Le thème de cette thèse est la théorie spatiale des valeurs extrêmes, et les objets principalement étudiés sont les processus max-stables à trajectoires continues. Nous commençons par déterminer la convergence des maximums de processus stochastiques indépendants, en utilisant la convergence de mesures empiriques vers des processus ponctuels de Poisson. Ensuite, nous déterminons les lois conditionnelles des processus max infiniment divisibles (max-i.d). La représentation des processus max-i.d par des processus ponctuels de Poisson permet l'introduction de notions telles que les fonctions extrémales et le hitting scénario qui permettent d'aboutir au résultat. Les processus max-stables étant des processus max-i.d, nous proposons un algorithme de simulation conditionnelle pour les champs max-stables puis nous l'utilisons pour des applications avec des données de précipitations autour de Zurich et de températures en Suisse. Nous trouvons aussi, une majoration du coefficient de β-mélange entre les restrictions d'un processus max-i.d sur deux sous-ensembles fermés et disjoints d'un espace métrique localement compact. Cette majoration permet d'obtenir de nouveaux critères pour le théorème de la limite central des processus stationnaires mélangeant. Enfin, nous terminons en démontrant qu'un processus stationnaire max-stable vérifiant la propriété de Markov est, quitte à renverser le temps, un processus max-autorégressif d’ordre 1. / The theme of this thesis is spatial extreme value theory and we focus on continuous max-stable processes. We begin with the convergence of the maximum of independent stochastic processes, by using the convergence of empirical measures to Poisson point processes. After that, we determine the regular conditional distributions of max infinitely divisible (max-i.d) processes. The representation of max-i.d. processes by Poisson point processes allows us to introduce the notions of extremal functions and hitting scenario. Our result relies on these new notions. Max-stable processes are max-i.d. processes, so we give an algorithm for conditional sampling and give an application to extreme precipitations around Zurich and extreme temperatures in Switzerland. We also find a upper bound for the β-mixing coefficient between the restrictions of a max-i.d. process on two disjoint closed subsets of a locally compact metric space. This entails a central limit theorem for stationary max-i.d processes. Finally, we prove that the class of stationary maxstable processes with the Markov property is equal, up to time reversal, to the class of stationary max-autoregressive processes of order 1.

<p>In this dissertation I study substantially the effects of disembodied technical change on the total factor productivity and inputs demand in U.S. Apparel industry during 1958-1996. A time series input-output data set over the sector employs to estimate an error corrected model of a four-factor transcendental logarithmic cost function. The empirical results indicate technical impact on the total factor productivity at the rate of 9% on average. Technical progress has in addition a biased effect on factor augmenting in the sector.</p>

In this dissertation I study substantially the effects of disembodied technical change on the total factor productivity and inputs demand in U.S. Apparel industry during 1958-1996. A time series input-output data set over the sector employs to estimate an error corrected model of a four-factor transcendental logarithmic cost function. The empirical results indicate technical impact on the total factor productivity at the rate of 9% on average. Technical progress has in addition a biased effect on factor augmenting in the sector.

