the measurement of the serial dependence of binary time series. In early studies the classical autocorrelation function was used, which, however, may not be an effective and informative means of revealing the dependence feature of a binary time series. Recently, the autopersistence function has been proposed as an alternative to the autocorrelation function for binary time series. The theoretical autopersistence functions and their sample analogues, the autopersistence graphs, are studied within a binary autoregressive model. Some properties of the autopcrsistencc functions and the asymptotic properties of the autopersistence graphs are discussed, justifying that the antopersistence graphs can be used to assess the dependence feature.
Besides binary time series, intcger-vall1ed time series arc perhaps the most commonly seen discrete-valued time series. A generalization of the Poisson autoregression model for non-negative integer-valued time series is proposed by imposing an additional threshold structure on the latent mean process of the Poisson autoregression. The geometric ergodicity of the threshold Poisson autoregression with perburbations in the latent mean process and the stochastic stability of the threshold Poisson autoregression are obtained. The maximum likelihood estimator for the parameters is discussed and the conditions for its consistency and asymptotic normally are given as well.
Furthermore, there is an increasing need for models of integer-valued time series which can accommodate series with negative observations and dependence structure more complicated than that of an autoregression or a moving average. In this regard, an integer-valued autoregressive moving average process induced by the so-called signed thinning operator is proposed. The first-order model is studied in detail. The conditions for the existence of stationary solution and the existence of finite moments are discussed under general assumptions. Under some further assumptions about the signed thinning operators and the distribution of the innovation, a moment-based estimator for the parameters is proposed, whose consistency and asymptotic normality are also proved. The problem of conducting one-step-ahead forecast is also considered based on hidden Markov chain theory.
Simulation studies arc conducted to demonstrate the validity of the theories and methods established above. Real data analysis such as the annual counts of major earthquakes data are also presented to show their potential usefulness in applications.<br>published_or_final_version<br>Statistics and Actuarial Science<br>Doctoral<br>Doctor of Philosophy
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Kwok, Sai-man Simon, and 郭世民. "Statistical inference of some financial time series models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B36885654.
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Lin, Zhongli. "On the statistical inference of some nonlinear time series models." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B43757625.
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Kidzinski, Lukasz. "Inference for stationary functional time series: dimension reduction and regression." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209226.
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Les progrès continus dans les techniques du stockage et de la collection des données permettent d'observer et d'enregistrer des processus d’une façon presque continue. Des exemples incluent des données climatiques, des valeurs de transactions financières, des modèles des niveaux de pollution, etc. Pour analyser ces processus, nous avons besoin des outils statistiques appropriés. Une technique très connue est l'analyse de données fonctionnelles (ADF).<p><p>L'objectif principal de ce projet de doctorat est d'analyser la dépendance temporelle de l’ADF. Cette dépendance se produit, par exemple, si les données sont constituées à partir d'un processus en temps continu qui a été découpé en segments, les jours par exemple. Nous sommes alors dans le cadre des séries temporelles fonctionnelles.<p><p>La première partie de la thèse concerne la régression linéaire fonctionnelle, une extension de la régression multivariée. Nous avons découvert une méthode, basé sur les données, pour choisir la dimension de l’estimateur. Contrairement aux résultats existants, cette méthode n’exige pas d'assomptions invérifiables. <p><p>Dans la deuxième partie, on analyse les modèles linéaires fonctionnels dynamiques (MLFD), afin d'étendre les modèles linéaires, déjà reconnu, dans un cadre de la dépendance temporelle. Nous obtenons des estimateurs et des tests statistiques par des méthodes d’analyse harmonique. Nous nous inspirons par des idées de Brillinger qui a étudié ces models dans un contexte d’espaces vectoriels.<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished
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Kwan, Chun-kit. "Statistical inference for some financial time series models with conditional heteroscedasticity." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B39794027.
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Lin, Zhongli, and 林中立. "On the statistical inference of some nonlinear time series models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B43757625.
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Pitrun, Ivet 1959. "A smoothing spline approach to nonlinear inference for time series." Monash University, Dept. of Econometrics and Business Statistics, 2001. http://arrow.monash.edu.au/hdl/1959.1/8367.
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Woo, Pao-sun. "Parametric inference for time series based upon goodness-of-fit /." Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk/hkuto/record.jsp?B23472613.
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胡寶璇 and Pao-sun Woo. "Parametric inference for time series based upon goodness-of-fit." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31226929.
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Li, Muyi, and 李木易. "Statistical inference on some long memory volatility models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B46482970.
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Kwan, Chun-kit, and 關進傑. "Statistical inference for some financial time series models with conditional heteroscedasticity." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B39794027.
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Zhou, Min. "The estimation and inference of complex models." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/387.
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In this thesis, we investigate the estimation problem and inference problem for the complex models. Two major categories of complex models are emphasized by us, one is generalized linear models, the other is time series models. For the generalized linear models, we consider one fundamental problem about sure screening for interaction terms in ultra-high dimensional feature space; for time series models, an important model assumption about Markov property is considered by us. The first part of this thesis illustrates the significant interaction pursuit problem for ultra-high dimensional models with two-way interaction effects. We propose a simple sure screening procedure (SSI) to detect significant interactions between the explanatory variables and the response variable in the high or ultra-high dimensional generalized linear regression models. Sure screening method is a simple, but powerful tool for the first step of feature selection or variable selection for ultra-high dimensional data. We investigate the sure screening properties of the proposal method from theoretical insight. Furthermore, we indicate that our proposed method can control the false discovery rate at a reasonable size, so the regularized variable selection methods can be easily applied to get more accurate feature selection in the following model selection procedures. Moreover, from the viewpoint of computational efficiency, we suggest a much more efficient algorithm-discretized SSI (DSSI) to realize our proposed sure screening method in practice. And we also investigate the properties of these two algorithms SSI and DSSI in simulation studies and apply them to some real data analyses for illustration. For the second part, our concern is the testing of the Markov property in time series processes. Markovian assumption plays an extremely important role in time series analysis and is also a fundamental assumption in economic and financial models. However, few existing research mainly focused on how to test the Markov properties for the time series processes. Therefore, for the Markovian assumption, we propose a new test procedure to check if the time series with beta-mixing possesses the Markov property. Our test is based on the Conditional Distance Covariance (CDCov). We investigate the theoretical properties of the proposed method. The asymptotic distribution of the proposed test statistic under the null hypothesis is obtained, and the power of the test procedure under local alternative hypothesizes have been studied. Simulation studies are conducted to demonstrate the finite sample performance of our test.
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Stark, J. Alex. "Statistical model selection techniques for data analysis." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390190.
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Siracusa, Michael Richard 1980. "Dynamic dependence analysis : modeling and inference of changing dependence among multiple time-series." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/53303.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 183-190).<br>In this dissertation we investigate the problem of reasoning over evolving structures which describe the dependence among multiple, possibly vector-valued, time-series. Such problems arise naturally in variety of settings. Consider the problem of object interaction analysis. Given tracks of multiple moving objects one may wish to describe if and how these objects are interacting over time. Alternatively, consider a scenario in which one observes multiple video streams representing participants in a conversation. Given a single audio stream, one may wish to determine with which video stream the audio stream is associated as a means of indicating who is speaking at any point in time. Both of these problems can be cast as inference over dependence structures. In the absence of training data, such reasoning is challenging for several reasons. If one is solely interested in the structure of dependence as described by a graphical model, there is the question of how to account for unknown parameters. Additionally, the set of possible structures is generally super-exponential in the number of time series. Furthermore, if one wishes to reason about structure which varies over time, the number of structural sequences grows exponentially with the length of time being analyzed. We present tractable methods for reasoning in such scenarios. We consider two approaches for reasoning over structure while treating the unknown parameters as nuisance variables. First, we develop a generalized likelihood approach in which point estimates of parameters are used in place of the unknown quantities. We explore this approach in scenarios in which one considers a small enumerated set of specified structures.<br>(cont.) Second, we develop a Bayesian approach and present a conjugate prior on the parameters and structure of a model describing the dependence among time-series. This allows for Bayesian reasoning over structure while integrating over parameters. The modular nature of the prior we define allows one to reason over a super-exponential number of structures in exponential-time in general. Furthermore, by imposing simple local or global structural constraints we show that one can reduce the exponential-time complexity to polynomial-time complexity while still reasoning over a super-exponential number of candidate structures. We cast the problem of reasoning over temporally evolving structures as inference over a latent state sequence which indexes structure over time in a dynamic Bayesian network. This model allows one to utilize standard algorithms such as Expectation Maximization, Viterbi decoding, forward-backward messaging and Gibbs sampling in order to efficiently reasoning over an exponential number of structural sequences. We demonstrate the utility of our methodology on two tasks: audio-visual association and moving object interaction analysis. We achieve state-of-the-art performance on a standard audio-visual dataset and show how our model allows one to tractably make exact probabilistic statements about interactions among multiple moving objects.<br>by Michael Richard Siracusa.<br>Ph.D.
