Reserves estimation in an unconventional-reservoir setting is a daunting task because of geologic uncertainty and complex flow patterns evolving in a long-stimulated horizontal well, among other variables. To tackle this complex problem, we present a reserves-evaluation workflow that couples the traditional decline-curve analysis with a probabilistic forecasting frame. The stretched-exponential production decline model (SEPD) underpins the production behavior. Our recovery appraisal workflow has two different applications: forecasting probabilistic future performance of wells that have production history; and forecasting production from new wells without production data. For the new field case, numerical model runs are made in accord with the statistical design of experiments for a range of design variables pertinent to the field of interest. In contrast, for the producing wells the early-time data often need adjustments owing to restimulation, installation of artificial-lift, etc. to focus on the decline trend. Thereafter, production data of either new or existing wells are grouped in accord with initial rates to obtain common SEPD parameters for similar wells. After determining the distribution of model parameters using well grouping, the methodology establishes a probabilistic forecast for individual wells. We present a probabilistic performance forecasting methodology in unconventional reservoirs for wells with and without production history. Unlike other probabilistic forecasting tools, grouping wells with similar production character allows estimation of self-consistent SEPD parameters and alleviates the burden of having to define uncertainties associated with reservoir and well-completion parameters.

The aim of this study is to get some approach which can help in improving the predictions of daily temperature of Umeå. Weather forecasts are available through various sources nowadays. There are various software and methods available for time series forecasting. Our aim is to investigate the daily maximum temperatures of Umeå, and compare the performance of some methods in forecasting these temperatures. Here we analyse the data of daily maximum temperatures and find the predictions for some local period using methods of autoregressive integrated moving average (ARIMA), exponential smoothing (ETS), and cubic splines.  The forecast package in R is used for this purpose and automatic forecasting methods available in the package are applied for modelling with ARIMA, ETS, and cubic splines. The thesis begins with some initial modelling on univariate time series of daily maximum temperatures. The data of daily maximum temperatures of Umeå from 2008 to 2013 are used to compare the methods using various lengths of training period. On the basis of accuracy measures we try to choose the best method. Keeping in mind the fact that there are various factors which can cause the variability in daily temperature, we try to improve the forecasts in the next part of thesis by using multivariate time series forecasting method on the time series of maximum temperatures together with some other variables. Vector auto regressive (VAR) model from the vars package in R is used to analyse the multivariate time series. Results: ARIMA is selected as the best method in comparison with ETS and cubic smoothing splines to forecast one-step-ahead daily maximum temperature of Umeå, with the training period of one year. It is observed that ARIMA also provides better forecasts of daily temperatures for the next two or three days. On the basis of this study, VAR (for multivariate time series) does not help to improve the forecasts significantly. The proposed ARIMA with one year training period is compatible with the forecasts of daily maximum temperature of Umeå obtained from Swedish Meteorological and Hydrological Institute (SMHI).

[pt] Desde o século XVI, já existia a idéia de que o poder de compra deveria influenciar no valor de cada moeda. A fim de se entender as relações entre câmbio e inflação, modelos autoregressivos lineares sempre apresentaram dificuldades para superar o passeio aleatório. Possíveis fricções em operações cambiais podem dificultar a arbitragem próxima do câmbio de equilíbrio considerado pelos agentes financeiros. À medida em que se distancia do valor considerado justo, a convergência se torna mais intensa, pois os custos já não seriam uma parcela tão relevante para o lucro potencial da operação. No modelo não-linear proposto, há dois regimes diferentes: um próximo do equilíbrio (comportamento de passeio aleatório) e um comportamento longe dele ocorrendo simultaneamente, mas com pesos variáveis. A depender do nível do câmbio em relação ao equilíbrio, um regime ganha mais peso e outro perde relevância. Essa tese tem o objetivo de avaliar o caráter preditivo do movimento cambiais. O modelo não-linear ESTAR é usado para montar cestas de moedas a serem compradas e vendidas e o retorno advindo de oscilações cambiais é computado. Por fim, incorporamos os efeitos de juros ao modelo para montar portfólios de moedas a fim de simular o retorno de um investimento usando essa estratégia. Para as cestas de moedas, o modelo gerou bons retornos e baixos riscos, tanto em termos de desvio padrão quanto em termos de drawdown. Tal característica foi observada no modelo in-sample e no out-of-sample o que indica um forte caráter preditivo. Levando em conta o efeito dos juros, os portfólios com menos moedas apresentaram retornos positivos, porém essa vantagem é perdida ao se aumentar a quantidade de moedas. / [en] Since the sixteenth century, there was already the idea that purchasing power should influence the value of each currency. In order to understand the relationship between exchange rate and inflation, linear autoregressive models always presented difficulties to beat the random walk. Possible frictions in foreign exchange operations may hinder arbitrage close to the equilibrium exchange rate considered by financial agents. As the exchange rate distances itself from the value considered fair, the convergence becomes more intense, because the costs would no longer be so relevant to the potential profit of the operation. In the proposed nonlinear model, there are two different regimes: one near equilibrium (random walk behavior) and one behavior away from it occurring simultaneously, but with variable weights. For different levels of the exchange rate relative to the equilibrium, one regime gains more weight and the other loses relevance. This thesis aims to evaluate the predictive nature of the exchange rate movement. The nonlinear model ESTAR is used to create baskets of currencies to be bought and sold and the aggregate return based on exchange rate movements is computed. Finally, we consider the interest rate effects on the model to set up currencies portfolios in order to simulate the return on an investment using this strategy. For the baskets of currencies, the model generated good returns and low risks, based on both standard deviation and drawdown. This characteristic was observed in the in-sample model and in the out-of-sample model, which indicates a strong predictive power. Considering the interest effect, portfolios with fewer currencies showed positive returns, but this advantage is lost by increasing the number of currencies.

