Ce travail se compose de trois parties consacrées à différents aspects des modèles ARCH (AutoRegressive Conditionally Heteroskedastic) quantiles. Dans ces modèles, l’hétéroscédasticité conditionnelle est à prendre dans un sens très large, et affecte de fa¸ con potentiellement différenciée tous les quantiles conditionnels (et donc la loi conditionnelle elle-même), et non seulement, comme dans les modèles ARCH classiques, l’échelle conditionnelle. La première partie étudie les problèmes de Value-at-Risk (VaR) dans les séries financières ainsi modélisées. Les approches traditionnelles présentent une caractéristique discutable, que nous relevons, et à laquelle nous apportons une correction fondée sur les lois résiduelles. Nous pensons que les fondements de cette nouvelle approche sont plus solides, et permettent de prendre en compte le fait que le comportement des processus empiriques résiduels (REP) des processus ARCH, contrairement à celui des REP des processus ARMA, continue à dépendre de certains des paramètres du modèle. La seconde partie approfondit l’étude générale des processus empiriques résiduels (REP) des processus ARCH dans l’optique de la régression quantile (QR) au sens de Koenker et Bassett (Econometrica 1978). La représentation de Bahadur des estimateurs QR, et dont découle la propriété de tension asymptotique des REP, est établie. Finalement, dans la troisième partie, nous mettons en évidence la nature semi-paramétrique des modèles ARCH quantiles, et l’invariance, sous l’action de certains groupes de transforma-tions, des sous-modèles obtenus en fixant la valeur des paramètres. Cette structure de groupe permet la construction de méthodes d’inférence invariantes qui, dans l’esprit des résultats de Hallin and Werker (Bernoulli 2003) préservent l’optimalité au sens semi-paramétrique. Ces méthodes sont fondées sur les rangs et les signes résiduels. Nous développons en particulier les R-estimateurs des modèles considérés et étudions leurs performances.

ARCH在財務分析近來頗受重視，然而實務在建構ARCH模式時參數估計值很難有效估計，而且參數數字本身亦常存在不確定性，其原因可能來自時間數列資料的模糊的性質。利用此一假性的數值來建構模式影響預測，也可能擴大預測結果和實際狀況的誤差，很難讓一般投資者使用並判斷。本文在建構ARCH模式中，加入模糊邏輯概念，以符合實際情況在建構ARCH模式時參數動態的不確定性。嘗試以模糊數的來建構股價加權指數FUZZY ARCH模式，進一步預測，並與ARCH模式作比較分析。 / ARCH is more emphasized in financial analysis recently. However, it is difficult to estimate the parameters of ARCH model in practice. Because of the fuzzy property in time series , there exists the uncertainty in the parameters. Use the fictitious value to construct model and forecast the model will make the errors largely between the forecasts and the practical ones. In this thesis, we add the concept of the fuzzy logic to construct the ARCH model in order to conform the real situation. Also, an analysis of the stock data is provided.

This thesis aims to construct an optimal portfolio and model as well as forecast its volatility. The performance of the optimal portfolio is then compared to two benchmarks, namely, an equally weighted portfolio and the market index SP 500. The volatility is estimated by employing two GARCH-type models known as standard GARCH, and GJR-GARCH. The GJR-GARCH outperformed its counterpart in terms of Log-likelihood, AIC, and BIC. The forecast performance is compared based on two statistical errors, root mean squared error, and mean absolute error. The optimal portfolio outperformed its counterparts in both statistical errors. Moreover, standard GARCH gave lower statistics than GJR-GARCH. These empirical results are of important significance to portfolio management and risk management processes.

This thesis analyses the relationship between month-ahead natural gas prices and imports into Europe against the backdrop of the 2022 Russian gas curtailment and gas price spike. Employing an ARCH model, the analysis focuses on the consortium of five major European consumers of natural gas: Italy, Germany, the Netherlands, the United Kingdom, and France. To gain a comprehensive understanding of the factors influencing natural gas prices in the European market, we include key variables such as natural gas consumption, production, storage levels, oil prices and temperature. The study finds that the European natural gas market is sensitive to decreased imports which exert a positive effect on prices and volatility. Therefore, we can infer that the proposed market factors influence gas prices in Europe. This research provides insights into the dynamics of natural gas pricing, presenting the implications of disruptions and uncertainties in the contemporary natural gas market.