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Ames, Allison Jennifer. "Monte Carlo Experiments on Maximum entropy Constructive Ensembles for Time Series Analysis and Inference." Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/32571.
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In econometric analysis, the traditional bootstrap and related methods often require the assumption of stationarity. This assumption says that the distribution function of the process remains unchanged when shifted in time by an arbitrary value, imposing perfect time-homogeneity. In terms of the joint distribution, stationarity implies that the date of the first time index is not relevant. There are many problems with this assumption however for time series data. With time series, the order in which random realizations occur is crucial. This is why theorists work with stochastic processes, with two implicit arguments, w and t, where w represents the sample space and t represents the order. The question becomes, is there a bootstrap procedure that can preserve the ordering without assuming stationarity? The new method for maximum entropy ensembles proposed by Dr. H. D. Vinod might satisfy the Ergodic and Kolmogorov theorems, without assuming stationarity.<br>Master of Science
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Murphy, James Kevin. "Hidden states, hidden structures : Bayesian learning in time series models." Thesis, University of Cambridge, 2014. https://www.repository.cam.ac.uk/handle/1810/250355.
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This thesis presents methods for the inference of system state and the learning of model structure for a number of hidden-state time series models, within a Bayesian probabilistic framework. Motivating examples are taken from application areas including finance, physical object tracking and audio restoration. The work in this thesis can be broadly divided into three themes: system and parameter estimation in linear jump-diffusion systems, non-parametric model (system) estimation and batch audio restoration. For linear jump-diffusion systems, efficient state estimation methods based on the variable rate particle filter are presented for the general linear case (chapter 3) and a new method of parameter estimation based on Particle MCMC methods is introduced and tested against an alternative method using reversible-jump MCMC (chapter 4). Non-parametric model estimation is examined in two settings: the estimation of non-parametric environment models in a SLAM-style problem, and the estimation of the network structure and forms of linkage between multiple objects. In the former case, a non-parametric Gaussian process prior model is used to learn a potential field model of the environment in which a target moves. Efficient solution methods based on Rao-Blackwellized particle filters are given (chapter 5). In the latter case, a new way of learning non-linear inter-object relationships in multi-object systems is developed, allowing complicated inter-object dynamics to be learnt and causality between objects to be inferred. Again based on Gaussian process prior assumptions, the method allows the identification of a wide range of relationships between objects with minimal assumptions and admits efficient solution, albeit in batch form at present (chapter 6). Finally, the thesis presents some new results in the restoration of audio signals, in particular the removal of impulse noise (pops and clicks) from audio recordings (chapter 7).
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Dou, Lixin. "Applications of Bayesian inference methods to time series data analysis and hyperfine parameter extractions in Mössbauer spectroscopy." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0020/NQ45170.pdf.
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Dou, Lixin. "Applications of Bayesian inference methods to time series data analysis and hyperfine parameter extractions in Mossbauer spectroscopy." Thesis, University of Ottawa (Canada), 1999. http://hdl.handle.net/10393/8483.
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The Bayesian statistical inference theory is studied and applied to two problems in applied physics: spectral analysis and parameter estimation in time series data and hyperfine parameter extraction in Mossbauer spectroscopy. The applications to spectral analysis and parameter estimation for both single- and multiple-frequency signals are presented in detail. Specifically, the marginal posterior probabilities for the amplitudes and frequencies of the signals are obtained by using Gibbs sampling without performing the integration, no matter whether the variance of the noise is known or unknown. The best estimates of the parameters can be inferred from these probabilities together with the corresponding variances. When the variance of the noise is unknown, an estimate about the variance of the noise can also be made. Comparisons of our results have been made with results using the Fast Fourier Transformation (FFT) method as well as Bretthorst's method. The same numerical approach is applied to some complicated models and conditions, such as periodic but non-harmonic signals, signals with decay, and signals with chirp. Results demonstrate that even under these complicated conditions the Bayesian inference and Gibbs sampling can still give very accurate results with respect to the true result. Also through the use of the Bayesian inference methods it is possible to choose the most probable model based on known prior information of data, assuming a model space. The Bayesian inference theory is applied to hyperfine parameter extraction in Mossbauer spectroscopy for the first time. The method is a free-form model extraction approach and gives full error analysis of hyperfine parameter distributions. Two applications to quadrupole splitting distribution analysis in Fe-57 Mossbauer spectroscopy are presented. One involves a single site of Fe3+ and the other involves two sites for Fe3+ and Fe2+. In each case the method gives a unique solution to the distributions with arbitrary shape and is not sensitive to the elemental doublet parameters. The Bayesian inference theory is also applied to the hyperfine field distribution extraction. Because of the complexity of the elemental lineshape, all the other extraction methods can only use the first order perturbation sextet as the lineshape function. We use Blaes' exact lineshape model to extract the hyperfine field distribution. This is possible because the Bayesian inference theory is a free-form model extraction method. By using Blaes' lineshape function, different cases of orientations between the electric field gradient principle axis directions and the magnetic hyperfine field can be studied without making any approximations. As an example the ground state hyperfine field distribution of Fe65Ni35 Invar is extensively studied by using the method. Some very interesting features of the hyperfine field distribution are identified.
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Bonander, Carl. "Assessing the effects of societal injury control interventions." Doctoral thesis, Karlstads universitet, Centrum för personsäkerhet, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-41204.
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Injuries have emerged as one of the biggest public health issues of the 21th century. Yet, the causal effects of injury control strategies are often questioned due to a lack of randomized experiments. In this thesis, a set of quasi-experimental methods are applied and discussed in the light of causal inference theory and the type of data commonly available in injury surveillance systems. I begin by defining the interrupted time series design as a special case of the regression-discontinuity design, and the method is applied to two empirical cases. The first is a ban on the sale and production of non-reduced ignition propensity (RIP) cigarettes, and the second is a tightening of the licensing rules for mopeds. A two-way fixed effects model is then applied to a case with time-varying starting dates, attempting to identify the causal effects of municipality-provided home help services for the elderly. Lastly, the effect of the Swedish bicycle helmet law is evaluated using the comparative interrupted time series and synthetic control methods. The results from the empirical studies suggest that the stricter licensing rules and the bicycle helmet law were effective in reducing injury rates, while the home help services and RIP cigarette interventions have had limited or no impact on safety as measured by fatalities and hospital admissions. I conclude that identification of the impact of injury control interventions is possible using low cost means. However, the ability to infer causality varies greatly by empirical case and method, which highlights the important role of causal inference theory in applied intervention research. While existing methods can be used with data from injury surveillance systems, additional improvements and development of new estimators specifically tailored for injury data will likely further enhance the ability to draw causal conclusions in natural settings. Implications for future research and recommendations for practice are also discussed.<br>Injuries have emerged as one of the biggest public health issues of the 21th century. Yet, the causal effects of injury control strategies are rarely known due to a lack of randomized experiments. In this thesis, a set of quasi-experimental methods are discussed in the light of causal inference theory and the type of data commonly available in injury surveillance systems. I begin by defining the identifying assumptions of the interrupted time series design as a special case of the regression-discontinuity design, and the method is applied to two empirical cases. The first is a ban on the sale and production of non-fire safe cigarettes and the second is a tightening of the licensing rules for mopeds. A fixed effects panel regression analysis is then applied to a case with time-varying starting dates, attempting to identify the causal effects of municipality-provided home help services for the elderly. Lastly, the causal effect of the Swedish bicycle helmet law is evaluated using a comparative interrupted time series design and a synthetic control design. I conclude that credible identification of the impact of injury control interventions is possible using simple and cost-effective means. Implications for future research and recommendations for practice are discussed.
