390 research outputs found

    Quasi maximum likelihood estimation for strongly mixing state space models and multivariate L\'evy-driven CARMA processes

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    We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-ime linear state space models and equidistantly observed multivariate L\'evy-driven continuoustime autoregressive moving average (MCARMA) processes. In the discrete-time setting, we prove strong consistency and asymptotic normality of the QML estimator under standard moment assumptions and a strong-mixing condition on the output process of the state space model. In the second part of the paper, we investigate probabilistic and analytical properties of equidistantly sampled continuous-time state space models and apply our results from the discrete-time setting to derive the asymptotic properties of the QML estimator of discretely recorded MCARMA processes. Under natural identifiability conditions, the estimators are again consistent and asymptotically normally distributed for any sampling frequency. We also demonstrate the practical applicability of our method through a simulation study and a data example from econometrics

    Brown-Resnick Processes: Analysis, Inference and Generalizations

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    This thesis deals with the analysis, inference and further generalizations of a rich and flexible class of max-stable random fields, the so-called Brown-Resnick processes. The first chapter gives the explicit distribution of the shape functions in the mixed moving maxima representation of the original Brown-Resnick process based on Brownian motions. The result is particularly useful for a fast simulation method. In chapter 2, a multivariate peaks-over-threshold approach for parameter estimation of HĂŒsler-Reiss distributions, a popular model in multivariate extreme value theory, is presented. As HĂŒsler-Reiss distributions constitute the finite dimensional margins of Brown-Resnick processes based on Gaussian random fields, the estimators directly enable statistical inference for this class of max-stable processes. As an application, a non-isotropic Brown-Resnick process is fitted to the extremes of 12-year data of daily wind speed measurements. Chapter 3 is concerned with the definition of Brown-Resnick processes based on LĂ©vy processes on the whole real line. Amongst others, it is shown that these LĂ©vy-Brown-Resnick processes naturally arise as limits of maxima of stationary stable Ornstein-Uhlenbeck processes. The last chapter is devoted to the study of maxima of d-variate Gaussian triangular arrays, where in each row the random vectors are assumed to be independent, but not necessarily identically distributed. The row-wise maxima converge to a new class of multivariate max-stable distributions, which can be seen as max-mixtures of HĂŒsler-Reiss distributions

    A hierarchical frailty model applied to two-generation melanoma data

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    We present a hierarchical frailty model based on distributions derived from non-negative Lévy processes. The model may be applied to data with several levels of dependence, such as family data or other general clusters, and is an alternative to additive frailty models. We present several parametric examples of the model, and properties such as expected values, variance and covariance. The model is applied to a case-cohort sample of age at onset for melanoma from the Swedish Multi-Generation Register, organized in nuclear families of parents and one or two children. We compare the genetic component of the total frailty variance to the common environmental term, and estimate the effect of birth cohort and gender. © 2010 The Author(s).published_or_final_versionSpringer Open Choice, 21 Feb 201

    Correlation properties of continuous-time autoregressive processes delayed by the inverse of the stable subordinator

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    We define the delayed LĂ©vy-driven continuous-time autoregressive process via the inverse of the stable subordinator. We derive correlation structure for the observed non-stationary delayed LĂ©vy-driven continuous-time autoregressive processes of order p, emphasizing low orders, and we show they exhibit long-range dependence property. Distributional properties are discussed as wel

    Stochastic timeseries analysis in electric power systems and paleo-climate data

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    In this thesis a data science study of elementary stochastic processes is laid, aided with the development of two numerical software programmes, applied to power-grid frequency studies and Dansgaard--Oeschger events in paleo-climate data. Power-grid frequency is a key measure in power grid studies. It comprises the balance of power in a power grid at any instance. In this thesis an elementary Markovian Langevin-like stochastic process is employed, extending from existent literature, to show the basic elements of power-grid frequency dynamics can be modelled in such manner. Through a data science study of power-grid frequency data, it is shown that fluctuations scale in an inverse square-root relation with their size, alike any other stochastic process, confirming previous theoretical results. A simple Ornstein--Uhlenbeck is offered as a surrogate model for power-grid frequency dynamics, with a versatile input of driving deterministic functions, showing not surprisingly that driven stochastic processes with Gaussian noise do not necessarily show a Gaussian distribution. A study of the correlations between recordings of power-grid frequency in the same power-grid system reveals they are correlated, but a theoretical understanding is yet to be developed. A super-diffusive relaxation of amplitude synchronisation is shown to exist in space in coupled power-grid systems, whereas a linear relation is evidenced for the emergence of phase synchronisation. Two Python software packages are designed, offering the possibility to extract conditional moments for Markovian stochastic processes of any dimension, with a particular application for Markovian jump-diffusion processes for one-dimensional timeseries. Lastly, a study of Dansgaard--Oeschger events in recordings of paleoclimate data under the purview of bivariate Markovian jump-diffusion processes is proposed, augmented by a semi-theoretical study of bivariate stochastic processes, offering an explanation for the discontinuous transitions in these events and showing the existence of deterministic couplings between the recordings of the dust concentration and a proxy for the atmospheric temperature

    Recovering Brownian and jump parts from high-frequency observations of a L\'evy process

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    We introduce two general non-parametric methods for recovering paths of the Brownian and jump components from high-frequency observations of a L\'evy process. The first procedure relies on reordering of independently sampled normal increments and thus avoids tuning parameters. The functionality of this method is a consequence of the small time predominance of the Brownian component, the presence of exchangeable structures, and fast convergence of normal empirical quantile functions. The second procedure amounts to filtering the increments and compensating with the final value. It requires a carefully chosen threshold, in which case both methods yield the same rate of convergence. This rate depends on the small-jump activity and is given in terms of the Blumenthal-Getoor index. Finally, we discuss possible extensions, including the multidimensional case, and provide numerical illustrations

    THE IMPACT OF TRAINING PROGRAMMES ON WAGES IN FRANCE: AN EVALUATION OF THE “QUALIFYING CONTRACT” USING PROPENSITY SCORES.

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    This paper evaluates the impact of a widely-used French training programme for youth on earnings. This programme is designed to increase labour market experience and education, validated by a formal diploma. It is not sure, however, whether this diploma and a similar diploma acquired through initial training have the same effect on post-training wages. To answer this question, we contrast the 2003 net wages of a group of participants enrolled in 1998 (the “treatment” group) to the 2003 net wages of a control group. The controls are individuals who completed their initial training in 1998 with diplomas similar to those obtained by the treated at the end of the programme. Using propensity score matching, we find a significantly positive effect of the treatment on the treated: participants in the programme benefit, five years after participation, from a positive wage premium. This suggests that firms do not simply value education: they value it more if it is coupled with some degree of labour market experience.active labour market policies; training programmes for youth; propensity score matching.
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