Financial time series studies indicate that the lognormal assumption for the return of an underlying security is often violated in practice. This is due to the presence of time-varying volatility in the return series. The most common departures are due to a fat left-tail of the return distribution, volatility clustering or persistence, and asymmetry of the volatility. To account for these characteristics of time-varying volatility, many volatility models have been proposed and studied in the financial time series literature. Two main conditional-variance model specifications are the autoregressive conditional heteroscedasticity (ARCH) and the stochastic volatility (SV) models. The SV model, proposed by Taylor (1986), is a useful alternative to the ARCH family (Engle (1982)). It incorporates time-dependency of the volatility through a latent process, which is an autoregressive model of order 1 (AR(1)), and successfully accounts for the stylized facts of the return series implied by the characteristics of time-varying volatility. In this thesis, we review both ARCH and SV models but focus on the SV model and its variations. We consider two modified SV models. One is an autoregressive process with stochastic volatility errors (AR--SV) and the other is the Markov regime switching stochastic volatility (MSSV) model. The AR--SV model consists of two AR processes. The conditional mean process is an AR(p) model , and the conditional variance process is an AR(1) model. One notable advantage of the AR--SV model is that it better captures volatility persistence by considering the AR structure in the conditional mean process. The MSSV model consists of the SV model and a discrete Markov process. In this model, the volatility can switch from a low level to a high level at random points in time, and this feature better captures the volatility movement. We study the moment properties and the likelihood functions associated with these models. In spite of the simple structure of the SV models, it is not easy to estimate parameters by conventional estimation methods such as maximum likelihood estimation (MLE) or the Bayesian method because of the presence of the latent log-variance process. Of the various estimation methods proposed in the SV model literature, we consider the simulated maximum likelihood (SML) method with the efficient importance sampling (EIS) technique, one of the most efficient estimation methods for SV models. In particular, the EIS technique is applied in the SML to reduce the MC sampling error. It increases the accuracy of the estimates by determining an importance function with a conditional density function of the latent log variance at time t given the latent log variance and the return at time t-1. Initially we perform an empirical study to compare the estimation of the SV model using the SML method with EIS and the Markov chain Monte Carlo (MCMC) method with Gibbs sampling. We conclude that SML has a slight edge over MCMC. We then introduce the SML approach in the AR--SV models and study the performance of the estimation method through simulation studies and real-data analysis. In the analysis, we use the AIC and BIC criteria to determine the order of the AR process and perform model diagnostics for the goodness of fit. In addition, we introduce the MSSV models and extend the SML approach with EIS to estimate this new model. Simulation studies and empirical studies with several return series indicate that this model is reasonable when there is a possibility of volatility switching at random time points. Based on our analysis, the modified SV, AR--SV, and MSSV models capture the stylized facts of financial return series reasonably well, and the SML estimation method with the EIS technique works very well in the models and the cases considered.

We study some Hölderian functional central limit theorems for the polygonal partial sum processes built on a first order nearly nonstationary autoregressive process and its least squares residuals Innovations are i.i.d. centered and at least square-integrable innovations. Two types of models are considered. For the first type model we prove that the limiting process depends on Ornstein – Uhlenbeck one. In the second type model, the convergence to Brownian motion is established in Hölder space in terms of the rate of coefficient and the integrability of the residuals. We also investigate some epidemic change in the innovations of the first order nearly nonstationary autoregressive process . We build the alpha-Hölderian uniform increments statistics based on the observations and on the least squares residuals to detect the short epidemic change in the process under consideration. Under the assumptions for innovations we find the limit of the statistics under null hypothesis, some conditions of consistency and we perform a test power analysis. / Disertacijoje nagrinėjami dalinių sumų laužčių procesai sudaryti iš pirmos eilės beveik nestacionaraus proceso bei jo mažiausių kvadratų liekanų. Inovacijos yra nepriklausomi, vienodai pasiskirstę ir bent kvadratu integruojami atsitiktiniai dydžiai su nuliniu vidurkiu. Įrodomos funkcinės ribinės teoremos šiems laužčių procesams Hiolderio erdvėje. Nagrinėjami du beveik nestacionaraus proceso atvejai. Vienu atveju įrodoma, kad ribinis procesas priklauso nuo Ornsteino–Uhlenbecko proceso. Kitu atveju, įrodomas konvergavimas į Brauno judesį Hiolderio erdvėje, atsižvelgiant į koeficiento divergavimo greitį bei inovacijų integruojamumą. Toliau nagrinėjamas epideminio pasikeitimo modelis beveik nestacionaraus pirmos eilės autoregresinio proceso inovacijoms. Nagrinėjami du modeliai. Iš stebėjimų bei liekanų konstruojama tolydžiųjų prieaugių alpha-Hiolderio statistika. Remiantis prielaidomis inovacijoms, randama statistikos ribinis procesas prie nulinės hipotezės, suderinamumo sąlygos, atliekama galios analizė.