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Bonander, Carl. "Searching for causal effects of road traffic safety interventions : applications of the interrupted time series design." Licentiate thesis, Karlstads universitet, Institutionen för miljö- och livsvetenskaper, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-35781.
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Traffic-related injuries represent a global public health problem, and contribute largely to mortality and years lived with disability worldwide. Over the course of the last decades, improvements to road traffic safety and injury surveillance systems have resulted in a shift in focus from the prevention of motor vehicle accidents to the control of injury events involving vulnerable road users (VRUs), such as cyclists and moped riders. There have been calls for improvements to the evaluation of safety interventions due to methodological problems associated with the most commonly used study designs. The purpose of this licentiate thesis was to assess the strengths and limitations of the interrupted time series (ITS) design, which has gained some attention for its ability to provide valid effect estimates. Two national road safety interventions involving VRUs were selected as cases: the Swedish bicycle helmet law for children under the age 15, and the tightening of licensing rules for Class 1 mopeds. The empirical results suggest that both interventions were effective in improving the safety of VRUs. Unless other concurrent events affect the treatment population at the exact time of intervention, the effect estimates should be internally valid. One of the main limitations of the study design is the inability to identify why the interventions were successful, especially if they are complex and multifaceted. A lack of reliable exposure data can also pose a further threat to studies of interventions involving VRUs if the intervention can affect the exposure itself. It may also be difficult to generalize the exact effect estimates to other regions and populations. Future studies should consider the use of the ITS design to enhance the internal validity of before-after measurements.<br>Traffic-related injuries represent a global public health problem, and contribute largely to mortality and years lived with disability. Over the course of the last decades, improvements to road traffic safety and injury surveillance systems have resulted in a shift in focus from motor vehicle accidents to injury events involving vulnerable road users (VRUs), such as cyclists and moped riders. There have been calls for improvements to the evaluation of safety interventions due to methodological problems associated with the most commonly used study designs. The purpose of this licentiate thesis was to assess the strengths and limitations of the interrupted time series (ITS) design, which has gained some attention for its ability to provide valid effect estimates while accounting for secular trends. Two national interventions involving VRUs were selected as cases: the Swedish bicycle helmet law for children under the age 15, and the tightening of licensing rules for Class 1 mopeds. The empirical results suggest that both interventions were effective. These results are discussed in the light of some methodological considerations regarding internal and external validity, data quality and the ability to fully understand key causal mechanisms behind complex interventions.
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Elling, Eva. "Effects of MIFID II on Stock Trade Volumes of Nasdaq Stockholm." Thesis, KTH, Matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-257510.
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Introducing new financial legislation to financial markets require caution to achieve the intended outcome. This thesis aims to investigate whether or not the newly installed revised Markets in Financial Instruments Directive- the MIFID II regulation - temporally influenced the trading stock volume levels of Nasdaq Stockholm during its introduction to the Swedish stock market. A first approach of a generalized Negative Binomial model is carried out on aggregated data, followed by an individual Fixed Effects model in an attempt to eliminate omitted variable bias caused by missing unobserved variables for the individual stocks. The aggregated data is attained by taking the equally weighted average of the trading volume and adjusting for seasonality through Seasonal and Trend decomposition using Loess in combination with a regression model with ARIMA errors to mitigate calendar effects. Due to robustness of the aggregated data, the Negative Binomial model manage to capture significant effects of the regulation on the Small Cap. segment, even though clusters of the data show signs of divergent reactions to MIFID II. Since the Fixed Effects model operate on non-aggregated TSCS data and because of the varying effects on each stock the Fixed Effect model fails in its attempt to do the same.<br>Implementation av nya finansiella regelverk på finansmarknaden kräver aktsamhet för att uppnå de tilltänka målen. Det här arbetet undersöker huruvida MIFID II regleringen orsakade en temporär medelvärdesskiftning av de handlade aktievolymerna på Nasdaq Stockholm under regelverkets introduktion på den svenska marknaden. Först testas en generaliserad Negative Binomial regression applicerat på aggregerad data, därefter en individuell Fixed Effects modell för att försöka eliminera fel på grund av saknade, okända variabler. Det aggrigerade datasettet erhålls genom att ta genomsnittet av handelsvolymerna och justera dessa för sässongsmässiga mönster med metoden STL i kombination med regression med ARIMA residualer för att även ta hänsyn till kalender relaterade effekter. Eftersom den aggrigerade datan är robust lyckas the Negative Binomial regressionen fånga signifikanta effekter av regleringen för Small Cap. segmentet trots att datat uppvisar tecken på att subgrupper inom segmentet reagerat väldigt olika på den nya regleringen. Eftersom Fixed Effects modellen är applicerad på icke-aggrigerad TSCS data och pågrund av den varierande effekten på de individuella aktierna lyckas inte denna modell med detta.
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Lebre, Sophie. "Stochastic process analysis for Genomics and Dynamic Bayesian Networks inference." Phd thesis, Université d'Evry-Val d'Essonne, 2007. http://tel.archives-ouvertes.fr/tel-00260250.
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This thesis is dedicated to the development of statistical and computational methods for the analysis of DNA sequences and gene expression time series.<br /><br />First we study a parsimonious Markov model called Mixture Transition Distribution (MTD) model which is a mixture of Markovian transitions. The overly high number of constraints on the parameters of this model hampers the formulation of an analytical expression of the Maximum Likelihood Estimate (MLE). We propose to approach the MLE thanks to an EM algorithm. After comparing the performance of this algorithm to results from the litterature, we use it to evaluate the relevance of MTD modeling for bacteria DNA coding sequences in comparison with standard Markovian modeling.<br /><br />Then we propose two different approaches for genetic regulation network recovering. We model those genetic networks with Dynamic Bayesian Networks (DBNs) whose edges describe the dependency relationships between time-delayed genes expression. The aim is to estimate the topology of this graph despite the overly low number of repeated measurements compared with the number of observed genes. <br /><br />To face this problem of dimension, we first assume that the dependency relationships are homogeneous, that is the graph topology is constant across time. Then we propose to approximate this graph by considering partial order dependencies. The concept of partial order dependence graphs, already introduced for static and non directed graphs, is adapted and characterized for DBNs using the theory of graphical models. From these results, we develop a deterministic procedure for DBNs inference. <br /><br />Finally, we relax the homogeneity assumption by considering the succession of several homogeneous phases. We consider a multiple changepoint<br />regression model. Each changepoint indicates a change in the regression model parameters, which corresponds to the way an expression level depends on the others. Using reversible jump MCMC methods, we develop a stochastic algorithm which allows to simultaneously infer the changepoints location and the structure of the network within the phases delimited by the changepoints. <br /><br />Validation of those two approaches is carried out on both simulated and real data analysis.