Os métodos geralmente empregados no mercado para o cálculo de medidas de risco baseiam-se na distribuição adotada para os retornos financeiros. Quando a distribuição Normal é adotada, estas avaliações tendem a subestimar o Value at Risk (valor em risco - VaR), pois a distribuição Normal tem caudas mais leves que as observadas nas séries financeiras. Muitas distribuições alternativas vêm sendo propostas na literatura, contudo qualquer modelo alternativo proposto deve ser avaliado com relação ao esforço computacional gasto para cálculo do valor em risco e comparado à simplicidade proporcionada pelo uso da distribuição Normal. Dessa forma, esta dissertação visa avaliar alguns modelos para cálculo do valor em risco, como a modelagem por quantis empíricos, a distribuição Normal e o modelo autorregressivo (AR), para verificação do melhor ajuste à cauda das distribuições das séries de retornos financeiros, além de avaliar o impacto do VaR para o ano seguinte. Nesse contexto, destaca-se o modelo autorregressivo com heterocedasticidade condicional (ARCH) capaz de detectar a volatilidade envolvida nas séries financeiras de retorno. Esse modelo tem-se mostrado mais eficiente, capaz de gerar informações relevantes aos investidores e ao mercado financeiro, com um esforço computacional moderado. / The most used methods for risk evaluation in the financial market usually depend strongly on the distribution assigned to the financial returns. When we assign a normal distribution, results tend to underestimate the Value at Risk (VaR), since the normal distribution usually has a lighter tail than those from the empirical distribution of financial time series. Many other distributions have been proposed in the literature, but we need to evaluate their computational effort for obtaining the value at risk when compared to the easiness of calculation of the normal distribution. In this work, we compare several models for calculating the value at risk, such as the normal, the empirical-quantile and the autoregressive (AR) models, evaluating their goodness-of-fit to the tail of the distribution of financial return time series and the impact of applying the calculated VaR to the following year. We also highlight the autoregressive conditional heteroskedasticity (ARCH) model due to its performance in detecting the volatility in the series. The ARCH model has proved to be efficient and able to generate relevant information to the investors and to the financial market with a moderate computational cost.

The diploma thesis deals with modelling of time series (stock and commodities) by using the models of volatility. The theoretical part focuses on the term of volatility and other terms connected to it. There is a theoretical description of the models as well. The practical part of the thesis focuses on the analysis of the time series and modelling of volatility using the program R.

Os métodos geralmente empregados no mercado para o cálculo de medidas de risco baseiam-se na distribuição adotada para os retornos financeiros. Quando a distribuição Normal é adotada, estas avaliações tendem a subestimar o Value at Risk (valor em risco - VaR), pois a distribuição Normal tem caudas mais leves que as observadas nas séries financeiras. Muitas distribuições alternativas vêm sendo propostas na literatura, contudo qualquer modelo alternativo proposto deve ser avaliado com relação ao esforço computacional gasto para cálculo do valor em risco e comparado à simplicidade proporcionada pelo uso da distribuição Normal. Dessa forma, esta dissertação visa avaliar alguns modelos para cálculo do valor em risco, como a modelagem por quantis empíricos, a distribuição Normal e o modelo autorregressivo (AR), para verificação do melhor ajuste à cauda das distribuições das séries de retornos financeiros, além de avaliar o impacto do VaR para o ano seguinte. Nesse contexto, destaca-se o modelo autorregressivo com heterocedasticidade condicional (ARCH) capaz de detectar a volatilidade envolvida nas séries financeiras de retorno. Esse modelo tem-se mostrado mais eficiente, capaz de gerar informações relevantes aos investidores e ao mercado financeiro, com um esforço computacional moderado. / The most used methods for risk evaluation in the financial market usually depend strongly on the distribution assigned to the financial returns. When we assign a normal distribution, results tend to underestimate the Value at Risk (VaR), since the normal distribution usually has a lighter tail than those from the empirical distribution of financial time series. Many other distributions have been proposed in the literature, but we need to evaluate their computational effort for obtaining the value at risk when compared to the easiness of calculation of the normal distribution. In this work, we compare several models for calculating the value at risk, such as the normal, the empirical-quantile and the autoregressive (AR) models, evaluating their goodness-of-fit to the tail of the distribution of financial return time series and the impact of applying the calculated VaR to the following year. We also highlight the autoregressive conditional heteroskedasticity (ARCH) model due to its performance in detecting the volatility in the series. The ARCH model has proved to be efficient and able to generate relevant information to the investors and to the financial market with a moderate computational cost.