Disertacijoje nagrinėjami dalinių sumų laužčių procesai sudaryti iš pirmos eilės beveik nestacionaraus proceso bei jo mažiausių kvadratų liekanų. Inovacijos yra nepriklausomi, vienodai pasiskirstę ir bent kvadratu integruojami atsitiktiniai dydžiai su nuliniu vidurkiu. Įrodomos funkcinės ribinės teoremos šiems laužčių procesams Hiolderio erdvėje. Nagrinėjami du beveik nestacionaraus proceso atvejai. Vienu atveju įrodoma, kad ribinis procesas priklauso nuo Ornsteino–Uhlenbecko proceso. Kitu atveju, įrodomas konvergavimas į Brauno judesį Hiolderio erdvėje, atsižvelgiant į koeficiento divergavimo greitį bei inovacijų integruojamumą. Toliau nagrinėjamas epideminio pasikeitimo modelis beveik nestacionaraus pirmos eilės autoregresinio proceso inovacijoms. Nagrinėjami du modeliai. Iš stebėjimų bei liekanų konstruojama tolydžiųjų prieaugių alpha-Hiolderio statistika. Remiantis prielaidomis inovacijoms, randama statistikos ribinis procesas prie nulinės hipotezės, suderinamumo sąlygos, atliekama galios analizė. / We study some Hölderian functional central limit theorems for the polygonal partial sum processes built on a first order nearly nonstationary autoregressive process and its least squares residuals Innovations are i.i.d. centered and at least square-integrable innovations. Two types of models are considered. For the first type model we prove that the limiting process depends on Ornstein – Uhlenbeck one. In the second type model, the convergence to Brownian motion is established in Hölder space in terms of the rate of coefficient and the integrability of the residuals. We also investigate some epidemic change in the innovations of the first order nearly nonstationary autoregressive process . We build the alpha-Hölderian uniform increments statistics based on the observations and on the least squares residuals to detect the short epidemic change in the process under consideration. Under the assumptions for innovations we find the limit of the statistics under null hypothesis, some conditions of consistency and we perform a test power analysis.

The increasing demand for high data rate transmission over broadband radio channels has imposed significant challenges in wireless communications. Accurate channel estimation has a major impact on the whole system performance. Specifically, reliable estimate of the channel state information (CSI) is more challenging for orthogonal frequency division multiplexing (OFDM) systems in doubly selective fading channels than for the slower fading channels over which OFDM has been deployed traditionally. With the help of a basis expansion model (BEM), a novel multivariate autoregressive (AR) process is developed to model the time evolution of the fast fading channel. Relying on pilot symbol aided modulation (PSAM), a novel Kalman smoothing algorithm based on a second-order dynamic model is exploited, where the mean square error (MSE) of the channel estimator is near to that of the optimal Wiener filter. To further improve the performance of channel estimation, a novel low-complexity iterative joint channel estimation and symbol detection procedure is developed for fast fading channels with a small number of pilots and low pilot power to achieve the bit error rate (BER) performance close to when the CSI is known perfectly. The new channel estimation symbol detection technique is robust to variations of the radio channel from the design values and applicable to multiple modulation and coding types. By use of the extrinsic information transfer (EXIT) chart, we investigate the convergence behavior of the new algorithm and analyze the modulation, pilot density, and error correction code selection for good system performance for a given power level. The algorithms developed in this thesis improve the performance of the whole system requiring only low ratios of pilot to data for excellent performance in fast fading channels. / Graduate

Financial time series studies indicate that the lognormal assumption for the return of an underlying security is often violated in practice. This is due to the presence of time-varying volatility in the return series. The most common departures are due to a fat left-tail of the return distribution, volatility clustering or persistence, and asymmetry of the volatility. To account for these characteristics of time-varying volatility, many volatility models have been proposed and studied in the financial time series literature. Two main conditional-variance model specifications are the autoregressive conditional heteroscedasticity (ARCH) and the stochastic volatility (SV) models. The SV model, proposed by Taylor (1986), is a useful alternative to the ARCH family (Engle (1982)). It incorporates time-dependency of the volatility through a latent process, which is an autoregressive model of order 1 (AR(1)), and successfully accounts for the stylized facts of the return series implied by the characteristics of time-varying volatility. In this thesis, we review both ARCH and SV models but focus on the SV model and its variations. We consider two modified SV models. One is an autoregressive process with stochastic volatility errors (AR--SV) and the other is the Markov regime switching stochastic volatility (MSSV) model. The AR--SV model consists of two AR processes. The conditional mean process is an AR(p) model , and the conditional variance process is an AR(1) model. One notable advantage of the AR--SV model is that it better captures volatility persistence by considering the AR structure in the conditional mean process. The MSSV model consists of the SV model and a discrete Markov process. In this model, the volatility can switch from a low level to a high level at random points in time, and this feature better captures the volatility movement. We study the moment properties and the likelihood functions associated with these models. In spite of the simple structure of the SV models, it is not easy to estimate parameters by conventional estimation methods such as maximum likelihood estimation (MLE) or the Bayesian method because of the presence of the latent log-variance process. Of the various estimation methods proposed in the SV model literature, we consider the simulated maximum likelihood (SML) method with the efficient importance sampling (EIS) technique, one of the most efficient estimation methods for SV models. In particular, the EIS technique is applied in the SML to reduce the MC sampling error. It increases the accuracy of the estimates by determining an importance function with a conditional density function of the latent log variance at time t given the latent log variance and the return at time t-1. Initially we perform an empirical study to compare the estimation of the SV model using the SML method with EIS and the Markov chain Monte Carlo (MCMC) method with Gibbs sampling. We conclude that SML has a slight edge over MCMC. We then introduce the SML approach in the AR--SV models and study the performance of the estimation method through simulation studies and real-data analysis. In the analysis, we use the AIC and BIC criteria to determine the order of the AR process and perform model diagnostics for the goodness of fit. In addition, we introduce the MSSV models and extend the SML approach with EIS to estimate this new model. Simulation studies and empirical studies with several return series indicate that this model is reasonable when there is a possibility of volatility switching at random time points. Based on our analysis, the modified SV, AR--SV, and MSSV models capture the stylized facts of financial return series reasonably well, and the SML estimation method with the EIS technique works very well in the models and the cases considered.