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Bianco-Martinez, Ezequiel Julian. "Information, causality, and observability approaches to understand complex systems." Thesis, University of Aberdeen, 2015. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=230030.
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The objective of this thesis is to propose fundamental concepts, analytical and numerical tools, and approaches to characterize, understand, and better observe complex systems. The scientific contribution of this thesis can be separated in tree topics. In the first one, we show how to theoretically estimate the Mutual Information Rate (MIR), the amount of mutual information transmitted per unit of time between two time-series. We then show how a quantity derived from it can be successfully used to infer the network structure of a complex system. The proposed inference methodology shows to be robust in the presence of additive noise, different time-series lengths, and heterogeneous node dynamics and coupling strengths. It also shows to be superior in performance for networks formed by nodes possessing different time-scales, as compared to inference methods based on mutual information (MI). In the second topic, a deep analysis of causality from the space-time properties of the observed probabilistic space is performed. We show the existence of special regions in the state space which indicate variable ranges responsible for most of the information exchanged between two variables. We define a new causality measure named CaMI that explores a property we have understood: in order to detect if there is a flow of information from X to Y, one only needs to check the positiveness of the MI between trajectories in X and Y, however assuming that the observational resolution in Y is larger than in X. Moreover, we show how the assessment of causality can be done when we consider partitions with arbitrary, but equal rectangular cells in the probabilist space, what naturally facilitates the calculation of CaMI. In the third topic, we develop a symbolic coefficient of observability that allows us to understand what is the reduced set of accessible variables to observe a complex system, such that it can be fully reconstructed from the set of observed variables, regardless of its dimension. Using this symbolic coefficient, we explain how it is possible to compare different complex systems from the point of view of observability and how to construct systems of any dimensionality that can be fully observed by only one variable.
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Safari, Katesari Hadi. "BAYESIAN DYNAMIC FACTOR ANALYSIS AND COPULA-BASED MODELS FOR MIXED DATA." OpenSIUC, 2021. https://opensiuc.lib.siu.edu/dissertations/1948.
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Available statistical methodologies focus more on accommodating continuous variables, however recently dealing with count data has received high interest in the statistical literature. In this dissertation, we propose some statistical approaches to investigate linear and nonlinear dependencies between two discrete random variables, or between a discrete and continuous random variables. Copula functions are powerful tools for modeling dependencies between random variables. We derive copula-based population version of Spearman’s rho when at least one of the marginal distribution is discrete. In each case, the functional relationship between Kendall’s tau and Spearman’s rho is obtained. The asymptotic distributions of the proposed estimators of these association measures are derived and their corresponding confidence intervals are constructed, and tests of independence are derived. Then, we propose a Bayesian copula factor autoregressive model for time series mixed data. This model assumes conditional independence and shares latent factors in both mixed-type response and multivariate predictor variables of the time series through a quadratic timeseries regression model. This model is able to reduce the dimensionality by accommodating latent factors in both response and predictor variables of the high-dimensional time series data. A semiparametric time series extended rank likelihood technique is applied to the marginal distributions to handle mixed-type predictors of the high-dimensional time series, which decreases the number of estimated parameters and provides an efficient computational algorithm. In order to update and compute the posterior distributions of the latent factors and other parameters of the models, we propose a naive Bayesian algorithm with Metropolis-Hasting and Forward Filtering Backward Sampling methods. We evaluate the performance of the proposed models and methods through simulation studies. Finally, each proposed model is applied to a real dataset.
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Hasegawa, Takanori. "Reconstructing Biological Systems Incorporating Multi-Source Biological Data via Data Assimilation Techniques." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/195985.
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Tanner, Whitney Ford. "Improved Standard Error Estimation for Maintaining the Validities of Inference in Small-Sample Cluster Randomized Trials and Longitudinal Studies." UKnowledge, 2018. https://uknowledge.uky.edu/epb_etds/20.
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Data arising from Cluster Randomized Trials (CRTs) and longitudinal studies are correlated and generalized estimating equations (GEE) are a popular analysis method for correlated data. Previous research has shown that analyses using GEE could result in liberal inference due to the use of the empirical sandwich covariance matrix estimator, which can yield negatively biased standard error estimates when the number of clusters or subjects is not large. Many techniques have been presented to correct this negative bias; However, use of these corrections can still result in biased standard error estimates and thus test sizes that are not consistently at their nominal level. Therefore, there is a need for an improved correction such that nominal type I error rates will consistently result.
First, GEEs are becoming a popular choice for the analysis of data arising from CRTs. We study the use of recently developed corrections for empirical standard error estimation and the use of a combination of two popular corrections. In an extensive simulation study, we find that nominal type I error rates can be consistently attained when using an average of two popular corrections developed by Mancl and DeRouen (2001, Biometrics 57, 126-134) and Kauermann and Carroll (2001, Journal of the American Statistical Association 96, 1387-1396) (AVG MD KC). Use of this new correction was found to notably outperform the use of previously recommended corrections.
Second, data arising from longitudinal studies are also commonly analyzed with GEE. We conduct a simulation study, finding two methods to attain nominal type I error rates more consistently than other methods in a variety of settings: First, a recently proposed method by Westgate and Burchett (2016, Statistics in Medicine 35, 3733-3744) that specifies both a covariance estimator and degrees of freedom, and second, AVG MD KC with degrees of freedom equaling the number of subjects minus the number of parameters in the marginal model.
Finally, stepped wedge trials are an increasingly popular alternative to traditional parallel cluster randomized trials. Such trials often utilize a small number of clusters and numerous time intervals, and these components must be considered when choosing an analysis method. A generalized linear mixed model containing a random intercept and fixed time and intervention covariates is the most common analysis approach. However, the sole use of a random intercept applies assumptions that will be violated in practice. We show, using an extensive simulation study based on a motivating example and a more general design, alternative analysis methods are preferable for maintaining the validity of inference in small-sample stepped wedge trials with binary outcomes. First, we show the use of generalized estimating equations, with an appropriate bias correction and a degrees of freedom adjustment dependent on the study setting type, will result in nominal type I error rates. Second, we show the use of a cluster-level summary linear mixed model can also achieve nominal type I error rates for equal cluster size settings.
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Nguyen, Van Duong. "Variational deep learning for time series modelling and analysis : applications to dynamical system identification and maritime traffic anomaly detection." Thesis, Ecole nationale supérieure Mines-Télécom Atlantique Bretagne Pays de la Loire, 2020. http://www.theses.fr/2020IMTA0227.
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Ce travail de thèse se focalise sur une classe de méthodes d’apprentissage profond, probabilistes et non-supervisées qui utilisent l’inférence variationnelle pour créer des modèles évolutifs de grande capacité pour ce type de données. Nous présentons deux classes d’apprentissage variationnel profond, puis nous les appliquons à deux problèmes spécifiques liés au domaine maritime. La première application est l’identification de systèmes dynamiques à partir de données bruitées et partiellement observées. Nous introduisons un cadre qui fusionne l’assimilation de données classique et l’apprentissage profond moderne pour retrouver les équations différentielles qui contrôlent la dynamique du système. En utilisant une formulation d’espace d’états, le cadre proposé intègre des composantes stochastiques pour tenir compte des variabilités stochastiques, des erreurs de modèle et des incertitudes de reconstruction. La deuxième application est la surveillance du trafic maritime à l’aide des données AIS. Nous proposons une architecture d’apprentissage profond probabiliste multitâche pouvant atteindre des performances très prometteuses dans différentes tâches liées à la surveillance du trafic maritime, telles que la reconstruction de trajectoire, l’identification du type de navire et la détection d’anomalie, tout en réduisant considérablement la quantité de données à stocker et le temps de calcul. temps. Pour la tâche la plus importante - la détection d’anomalie, nous introduisons un détecteur géospatialisé qui utilise l’apprentissage profond variationnel pour construire une représentation probabiliste des trajectoires AIS, puis détecter les anomalies en jugeant la probabilité de cette trajectoire<br>This thesis work focuses on a class of unsupervised, probabilistic deep learning methods that use variational inference to create high capacity, scalable models for time series modelling and analysis. We present two classes of variational deep learning, then apply them to two specific problems related to the maritime domain. The first application is the identification of dynamical systems from noisy and partially observed data. We introduce a framework that merges classical data assimilation and modern deep learning to retrieve the differential equations that control the dynamics of the system. Using a state space formulation, the proposed framework embeds stochastic components to account for stochastic variabilities, model errors and reconstruction uncertainties. The second application is maritime traffic surveillance using AIS data. We propose a multitask probabilistic deep learning architecture can achieve state-of-the-art performance in different maritime traffic surveillance related tasks, such as trajectory reconstruction, vessel type identification and anomaly detection, while reducing significantly the amount data to be stored and the calculation time. For the most important task—anomaly detection, we introduce a geospatial detector that uses variational deep learning to builds a probabilistic representation of AIS trajectories, then detect anomalies by judging how likely this trajectory is
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Massaroppe, Lucas. "Caracterização da conectividade entre regiões cerebrais via entropia aproximada e causalidade de Granger." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/3/3142/tde-04112011-140951/.