This paper focuses on analysing and modelling inflation and its dynamics in Czech Republic applying a special kind of econometric models. Firstly economic theory of inflation is mentioned - fundamental terms, measuring methods of inflation, the way Czech national bank is monitoring the inflation and obviously a short summary of historical evolution of inflation in Czech economy. In the second part of this paper two econometric concepts of modelling time series are introduced - vector autoregression models (VAR models) and volatility models, concretely ARCH and GARCH models. In connection with the VAR models, Granger causality, impulse response functions, cointegration and error correction models are described. The empirical part includes application of selected models on real time series of chosen macroeconomic indicators. The estimation outputs are interpreted and forecasts are implemented. The quality of chosen econometric models for modelling inflation in Czech Republic is discussed.

Ce travail se compose de trois parties consacrées à différents aspects des modèles ARCH (AutoRegressive Conditionally Heteroskedastic) quantiles. Dans ces modèles, l’hétéroscédasticité conditionnelle est à prendre dans un sens très large, et affecte de fa¸ con potentiellement différenciée tous les quantiles conditionnels (et donc la loi conditionnelle elle-même), et non seulement, comme dans les modèles ARCH classiques, l’échelle conditionnelle.<p><p>La première partie étudie les problèmes de Value-at-Risk (VaR) dans les séries financières ainsi modélisées. Les approches traditionnelles présentent une caractéristique discutable, que nous relevons, et à laquelle nous apportons une correction fondée sur les lois résiduelles. Nous pensons que les fondements de cette nouvelle approche sont plus solides, et permettent de prendre en compte le fait que le comportement des processus empiriques résiduels (REP) des processus ARCH, contrairement à celui des REP des processus ARMA, continue à dépendre de certains des paramètres du modèle.<p><p>La seconde partie approfondit l’étude générale des processus empiriques résiduels (REP) des processus ARCH dans l’optique de la régression quantile (QR) au sens de Koenker et Bassett (Econometrica 1978). La représentation de Bahadur des estimateurs QR, et dont découle la propriété de tension asymptotique des REP, est établie.<p><p>Finalement, dans la troisième partie, nous mettons en évidence la nature semi-paramétrique des modèles ARCH quantiles, et l’invariance, sous l’action de certains groupes de transforma-tions, des sous-modèles obtenus en fixant la valeur des paramètres. Cette structure de groupe permet la construction de méthodes d’inférence invariantes qui, dans l’esprit des résultats de Hallin and Werker (Bernoulli 2003) préservent l’optimalité au sens semi-paramétrique. Ces méthodes sont fondées sur les rangs et les signes résiduels. Nous développons en particulier les R-estimateurs des modèles considérés et étudions leurs performances. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

This doctoral thesis focuses on the research of the pedestrian bridges formed by the flat arch. To understand the basic static behaviour of the flat arch it was necessary to make a study of the development of the direct flat arch as footbridge with large span and the impact of stiffness on its camber. For the mathematical modeling FEM software ANSYS were used. The calculation has shown that a design of purely concrete flat arch would demand enormous bending stiffness, which can be achieved only through a massive cross-section. The findings gained in this chapter were further used to design a unique pedestrian bridge formed by the curved in plan flat arch, where to transfer of the large bending moments a steel pipe was designed. Several variants with different span and rise of the arch in plan were tested. From the tested variants was then selected footbridge with a span of 45 m and with the rise of the arch 10 m, which seemed to be the best solution according to the calculations and it was further analyzed in detail. The studied structure is formed by curved concrete slab that is stiffened through the steel brackets on the inner side of a steel tube with a graded thickness. The external cables that are situated in the handrail pipe balance the dead load torsional moment. Designed structure and the static analysis procedure were verified on a fully functional 1:6 scale model. The thesis describes the model analogy used for the design of the model, its structural design and its implementation. Load tests on the model confirmed correctness of the design of the proposed curved in plan pedestrian bridge, its high carrying capacity and the accuracy of the developed procedure of static analysis. Results and experiences acquired from the design and the realization of model are the basis for a practical realization of studied structures. The last part of the thesis deals with the possibility of replacement of the steel components with concrete in pedestrian bridges formed