Σχολή Επιστημών και Τεχνολογίας της Πληροφορίας
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Πλοήγηση Σχολή Επιστημών και Τεχνολογίας της Πληροφορίας ανά Συγγραφέα "Alexopoulos, Angelis N."
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Τεκμήριο Bayesian modelling of high dimensional financial data using latent gaussian modelsAlexopoulos, Angelis N.; Αλεξόπουλος, Αγγελής Ν.; Athens University of Economics and Business, Department of Statistics; Dellaportas, Petros; Papaspiliopoulos, OmirosThe present thesis deals with the problem of developing statistical methodology for modellingand inference of high dimensional financial data. The motivation of our research wasthe identification of infrequent and extreme movements, which are called jumps, in the pricesof the 600 stocks of Euro STOXX index. This is known in the financial and statistical literatureas the problem of separating jumps from the volatility of the underlying process whichis assumed for the evolution of the stock prices.The main contribution of the thesis is the modelling and the development of methodsfor inference on the characteristics of the jumps across multiple stocks, as well as across thetime horizon. Following the Bayesian paradigm we use prior information in order to modela known characteristic of financial crises, which is that jumps in stock prices tend to occurclustered in time and to a↵ect several markets within a sort period of time. An improvementin the prediction of future stock prices has been achieved.The proposed model combines the stochastic volatility (SV) model with a multivariatejump process and belongs to the very broad class of latent Gaussian models. Bayesian inferencefor latent Gaussian models relies on a Markov chain Monte Carlo (MCMC) algorithmwhich alternates sampling from the distribution of the latent states of the model conditionalon the parameters and the observations, and sampling from the distribution of the parametersof the model conditional on the latent states and the observations. In the case of SVmodels with jumps, sampling the latent volatility process of the model is not a new problem.Over the last few years several methods have been proposed for separating the jumps fromthe volatility process but there is not a satisfactory solution yet, since sampling from a highdimensional nonlinear and non-Gaussian distribution is required. In the present thesis wepropose a Metropolis-Hastings algorithm in which we sample the whole path of the volatilityprocess of the model without using any approximation. We compare the resulting MCMCalgorithm with existing algorithms. We apply our proposed methodology on univariate SVwith jumps models in order to identify jumps in the stock prices of the real dataset thatmotivated our research.To model the propagation of the jumps across stocks and across time we combine the SVmodel with a doubly stochastic Poisson process, also known as Cox process. The intensityof the jumps in the Poisson process is modelled using a dynamic factor model. Furthermore,we develop an MCMC algorithm to conduct Bayesian inference for the parameters and thelatent states of the proposed model. We test the proposed methods on simulated data and weapplied them on our real dataset. We compare the prediction of future stock prices using theproposed model with the predictions obtained using existing models. The proposed modelprovides better predictions of future stock prices and this is an indication for a predictablepart of the jump process of SV models.IIIThe MCMC algorithm that is implemented in order to conduct Bayesian inference forthe aforementioned models is also employed on a demographic application. More precisely,within the context of latent Gaussian models we present a novel approach to model andpredict mortality rates of individuals.Τεκμήριο Bayesian regression models for mortality dataAlexopoulos, Angelis N.; Αλεξόπουλος, Αγγελής Ν.; Athens University of Economics and Business, Department of Statistics; Dellaportas, PetrosThe main theme of this thesis is to provide forecasts for mortality rates by using two different approaches. First, we employ dynamic non-linear logistic models based on Helingman-Pollard formula. Second, we assume that the dynamics of the mortality rates can be modeled through a Gaussian Markov random field. Both methodologies are tested with past data and are used to forecast mortality rates for UK and Wales up to 30 years ahead. In this thesis we make, firstly Bayesian analysis for mortality data. Many researchers in published papers have noticed that estimation of the parameters of the Heligman-Pollard model, Heligman and Pollard (1980), is problematic because of the overparameterization of the model. They also noted that using the weighted least squares approach for the estimation the numerical instabilities can removed only by fixing two parameters to be constant. The above problems can be tackled with Bayesian methods. Dellaportas et al. (2001) adopt a Bayesian inference approach for the Heligman-Pollard model. This approach has the following advantages. First the use of informative priors solves the problem of overparameterization. Secondly the non-normality of the likelihood surface means that the least squares estimates are inadequate. So, as a starting point, we repeated the work of Dellaportas et al. (2001) for recent mortality data. Then, I focused on the important issue of dynamic modeling of mortality data. The approach adopted till now is to first estimate the parameters of mortality rates model for each year (or 5-year) interval, and then modeling the estimated parameters via a time series model. Clearly, the parameter uncertainty and the within model parameter dependence is ignored. In this thesis we worked on this problem with data collected from the Human mortality database (www.mortality.org). Our first attempt was to assume a dynamic non-linear generalized model. The dynamic part is added to account for the dynamic projections of demographic characteristics across years. Inference of such a model is very hard, and in particular only ad-hoc solutions for dynamic linear generalized linear models exist. The othermodel-perspective that we attempted is based on non-isotropic Gaussian Processes. Here, our data (mortality rates), were viewed as coming from a huge multivariate normal distribution, in which we estimated the correlation structure and we made forecasts for the future mortality rates, based on this.