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Essa dissertação apresenta o desenvolvimento métodos para caracterização da conectividade entre séries temporais neurofisiológicas. Utilizam-se metodologias provenientes da Teoria da Informação Entropias Aproximada e Amostral para representar a complexidade da série no tempo, o que permite inferir como sua variabilidade se transfere a outras sequências, através do uso da coerência parcial direcionada. Para cada sistema analisado: (1) Faz-se uma transformação em outro, relacionando-o às medidas de entropia, (2) Estima-se a conectividade pela coerência parcial direcionada e (3) Avalia-se a robustez do procedimento via simulações de Monte Carlo e análise de sensibilidade. Para os exemplos simulados, a técnica proposta é capaz de oferecer resultados plausíveis, através da correta inferência da direção de conectividade em casos de acoplamento não-linear (quadrático), com número reduzido de amostras temporais dos sinais, em que outras abordagens falham. Embora de simples implementação, conclui-se que o processo mostra-se como uma extensão da causalidade de Granger para o caso não-linear.<br>The purpose of this work is to present the development of methods for characterizing the connectivity between nonlinear neurophysiological time series. Methodologies from Information Theory Approximate and Sample Entropies are used to represent the complexity of the series in a period of time, which allows inferring on how its variability is transferred to other sequences, using partial directed coherence. Methods: For each system under consideration, (1) It is done a transformation in another, relating it to measures of entropy, (2) The connectivity is estimated by the use of partial directed coherence and (3) The robustness of the procedure is analyzed via Monte Carlo simulations and sensitivity analysis. Results: For the simulated examples, the proposed technique is able to offer plausible results, through the correct inference of the connectivity direction, in cases of nonlinear coupling (quadratic), with a reduced number of signals samples, where other approaches fail. Conclusion: The process proves to be an extension of the Granger causality to the nonlinear case.
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Silvestrini, Andrea. "Essays on aggregation and cointegration of econometric models." Doctoral thesis, Universite Libre de Bruxelles, 2009. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210304.
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This dissertation can be broadly divided into two independent parts. The first three chapters analyse issues related to temporal and contemporaneous aggregation of econometric models. The fourth chapter contains an application of Bayesian techniques to investigate whether the post transition fiscal policy of Poland is sustainable in the long run and consistent with an intertemporal budget constraint.<p><p><p>Chapter 1 surveys the econometric methodology of temporal aggregation for a wide range of univariate and multivariate time series models. <p><p><p>A unified overview of temporal aggregation techniques for this broad class of processes is presented in the first part of the chapter and the main results are summarized. In each case, assuming to know the underlying process at the disaggregate frequency, the aim is to find the appropriate model for the aggregated data. Additional topics concerning temporal aggregation of ARIMA-GARCH models (see Drost and Nijman, 1993) are discussed and several examples presented. Systematic sampling schemes are also reviewed.<p><p><p>Multivariate models, which show interesting features under temporal aggregation (Breitung and Swanson, 2002, Marcellino, 1999, Hafner, 2008), are examined in the second part of the chapter. In particular, the focus is on temporal aggregation of VARMA models and on the related concept of spurious instantaneous causality, which is not a time series property invariant to temporal aggregation. On the other hand, as pointed out by Marcellino (1999), other important time series features as cointegration and presence of unit roots are invariant to temporal aggregation and are not induced by it.<p><p><p>Some empirical applications based on macroeconomic and financial data illustrate all the techniques surveyed and the main results.<p><p>Chapter 2 is an attempt to monitor fiscal variables in the Euro area, building an early warning signal indicator for assessing the development of public finances in the short-run and exploiting the existence of monthly budgetary statistics from France, taken as "example country". <p><p><p>The application is conducted focusing on the cash State deficit, looking at components from the revenue and expenditure sides. For each component, monthly ARIMA models are estimated and then temporally aggregated to the annual frequency, as the policy makers are interested in yearly predictions. <p><p><p>The short-run forecasting exercises carried out for years 2002, 2003 and 2004 highlight the fact that the one-step-ahead predictions based on the temporally aggregated models generally outperform those delivered by standard monthly ARIMA modeling, as well as the official forecasts made available by the French government, for each of the eleven components and thus for the whole State deficit. More importantly, by the middle of the year, very accurate predictions for the current year are made available. <p><p>The proposed method could be extremely useful, providing policy makers with a valuable indicator when assessing the development of public finances in the short-run (one year horizon or even less). <p><p><p>Chapter 3 deals with the issue of forecasting contemporaneous time series aggregates. The performance of "aggregate" and "disaggregate" predictors in forecasting contemporaneously aggregated vector ARMA (VARMA) processes is compared. An aggregate predictor is built by forecasting directly the aggregate process, as it results from contemporaneous aggregation of the data generating vector process. A disaggregate predictor is a predictor obtained from aggregation of univariate forecasts for the individual components of the data generating vector process. <p><p>The econometric framework is broadly based on Lütkepohl (1987). The necessary and sufficient condition for the equality of mean squared errors associated with the two competing methods in the bivariate VMA(1) case is provided. It is argued that the condition of equality of predictors as stated in Lütkepohl (1987), although necessary and sufficient for the equality of the predictors, is sufficient (but not necessary) for the equality of mean squared errors. <p><p><p>Furthermore, it is shown that the same forecasting accuracy for the two predictors can be achieved using specific assumptions on the parameters of the VMA(1) structure. <p><p><p>Finally, an empirical application that involves the problem of forecasting the Italian monetary aggregate M1 on the basis of annual time series ranging from 1948 until 1998, prior to the creation of the European Economic and Monetary Union (EMU), is presented to show the relevance of the topic. In the empirical application, the framework is further generalized to deal with heteroskedastic and cross-correlated innovations. <p><p><p>Chapter 4 deals with a cointegration analysis applied to the empirical investigation of fiscal sustainability. The focus is on a particular country: Poland. The choice of Poland is not random. First, the motivation stems from the fact that fiscal sustainability is a central topic for most of the economies of Eastern Europe. Second, this is one of the first countries to start the transition process to a market economy (since 1989), providing a relatively favorable institutional setting within which to study fiscal sustainability (see Green, Holmes and Kowalski, 2001). The emphasis is on the feasibility of a permanent deficit in the long-run, meaning whether a government can continue to operate under its current fiscal policy indefinitely.<p><p>The empirical analysis to examine debt stabilization is made up by two steps. <p><p>First, a Bayesian methodology is applied to conduct inference about the cointegrating relationship between budget revenues and (inclusive of interest) expenditures and to select the cointegrating rank. This task is complicated by the conceptual difficulty linked to the choice of the prior distributions for the parameters relevant to the economic problem under study (Villani, 2005).<p><p>Second, Bayesian inference is applied to the estimation of the normalized cointegrating vector between budget revenues and expenditures. With a single cointegrating equation, some known results concerning the posterior density of the cointegrating vector may be used (see Bauwens, Lubrano and Richard, 1999). <p><p>The priors used in the paper leads to straightforward posterior calculations which can be easily performed.<p>Moreover, the posterior analysis leads to a careful assessment of the magnitude of the cointegrating vector. Finally, it is shown to what extent the likelihood of the data is important in revising the available prior information, relying on numerical integration techniques based on deterministic methods.<p><br>Doctorat en Sciences économiques et de gestion<br>info:eu-repo/semantics/nonPublished
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Lohier, Théophile. "Analyse temporelle de la dynamique de communautés végétales à l'aide de modèles individus-centrés." Thesis, Clermont-Ferrand 2, 2016. http://www.theses.fr/2016CLF22683/document.
