Os modelos ARFIMA de memória longa mostraram-se nesse trabalho mais versáteis à análise da persistência em séries temporais em comparação aos modelos ARIMA. As funções impulso-resposta dos modelos de integração fracionária indicam que essa classe de modelos capta mais adequadamente as informações contidas nas baixas freqüências das séries e, portanto, estes modelos são mais capacitados para avaliar como os choques econômicos são acomodados no médio e longo prazo. Os estudos simulatórios mostraram que os testes de raiz unitária aplicados a processos com memória longa possuem baixo poder, e que os estimadores por máxima verossimilhança e os baseados no espectro de ondaletas são eficientes para estimar o parâmetro de integração fracionária. Os estudos empíricos encontraram componentes altamente persistentes nas séries brasileiras do produto, desemprego e consumo. A análise de co-integração fracionária refutou os resultados do arcabouço I(1)-I(0) que sugerem a não co-integração entre as séries consumo das famílias e renda disponível. A variabilidade relativa dessas séries foi analisada por meio da análise em multiresolução de ondaletas. Concluiu-se que, nas baixas escalas, a variabilidade entre as séries varia em função da escala temporal envolvida. A doutrina da paridade do poder de compra com dados brasileiros foi revisitada por meio da análise de co-integração fracionária. / The long-memory ARFIMA models proved to be more versatile in this study to the analysis of endurance in time series compare to the ARIMA models. The impulse-response functions of the fractionally integrated models indicate that this class of models more adequately gathers the data enclosed in the low frequencies of the series and thus these models are more befitted to evaluate how economic shocks are settled in the medium and long terms. Simulation studies unveiled that the unit root tests applied to long-memory processes have low power, and that the maximum likelihood estimators as well as those based on wavelet spectrum are efficient in estimating the fractional difference parameter. Empirical studies have found highly persistent components in the Brazilian series of the product, unemployment and consumption. The fractional co-integration analysis rebutted the results of the I(1)-I(0) framework, which suggest the non co-integration between the series of families\' consumption and the disposable income. The relative variability of these series was investigated through a wavelet multiresolution analysis. It was concluded that, in small scales, the variability between the series changes according to the time scale involved. The Purchasing Power Parity doctrine with Brazilian data has been revisited through the fractional co-integration analysis.

Récemment, la localisation statique et dynamique d'un objet ou d'une personne est devenue l'un des plus importantes fonctionnalités d'un système de communication, du fait de ses multiples applications. En effet, connaître la position d'un terminal mobile (MT), en milieu extérieur ou intérieur, est généralement d'une importance majeure pour des applications fournissant des services basés sur la localisation. Ce développement des systèmes de localisation est dû au faible coût des infrastructures de réseau sans fil en milieu intérieur (WLAN). Les techniques permettant de localiser des MTs diffèrent selon les paramètres extraits des signaux radiofréquences émis entre des stations de base (BSs) et des MTs. Les conditions idéales pour effectuer des mesures sont des environnements dépourvus de tout obstacle, permettant des émissions directes entre BS et MT. Ce n'est pas le cas en milieu intérieur, du fait de la présence continuelle d'obstacles dans l'espace, qui dispersent les rayonnements. Les mesures prises dans ces conditions (NLOS, pour Non Line of Sight) sont imprévisibles et diffèrent de celles prises en condition LOS. Afin de réduire les erreurs de mesure, différentes techniques peuvent être utilisées, comme la mitigation, l'approximation, la correction à priori, ou le filtrage. En effet, l'application de systèmes de suivi (TSs) constitue une base substantielle pour la navigation individuelle, les réseaux sociaux, la gestion du trafic, la gestion des ressources mobiles, etc. Différentes techniques sont appliquées pour construire des TSs en milieu intérieur, où le signal est bruité, faible voire inexistant. Bien que les systèmes de localisation globaux (GPS) et les travaux qui en découlent fonctionnent bien hors des bâtiments et dans des canyons urbains, le suivi d'utilisateurs en milieu intérieur est bien plus problématique. De ce fait, le problème de prédiction reste un obstacle essentiel à la construction de TSs fiable dans de tels environnements. Une étape de prédiction est inévitable, en particulier, dans le cas où l'on manque d'informations. De multiples approches ont été proposées dans la littérature, la plupart étant basées sur un filtre linéaire (LF), un filtre de Kalman (KF) et ses variantes, ou sur un filtre particulaire (PF). Les filtres de prédiction sont souvent utilisés dans des problèmes d'estimation et l'application de la dérivation non entière peut limiter l'impact