Cette thèse est consacrée à l’étude de théorèmes limites : grandes déviations et déviations modérées pour des estimateurs liés à des modèles financiers. Dans une première partie, nous nous sommes intéressés à l’étude des déviations grandes et modérées des estimateurs de la covariation et de la (co)volatilité réalisée issus des fonctionnelles associées à deux processus de diffusion couplés de manière synchronisée. Les techniques utilisées dans ces travaux sont basées d’une part sur celles utilisées dans Djellout-Guillin-Wu et sur la sous additivité et sur la notion d’approximation exponentielle inspirées des travaux de J. Najim d’autre part. Dans une deuxième partie, on considère que les deux processus de diffusion sont observés de manière non synchronisée et on établit des déviations modérées pour l’estimateur de la variation généralisée et pour celui de Hayashi-Yoshida. Les résultats sont obtenus par l’utilisation d’une nouvelle approche sur les déviations modérées des variables aléatoires m−dépendantes vérifiant des conditions de type "Chen-Ledoux". Dans la troisième et dernière partie, on s’intéresse à l’étude processus autorégressif d’ordre p dont le bruit est un processus autorégressif d’ordre q. On montre des déviations modérées pour certains estimateurs associés à notre modèle dont la statistique de Durbin-Watson. Les résultats sont donnés dans le cas où le bruit est gaussien puis dans le cas de condition de type "Chen-Ledoux" portant sur le bruit. / This thesis is devoted to the study of the limits theorem : large and moderate déviations for some financial mathematicals estimators. In the first part, we studied the large and moderate deviations of the estimators of covariation and the realized (co)volatility obtained from the functional associated to two diffusion processes coupled in synchronous manner. The techniques used in this work are based, on the one hand, on those used in Djellout-Guillin-Wu and the subadditivity and the exponential approximation notion inspired by J. Najim results on the other hand. In the second part, we consider that ours two diffusion processes are observed in a nonsynchronized manner and on the establish the moderate deviations for the generalised bipower variation estimator and the Hayashi-Yoshida estimator. The results are obtained by using a new approach on the moderate deviations of the m−dependent random variables based on the Chen-Ledoux type condition. In the third and last part, we study the stable autoregressive process of order p where the driven noise is also given by a q-order autoregressive process. We prove the moderate deviations for some estimators associated with our model such as the Durbin-Watson statistic. The results are given in the case where the driven noise is the normally distributed then in the case where the driven noise satisfy a Chen-Ledoux type condition.

The emphasis of this diploma thesis is placed on the verification of stationarity in time series using the Unit Root Tests and their most common modifications that are introduced in the theoretical part of this paper. Tests mainly by Dickey and Fuller, Phillips and Perron, and KPSS test are introduced as well as their modifications in the form of ERS, Ng and Perron, and Leybourne and McCabe tests. Moreover the HEGY test for testing stationarity in the seasonal Time series and Perron test of structural breaks for Time series with shocks are described. There is also outlined the process of testing multiple Unit Roots. The empirical part of this paper consists of simulations of AR(1) time series generated using the software R, their testing for stationarity by selected Unit Root tests and the comparison of power of these tests. The conclusion includes recommendations which tests and under what conditions are the most suitable for testing Time series for the presence of Unit Root.