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Les communautés végétales constituent des systèmes complexes au sein desquels de nombreuses espèces, pouvant présenter une large variété de traits fonctionnels, interagissent entre elles et avec leur environnement. En raison de la quantité et de la diversité de ces interactions les mécanismes qui gouvernent les dynamiques des ces communautés sont encore mal connus. Les approches basées sur la modélisation permettent de relier de manière mécaniste les processus gouvernant les dynamiques des individus ou des populations aux dynamiques des communautés qu'ils forment. L'objectif de cette thèse était de développer de telles approches et de les mettre en oeuvre pour étudier les mécanismes sous-jacents aux dynamiques des communautés. Nous avons ainsi développés deux approches de modélisation. La première s'appuie sur un cadre de modélisation stochastique permettant de relier les dynamiques de populations aux dynamiques des communautés en tenant compte des interactions intra- et interspécifiques et de l'impact des variations environnementale et démographique. Cette approche peut-être aisément appliquée à des systèmes réels et permet de caractériser les populations végétales à l'aide d'un petit nombre de paramètres démographiques. Cependant nos travaux suggèrent qu'il n'existe pas de relation simple entre ces paramètres et les traits fonctionnels des espèces, qui gouvernent pourtant leur réponse aux facteurs externes. La seconde approche a été développée pour dépasser cette limite et s'appuie sur le modèle individu-centré Nemossos qui représente de manière explicite le lien entre le fonctionnement des individus et les dynamiques de la communauté qu'ils forment. Afin d'assurer un grand potentiel d'application à Nemossos, nous avons apportés une grande attention au compromis entre réalisme et coût de paramétrisation. Nemossos a ainsi pu être entièrement paramétré à partir de valeur de traits issues de la littérature , son réalisme a été démontré, et il a été utilisé pour mener des expériences de simulations numériques sur l'importance de la variabilité temporelle des conditions environnementales pour la coexistence d'espèces fonctionnellement différentes. La complémentarité des deux approches nous a permis de proposer des éléments de réponse à divers questions fondamentales de l'écologie des communautés incluant le rôle de la compétition dans les dynamiques des communautés, l'effet du filtrage environnementale sur leur composition fonctionnel ou encore les mécanismes favorisant la coexistence des espèces végétales. Ici ces approches ont été utilisées séparément mais leur couplage peut offrir des perspectives intéressantes telles que l'étude du lien entre le fonctionnement des plantes et les dynamiques des populations. Par ailleurs chacune des approches peut être utilisée dans une grande variété d'expériences de simulation susceptible d'améliorer notre compréhension des mécanismes gouvernant les communautés végétales<br>Plant communities are complex systems in which multiple species differing by their functional attributes interact with their environment and with each other. Because of the number and the diversity of these interactions the mechanisms that drive the dynamics of theses communities are still poorly understood. Modelling approaches enable to link in a mechanistic fashion the process driving individual plant or population dynamics to the resulting community dynamics. This PhD thesis aims at developing such approaches and to use them to investigate the mechanisms underlying community dynamics. We therefore developed two modelling approaches. The first one is based on a stochastic modelling framework allowing to link the population dynamics to the community dynamics whilst taking account of intra- and interspecific interactions as well as environmental and demographic variations. This approach is easily applicable to real systems and enables to describe the properties of plant population through a small number of demographic parameters. However our work suggests that there is no simple relationship between these parameters and plant functional traits, while they are known to drive their response to extrinsic factors. The second approach has been developed to overcome this limitation and rely on the individual-based model Nemossos that explicitly describes the link between plant functioning and community dynamics. In order to ensure that Nemossos has a large application potential, a strong emphasis has been placed on the tradeoff between realism and parametrization cost. Nemossos has then been successfully parameterized from trait values found in the literature, its realism has been demonstrated and it has been used to investigate the importance of temporal environmental variability for the coexistence of functionally differing species. The complementarity of the two approaches allows us to explore various fundamental questions of community ecology including the impact of competitive interactions on community dynamics, the effect of environmental filtering on their functional composition, or the mechanisms favoring the coexistence of plant species. In this work, the two approaches have been used separately but their coupling might offer interesting perspectives such as the investigation of the relationships between plant functioning and population dynamics. Moreover each of the approaches might be used to run various simulation experiments likely to improve our understanding of mechanisms underlying community dynamics
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Phan, Thi-Thu-Hong. "Elastic matching for classification and modelisation of incomplete time series." Thesis, Littoral, 2018. http://www.theses.fr/2018DUNK0483/document.
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Les données manquantes constituent un challenge commun en reconnaissance de forme et traitement de signal. Une grande partie des techniques actuelles de ces domaines ne gère pas l'absence de données et devient inutilisable face à des jeux incomplets. L'absence de données conduit aussi à une perte d'information, des difficultés à interpréter correctement le reste des données présentes et des résultats biaisés notamment avec de larges sous-séquences absentes. Ainsi, ce travail de thèse se focalise sur la complétion de larges séquences manquantes dans les séries monovariées puis multivariées peu ou faiblement corrélées. Un premier axe de travail a été une recherche d'une requête similaire à la fenêtre englobant (avant/après) le trou. Cette approche est basée sur une comparaison de signaux à partir d'un algorithme d'extraction de caractéristiques géométriques (formes) et d'une mesure d'appariement élastique (DTW - Dynamic Time Warping). Un package R CRAN a été développé, DTWBI pour la complétion de série monovariée et DTWUMI pour des séries multidimensionnelles dont les signaux sont non ou faiblement corrélés. Ces deux approches ont été comparées aux approches classiques et récentes de la littérature et ont montré leur faculté de respecter la forme et la dynamique du signal. Concernant les signaux peu ou pas corrélés, un package DTWUMI a aussi été développé. Le second axe a été de construire une similarité floue capable de prender en compte les incertitudes de formes et d'amplitude du signal. Le système FSMUMI proposé est basé sur une combinaison floue de similarités classiques et un ensemble de règles floues. Ces approches ont été appliquées à des données marines et météorologiques dans plusieurs contextes : classification supervisée de cytogrammes phytoplanctoniques, segmentation non supervisée en états environnementaux d'un jeu de 19 capteurs issus d'une station marine MAREL CARNOT en France et la prédiction météorologique de données collectées au Vietnam<br>Missing data are a prevalent problem in many domains of pattern recognition and signal processing. Most of the existing techniques in the literature suffer from one major drawback, which is their inability to process incomplete datasets. Missing data produce a loss of information and thus yield inaccurate data interpretation, biased results or unreliable analysis, especially for large missing sub-sequence(s). So, this thesis focuses on dealing with large consecutive missing values in univariate and low/un-correlated multivariate time series. We begin by investigating an imputation method to overcome these issues in univariate time series. This approach is based on the combination of shape-feature extraction algorithm and Dynamic Time Warping method. A new R-package, namely DTWBI, is then developed. In the following work, the DTWBI approach is extended to complete large successive missing data in low/un-correlated multivariate time series (called DTWUMI) and a DTWUMI R-package is also established. The key of these two proposed methods is that using the elastic matching to retrieving similar values in the series before and/or after the missing values. This optimizes as much as possible the dynamics and shape of knowledge data, and while applying the shape-feature extraction algorithm allows to reduce the computing time. Successively, we introduce a new method for filling large successive missing values in low/un-correlated multivariate time series, namely FSMUMI, which enables to manage a high level of uncertainty. In this way, we propose to use a novel fuzzy grades of basic similarity measures and fuzzy logic rules. Finally, we employ the DTWBI to (i) complete the MAREL Carnot dataset and then we perform a detection of rare/extreme events in this database (ii) forecast various meteorological univariate time series collected in Vietnam
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Massaroppe, Lucas. "Estimação da causalidade de Granger no caso de interação não-linear." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/3/3142/tde-20122016-083110/.