Neste trabalho, estudamos uma generalização dos semigrupos gradientes, os semigrupos gradiente-like, algumas de suas propriedades e a sua invariância por pequenas perturbações; isto é, pequenas perturbações de sistemas gradiente-like continuam sendo gradiente-like. Como consequência da caracterização dos atratores para este tipo de sistema, estudamos a atração exponencial de atratores. Por fim, estudamos o concetio de dimensão de Hausdorff e dimensão fractal de atratores e apresentamos alguns resultados sobre este assunto, e estudamos a construção de uma nova classe de atratores, os atratores exponenciais fractais / In this work, we study a generalization of gradient discrete semigroups, the gradientlike semigroups, some of its properties and its invariance under small perturbations; that is, small perturbations of gradient-like semigroups are still gradient-like semigroups. As a consequence of the characterization of the attractors for this sort of semigroups, we study the exponential attraction of attractors. Finally, we study some concepts of Hausdorff dimension and fractal dimension and present some results about this subject, and we studied the construction of a new class of attractors, the exponential fractal attractors

L’objectif de cette thèse est d’étudier et de donner des outils pour la compréhension des problèmes de perturbations singulières pour des modèles épidémiques et des problèmes de dynamiques de populations. Les modèles considérés sont des équations structurées en âge qui peuvent dans certains cas se réécrire comme des équations à retard. L’étude de ces classes d’exemples s’est faite avec succès et a permis de comprendre et de mettre en évidence toute la complexité et l’étendue de ces problèmes. Comme on peut le remarquer dans la littérature, l’une des clés fondamentales à la compréhension de ces problèmes est l’étude des variétés normalement hyperboliques en dimension infinie que nous avons largement étudiées dans cette thèse. L’approche utilisée est la méthode de Lyapunov-Perron. Ce qui nous a amené à étudier les problèmes de persistance et d’existence de trichotomie (dichotomie) exponentielle qui sont des éléments fondamentaux dans l’utilisation de cette méthode. / In this thesis we aim to give tools to understand singular perturbations in epidemic model sand population dynamic models. We study some singularly perturbed delay differential equation which does not enter into the class frame work of geometric singular perturbation for delay differential equations. An example of singularly perturbed age structured model is also studied. The study of these examples allowed us to understand and highlight some complexities of these problems. One of the main tools in understanding such questions is the normally hyperbolic manifolds theory which is our central focus in this thesis. The approach used here is the Lyapunov-Perron method. Therefore the problems of persistence and existence of exponential trichotomy (dichotomy) are also stressed since there are one of the mainingredients of this method.