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Esta tese examina o problema de detecção de conectividade entre séries temporais no sentido de Granger no caso em que a natureza não linear das interações não permite sua determinação por meio de modelos auto-regressivos lineares vetoriais. Mostra-se que é possível realizar esta detecção com auxílio dos chamados métodos de Kernel, que se tornaram populares em aprendizado por máquina (\'machine learning\') já que tais métodos permitem definir formas generalizadas de teste de Granger, coerência parcial direcionada e função de transferência direcionada. Usando simulações, mostram-se alguns exemplos de detecção nos quais fica também evidente que resultados assintóticos deduzidos originalmente para estimadores lineares podem ser generalizados de modo análogo, mostrando-se válidos no presente contexto kernelizado.<br>This work examines the connectivity detection problem between time series in the Granger sense when the nonlinear nature of interactions determination is impossible via linear vector autoregressive models, but is, nonetheless, feasible with the aid of the so-called Kernel methods that are popular in machine learning. The kernelization approach allows defining generalised versions for Granger tests, partial directed coherence and directed transfer function, which the simulation of some examples shows that the asymptotic detection results originally deducted for linear estimators, can also be employed under kernelization if suitably adapted.
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Chen, Siyuan. "Causality inference between time series data and its applications." Thesis, 2020. https://doi.org/10.7916/d8-8w9b-zx36.
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Ever since Granger first proposed the idea of quantitatively testing the causal relationship between data streams, the endeavor of accurately inferring the causality in data and using that information to predict the future has not stopped. Artificial Intelligence (AI), by utilizing the massive amounts of data, helps to solve complex problems, whether they include the diagnosis and detection of disease through medical imaging, email spam detection, or self-driving vehicles. Perhaps, this thesis will be trivial in ten years from now. AI has pushed humankind to reach the next technological level in technology. Nowadays, among most machine leaning inquiries, statistical relationships are determined using correlation measures. By feeding data into machine learning algorithms, computers update the algorithm’s parameters iteratively by extracting and mapping features to learning targets until the correlation increases to a significant level to cease the training process. However, with the increasing developments of powerful AI, there is really a shortage of exploring causality in data.
It is almost self-evident that ”correlation is not causality." Sometimes, the strong correlation established between variables through machine learning can be absurd and meaningless. Providing insight into causality information through data, which most of the machine learning methods fall short to do, is of paramount importance.
The subsequent chapters detail the four endeavors of studying causality in financial markets, earthquakes, animal/human brain signals, the predictivity of data sets. In Chapter 2, we further developed the concept of causality networks into a higher-order causality network. We applied these to financial data and tested their validity and ability to capture the system’s causal relationship. In next Chapter 3, We examined another type of time series-earthquakes. Violent seismic activities decimate people's lives and destroy entire cities and areas. This begs us to understand how earthquakes work and help us make reliably and evacuation-actionable predictions. The causal relationships of seismic activities in different areas are studied and established. Biological data, specifically brain signals, are time-series data and their causal pattern are explored and studied. Different human and mice brain signals are analyzed and clustered in Chapter 4 using their unique causal pattern to understand different brain cell activity. Finally, we realized that the causal pattern in the time series can be used to compress data. A causal compression ratio is invented and used as the data stream’s predictivity index. We describe this in Chapter 5.
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Jiang, Yu Geweke John. "Inference and prediction in a multiple structural break model of economic time series." 2009. http://ir.uiowa.edu/etd/244/.
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"Statistical inference for FIGARCH and related models." Thesis, 2007. http://library.cuhk.edu.hk/record=b6074359.
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A major objective of this thesis is to study the statistical inference problem for GARCH-type models, including fractionally-integrated (FI) GARCH, fractional (F) GARCH, long-memory (LM) GARCH, and non-stationary GARCH models.<br>Among various types of generalizations to the ARCH models, fractionally-integrated (FI) GARCH model proposed in Baillie et al. (1996) and Bollerslev and Mikkelson (1996) is one of the most interesting ones as it offered many challenging theretical problems.<br>Parameters in the ARCH-type models are commonly estimated using the quasi-maximum likelihood estimator (QMLE). To establish consistency and asymptotic normality of the QMLE, one usually has to impose stringent assumptions, see Robinson and Zaffaroni (2006) and Straumann (2005). They have to assume that a stationary solution to the true model exists and this solution has some finite moments. These two assumptions are too restrictive to be applied to FIGARCH models. Formal results of the asymptotic properties of the QMLE of the FIGARCH models are still not available. Progresses on asymptotic theory of QMLE have only been made on certain models that resemble the FIGARCH model, including the FGARCH model of Ding and Granger (1996) and Robinson and Zaffaroni (2006), the LM-GARCH model of Robinson and Zaffaroni (1997) and the non-stationary ARCH model, but not the FIGARCH model itself.<br>This study attempts to solve the FIGARCH problem and extend the current findings on FGARCH, LM-GARCH and non-stationary GARCH models. We show that if the fractional parameter d is known, the QMLE for the parameters are strongly consistent and asymptotically normal. The results of LM-GARCH (0, d, 0) model in Konlikov (2003a,b) will be generalized to encompass the LM-GARCH(p, d, q) models. We also furnish a general result for non-stationary GARCH (p, q) models, extending the results of Jensen and Rahbek (2004) on weak consistency and asymptotic normality of the QMLE of the non-stationary GARCH (1, 1) models.<br>Ng, Chi Tim.<br>"June 2007."<br>Adviser: Chan Ngai Hang.<br>Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0398.<br>Thesis (Ph.D.)--Chinese University of Hong Kong, 2007.<br>Includes bibliographical references.<br>Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.<br>Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.<br>Abstracts in English and Chinese.<br>School code: 1307.
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Bhattacharya, Indranil. "Feature Selection under Multicollinearity & Causal Inference on Time Series." Thesis, 2017. http://etd.iisc.ernet.in/2005/3980.
Full textAbstract:
In this work, we study and extend algorithms for Sparse Regression and Causal Inference problems. Both the problems are fundamental in the area of Data Science.
The goal of regression problem is to nd out the \best" relationship between an output variable and input variables, given samples of the input and output values. We consider sparse regression under a high-dimensional linear model with strongly correlated variables, situations which cannot be handled well using many existing model selection algorithms. We study the performance of the popular feature selection algorithms such as LASSO, Elastic Net, BoLasso, Clustered Lasso as well as Projected Gradient Descent algorithms under this setting in terms of their running time, stability and consistency in recovering the true support. We also propose a new feature selection algorithm, BoPGD, which cluster the features rst based on their sample correlation and do subsequent sparse estimation using a bootstrapped variant of the projected gradient descent method with projection on the non-convex L0 ball. We attempt to characterize the efficiency and consistency of our algorithm by performing a host of experiments on both synthetic and real world datasets.
Discovering causal relationships, beyond mere correlation, is widely recognized as a fundamental problem. The Causal Inference problems use observations to infer the underlying causal structure of the data generating process. The input to these problems is either a multivariate time series or i.i.d sequences and the output is a Feature Causal Graph where the nodes correspond to the variables and edges capture the direction of causality. For high dimensional datasets, determining the causal relationships becomes a challenging task because of the curse of dimensionality. Graphical modeling of temporal data based on the concept of \Granger Causality" has gained much attention in this context. The blend of Granger methods along with model selection techniques, such as LASSO, enables efficient discovery of a \sparse" sub-set of causal variables in high dimensional settings. However, these temporal causal methods use an input parameter, L, the maximum time lag. This parameter is the maximum gap in time between the occurrence of the output phenomenon and the causal input stimulus. How-ever, in many situations of interest, the maximum time lag is not known, and indeed, finding the range of causal e ects is an important problem. In this work, we propose and evaluate a data-driven and computationally efficient method for Granger causality inference in the Vector Auto Regressive (VAR) model without foreknowledge of the maximum time lag. We present two algorithms Lasso Granger++ and Group Lasso Granger++ which not only constructs the
hypothesis feature causal graph, but also simultaneously estimates a value of maxlag (L) for each variable by balancing the trade-o between \goodness of t" and \model complexity".
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Taylor, James. "Objective Approaches to Single-Molecule Time Series Analysis." Thesis, 2012. http://hdl.handle.net/1911/71695.
Full textAbstract:
Single-molecule spectroscopy has provided a means to uncover pathways and heterogeneities that were previously hidden beneath the ensemble average. Such
heterogeneity, however, is often obscured by the artifacts of experimental noise and
the occurrence of undesired processes within the experimental medium. This has
subsequently caused in the need for new analytical methodologies. It is particularly
important that objectivity be maintained in the development of new analytical
methodology so that bias is not introduced and the results improperly characterized.
The research presented herein identifies two such sources of experimental uncertainty,
and constructs objective approaches to reduce their effects in the experimental results.
The first, photoblinking, arises from the occupation of dark electronic states within the
probe molecule, resulting in experimental data that is distorted by its contribution. A
method based in Bayesian inference is developed, and is found to nearly eliminate
photoblinks from the experimental data while minimally affecting the remaining data
and maintaining objectivity. The second source of uncertainty is electronic shot-noise,
which arises as a result of Poissonian photon collection. A method based in wavelet
decomposition is constructed and applied to simulated and experimental data. It is
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found that, while making only one assumption, that photon collection is indeed a
Poisson process, up to 75% of the shot-noise contribution may be removed from the
experimental signal by the wavelet-based procedure. Lastly, in an effort to connect
model-based approaches such as molecular dynamics simulation to model-free
approaches that rely solely on the experimental data, a coarse-grained molecular model
of a molecular ionic fluorophore diffusing within an electrostatically charged polymer
brush is constructed and characterized. It is found that, while the characteristics of the
coarse-grained simulation compare well with atomistic simulations, the model is lacking
in its representation of the electrostatically-driven behavior of the experimental system.
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Wan, Phyllis. "Application of Distance Covariance to Extremes and Time Series and Inference for Linear Preferential Attachment Networks." Thesis, 2018. https://doi.org/10.7916/D8Q25GQB.
Full textAbstract:
This thesis covers four topics: i) Measuring dependence in time series through distance covariance; ii) Testing goodness-of-fit of time series models; iii) Threshold selection for multivariate heavy-tailed data; and iv) Inference for linear preferential attachment networks.
Topic i) studies a dependence measure based on characteristic functions, called distance covariance, in time series settings. Distance covariance recently gathered popularity for its ability to detect nonlinear dependence. In particular, we characterize a general family of such dependence measures and use them to measure lagged serial and cross dependence in stationary time series. Assuming strong mixing, we establish the relevant asymptotic theory for the sample auto- and cross- distance correlation functions.
Topic ii) proposes a goodness-of-fit test for general classes of time series model by applying the auto-distance covariance function (ADCV) to the fitted residuals. Under the correct model assumption, the limit distribution for the ADCV of the residuals differs from that of an i.i.d. sequence by a correction term. This adjustment has essentially the same form regardless of the model specification.
Topic iii) considers data in the multivariate regular varying setting where the radial part $R$ is asymptotically independent of the angular part $\Theta$ as $R$ goes to infinity. The goal is to estimate the limiting distribution of $\Theta$ given $R\to\infty$, which characterizes the tail dependence of the data. A typical strategy is to look at the angular components of the data for which the radial parts exceed some threshold. We propose an algorithm to select the threshold based on distance covariance statistics and a subsampling scheme.
Topic iv) investigates inference questions related to the linear preferential attachment model for network data. Preferential attachment is an appealing mechanism based on the intuition “the rich get richer” and produces the well-observed power-law behavior in net- works. We provide methods for fitting such a model under two data scenarios, when the network formation is given, and when only a single-time snapshot of the network is observed.
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Schumacher, Johannes. "Time Series Analysis informed by Dynamical Systems Theory." Doctoral thesis, 2015. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2015061113245.
Full textAbstract:
This thesis investigates time series analysis tools for prediction, as well as detection and characterization of dependencies, informed by dynamical systems theory.
Emphasis is placed on the role of delays with respect to information processing
in dynamical systems, as well as with respect to their effect in causal interactions between systems.
The three main features that characterize this work are, first, the assumption that
time series are measurements of complex deterministic systems. As a result, functional mappings for statistical models in all methods are justified by concepts from
dynamical systems theory. To bridge the gap between dynamical systems theory and data, differential topology is employed in the analysis. Second, the Bayesian paradigm of statistical inference is used to formalize uncertainty by means of a consistent
theoretical apparatus with axiomatic foundation. Third, the statistical models
are strongly informed by modern nonlinear concepts from machine learning and nonparametric modeling approaches, such as Gaussian process theory. Consequently,
unbiased approximations of the functional mappings implied by the prior system level analysis can be achieved.
Applications are considered foremost with respect to computational neuroscience
but extend to generic time series measurements.
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Jalali, Ali 1982. "Dirty statistical models." Thesis, 2012. http://hdl.handle.net/2152/ETD-UT-2012-05-5088.
Full textAbstract:
In fields across science and engineering, we are increasingly faced with problems where the number of variables or features we need to estimate is much larger than the number of observations. Under such high-dimensional scaling, for any hope of statistically consistent estimation, it becomes vital to leverage any potential structure in the problem such as sparsity, low-rank structure or block sparsity. However, data may deviate significantly from any one such statistical model. The motivation of this thesis is: can we simultaneously leverage more than one such statistical structural model, to obtain consistency in a larger number of problems, and with fewer samples, than can be obtained by single models? Our approach involves combining via simple linear superposition, a technique we term dirty models. The idea is very simple: while any one structure might not capture the data, a superposition of structural classes might. Dirty models thus searches for a parameter that can be decomposed into a number of simpler structures such as (a) sparse plus block-sparse, (b) sparse plus low-rank and (c) low-rank plus block-sparse. In this thesis, we propose dirty model based algorithms for different problems such as multi-task learning, graph clustering and time-series analysis with latent factors. We analyze these algorithms in terms of the number of observations we need to estimate the variables. These algorithms are based on convex optimization and sometimes they are relatively slow. We provide a class of low-complexity greedy algorithms that not only can solve these optimizations faster, but also guarantee the solution. Other than theoretical results, in each case, we provide experimental results to illustrate the power of dirty models.<br>text
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Themeẞl, Nathalie. "Asteroseismic inferences from red-giant stars." Doctoral thesis, 2018. http://hdl.handle.net/11858/00-1735-0000-002E-E5F1-E.
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