New algorithms for the matrix exponential and its Fréchet derivative are presented. First, we derive a new scaling and squaring algorithm (denoted expm[new]) for computing eA, where A is any square matrix, that mitigates the overscaling problem. The algorithm is built on the algorithm of Higham [SIAM J.Matrix Anal. Appl., 26(4): 1179-1193, 2005] but improves on it by two key features. The first, specific to triangular matrices, is to compute the diagonal elements in the squaring phase as exponentials instead of powering them. The second is to base the backward error analysis that underlies the algorithm on members of the sequence {||Ak||1/k} instead of ||A||. The terms ||Ak||1/k are estimated without computing powers of A by using a matrix 1-norm estimator. Second, a new algorithm is developed for computing the action of the matrix exponential on a matrix, etAB, where A is an n x n matrix and B is n x n₀ with n₀ << n. The algorithm works for any A, its computational cost is dominated by the formation of products of A with n x n₀ matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix etAB or a sequence etkAB on an equally spaced grid of points tk. It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. It determines the amount of scaling and the Taylor degree using the strategy of expm[new].Preprocessing steps are used to reduce the cost of the algorithm. An important application of the algorithm is to exponential integrators for ordinary differential equations. It is shown that the sums of the form $\sum_{k=0}^p\varphi_k(A)u_k$ that arise in exponential integrators, where the $\varphi_k$ are related to the exponential function, can be expressed in terms of a single exponential of a matrix of dimension $n+p$ built by augmenting $A$ with additional rows and columns. Third, a general framework for simultaneously computing a matrix function, $f(A)$, and its Fréchet derivative in the direction $E$, $L_f(A,E)$, is established for a wide range of matrix functions. In particular, we extend the algorithm of Higham and $\mathrm{expm_{new}}$ to two algorithms that intertwine the evaluation of both $e^A$ and $L(A,E)$ at a cost about three times that for computing $e^A$ alone. These two extended algorithms are then adapted to algorithms that simultaneously calculate $e^A$ together with an estimate of its condition number. Finally, we show that $L_f(A,E)$, where $f$ is a real-valued matrix function and $A$ and $E$ are real matrices, can be approximated by $\Im f(A+ihE)/h$ for some suitably small $h$. This approximation generalizes the complex step approximation known in the scalar case, and is proved to be of second order in $h$ for analytic functions $f$ and also for the matrix sign function. It is shown that it does not suffer the inherent cancellation that limits the accuracy of finite difference approximations in floating point arithmetic. However, cancellation does nevertheless vitiate the approximation when the underlying method for evaluating $f$ employs complex arithmetic. The complex step approximation is attractive when specialized methods for evaluating the Fréchet derivative are not available.

The aim of this paper is to investigate various versions of the Phillips curve and their inflation forecasting ability for Euro Area. We consider autoregressive distributed lag models and use two types of trend estimation -- successive (the trend is estimated before the remaining parameters are) and join, using exponential smoothing. The versions of the Phillips curve are evaluated by rolling and recursive window methods, various selection criteria for lag variables and different combination of the inflation indicators. To evaluate the forecasted values, we calculate the RMSE in three 7-year periods: 1993-1999 (run up Euro area), 2000-2006 (stable inflation period) and 2007-2013 (financial crisis). According to all our modifications, we find some models which achieve satisfying results in terms of the RMSE, albeit not for all forecasting periods. We notice that some models are satisfactory only in the stable period however not in the periods with low inflation and vice versa.

Cieľom tejto diplomovej práce je predstavenie Experimentálnej modálnej analýzy a štúdium a použitie algoritmov pre výpočet modálnych parametrov z odmeraných vibrácií pri Experimentálnej modálnej analýze. Bodom záujmu sú predovšetkým algoritmy, pracujúce s odmeranými dátami v časovej oblasti. Diplomová práca sa zaoberá programovaním algoritmu ITD a jeho implementáciou pre Experimentálnu modálnu analýzu. Ďaľšou časťou práce je štúdium citlivosti algoritmu na okrajové podmienky meranej sústavy pri výpočte modálnych parametrov a štúdium možnosti využitia algoritmu pri Operačnej modálnej analýze.

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Master of Science / Department of Statistics / James J. Higgins / The time for an event to take place in an individual is called a survival time. Examples include the time that an individual survives after being diagnosed with a terminal illness or the time that an electronic component functions before failing. A popular parametric model for this type of data is the Weibull model, which is a flexible model that allows for the inclusion of covariates of the survival times. If distributional assumptions are not met or cannot be verified, researchers may turn to the semi-parametric Cox proportional hazards model. This model also allows for the inclusion of covariates of survival times but with less restrictive assumptions. This report compares estimates of the slope of the covariate in the proportional hazards model using the parametric Weibull model and the semi-parametric Cox proportional hazards model to estimate the slope. Properties of these models are discussed in Chapter 1. Numerical examples and a comparison of the mean square errors of the estimates of the slope of the covariate for various sample sizes and for uncensored and censored data are discussed in Chapter 2. When the shape parameter is known, the Weibull model far out performs the Cox proportional hazards model, but when the shape parameter is unknown, the Cox proportional hazards model and the Weibull model give comparable results.