de la perte de performances. Ce travail présente une nouvelle approche pour la localisation intérieure par WLAN utilisant un groupement des coordonnées. Ensuite, une étude comparative des techniques déterministes et des techniques d'apprentissage pour la localisation intérieure est présentée. Enfin, une nouvelle approche souple pour les systèmes de suivi en milieu intérieur, par application de la dérivation non entière, est présentée / Recently, the static and dynamic geo-location of a device or a person has become one of the most important aspects of communication systems because of its multiple applications. In general, knowing the position of a mobile terminal (MT) in outdoor or indoor environments is of major importance for applications providing services based on the location. The development of localization systems has been mainly driven by the avail- ability of the affordable cost of indoor wireless local area network (WLAN) infrastructure. There exist different techniques to localize MTs with the different mainly depending on the type of the metrics extracted from the radio frequency signals communicated between base stations (BSs) and MTs. Ideal measurements are taken in environments which are free of obstacles and in direct ray tracings between BS and MT. This is not the case in indoor environment because the daily use of permanent obstacles in the work space scatters the ray tracings. Measurements taken in Non Line Of Sight (NLOS) are unpredictable and different from those taken in LOS. In order to reduce measurement errors, one can apply different techniques such as mitigation, approximation, prior correction, or filtering. Tracking systems (TSs) have many concrete applications in the space of individual navigation, social net- working, asset management, traffic management, mobile resource management, etc. Different techniques are applied to build TSs in indoor environments, where the signal is noisy, weak or even non-existent. While the Global Positioning System (GPS) devices work well outside buildings and in urban canyons, tracking an indoor user in a real-world environment is much more problematic. The prediction problem remains an essential obstacle to construct reliable indoor TSs. Then lacks of reliable wireless signals represent the main issue for indoor geo-location systems. This obviously calls for some sort of predictions and corrections to overcome signal reliability, which unavoidably open the door for a multitude of challenges. Varieties of approaches were proposed in the literature. The most used are the ones based on prediction filters, such as Linear Filter (LF), Kalman Filter (KF) and its derivatives, and Particle Filters (PF). Prediction filters are often used in estimation problems and applying Digital Fractional Differentiation can limit the impact of performance degradations. This work presents a novel approach for the WLAN indoor geo-location by using coordinates clustering. This approach allows overcoming the limitations of NLOS methods without applying any of mitigation, approximation, prior correction, or filtering approaches. Then a comparison study of deterministic and learning techniques for indoor geo-location is presented. Finally, it presents a novel soft approach for indoor tracking system by applying digital fractional integration (DFI) to classical prediction filters

Ce travail de thèse aborde le problème de l'alignement d'images 2D obtenues en tomographie électronique dans la perspective d'une reconstruction tridimensionnelle et la détection des ribosomes à partir de l'objet reconstruit. Une méthode d'optimisation globale est proposée pour minimiser un coût qui permet d'effectuer l'alignement 3D et la reconstruction de manière conjointe. La thèse traite également le problème de la segmentation des images 3D reconstruites avec une méthode de classification probabiliste. Cependant, la nature des images de cryo-tomographie révèle des problèmes de bruit et de contraste. Deux méthodes de filtrage 3D ont été proposées comme prétraitement du processus de segmentation. La première méthode est basée sur l'intégration fractionnaire. La seconde est basée sur l'analyse multi-fractale. L'institut de recherche biomédicale IGBMC de Strasbourg a fourni les images de projection utilisées dans cette thèse. / This thesis deals with the problem of the alignment of 2D images obtained by transmission electron microscopy in the perspective of a three-dimensional reconstruction and the detection of ribosomes from the reconstructed object. A global optimization method is proposed to minimize a cost that allows the 3D alignment and reconstruction to be carried out jointly. The thesis also deals with the problem of segmentation of reconstructed 3D images with a probabilistic classification method. However, the nature of cryo-tomography images reveals noise and contrast problems. For this reason, two methods of 3D filtering have been proposed as pre-processing of segmentation, one is based on fractional integration, and the other on a multi-fractal analysis. The institute of biomedical research IGBMC in Strasbourg provides the projection images used in this thesis.

Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2022 / Using the ARFIMA (autoregressive and fractionally integrated moving aver age) model extended with sGARCH (standard generalised autoregressive con ditional heteroscedasticity) and ’gjrGARCH (Glosten-Jagannathan-Runkle gen eralised autoregressive conditional heteroscedascity) innovations, fractional in tegration approach and state space model, this study has empirically examined persistency of inflation dynamics of Ghana and South Africa, the only two coun tries in Sub-Saharan Africa with Inflation Targeting (IT) monetary policy. The first part of the analysis employed monthly CPI (Consumer Price Index) in flation series for the period January 1971 to October 2014 obtained from the Bank of Ghana (BoG), and for the period January 1995 to December 2014 ob tained from Statistics South Africa. The second part involves the estimation of threshold effect of inflation on economic growth using annual data obtained from the IMF (International Monetary Fund) database for the period 1981 to 2014, for both countries. Results from the study showed that structural breaks, long memory and non linearities (or regime shifts) are largely responsible for inflation persistence, hence the ever-changing nature of inflation rates of Ghana and South Africa. ARFIMA(3,0.35,1)-‘gjrGARCH(1,1) under Generalised Error Distribution (GED) and ARFIMA(3,0.50,1)-‘gjrGARCH(1,1) under Student-t Distribution (STD) mod els provided the best fit for persistence in the conditional mean (or level) of CPI for Ghana and South Africa, respectively. The results from these models pro vided evidence of time-varying conditional mean and volatility in CPI inflation rates of both countries. The two models also revealed an asymmetric effect of inflationary shocks, where negative shocks appear to have greater impact than positive shocks, in terms of persistence on the conditional mean with time varying volatility. This thesis proposes a model that combines fractional integration with non linear deterministic terms based on the Chebyshev polynomials in time for the analysis of CPI inflation rates of Ghana and South Africa. We tested for non-linear deterministic terms in the context of fractional integration and esti mated the fractional differencing parameters, d to be 1.11 and 1.32 respectively, for the Ghanaian and the South African inflation rates, but the non-linear trends were found to be statistically insignificant in the two series. New ev idence from this thesis depicts that inflation rate of Ghana is highly persistent and non-mean reverting, with an estimated fractional differencing parameter, d > 1.0, and will therefore require some policy action to steer inflation back to stability. However, the South African inflation series was found to be a cyclical process with an order of integration estimated to be d = 0.7, depicting mean reversion, with the length of the cycles approximated to last for 80 months. Finally, the thesis incorporated structural breaks, long memory, non-linearity, and some explanatory variables into a state space model and estimated the threshold effect of inflation on economic growth. The empirical results suggest that inflation below the estimated levels of 9% and 6% for Ghana and South Africa respectively, will be conducive for economic growth. The policy implications of these results for both countries are as follows. First, both series had similar properties responsible for inducing inflation persistence such as structural breaks, non-linearities, long memory and asymmetric re sponse to negatives shocks - but with varied degrees of magnitude. For both countries, the conditional mean and unobserved components such as volatility for both countries were found to be time-varying. This thesis, therefore, recom mends to the BoG and the South African Reserve Bank (SARB) - responsible for monetary policies, and the Finance Ministers of both governments - respon sible for fiscal policies, to take the above-mentioned properties into account in the formulation of their monetary policies. Second, the thesis recommends that the BoG and the SARB consolidate the IT policy, since keeping inflation below the targets set of 9% and 6%, respectively for Ghana and South Africa, will boost economic growth. Third, policymakers could also design measures (monetary and fiscal policies) such as increase in interest rates, credit control, and reduction of unnecessary expenditure, among others, to control inflation due to its adverse effects on market volatility. Even though an increase in interest rates could assist in curtailing the recent and anticipated increase in inflation rates in both countries, where targets have been missed by Ghana and South Africa, it will also be prudent to legislate monetary policies around demand-supply side since the problem of both coun tries appears to be more of a structuralist than a monetarist. It is, therefore, recommended that both countries tighten the IT monetary policy in order to re duce inflation persistence. This will eventually impact on poverty and income distribution with ramifications for economic growth and/or development. The fourth implication of these results is that governments and central banks should be mindful of the actions and decisions they take, in the sense that unguarded decisions and unnecessary alarms could raise uncertainties in the economy, which could, in turn, affect the future trajectory of inflation. Finally, the thesis recommends that governments of both countries strengthen the pri vate sector, which is the engine of growth. For small and open economies such as Ghana and South Africa, this will grow the economy through job creation and restore investor confidence. / National Research Foundation (NRF), Department of Science and Technology (DST), Telkom’s Tertiary Education Support Programme (TESP) and the NRF-DST Centre of Excellence for Mathematical and Statistical Sciences (CoE-MaSS)

L'objet de cette thèse est d'étudier les systèmes de cointégration fractionnaire de forme triangulaire mais également d'analyser l'apport de ces systèmes dans la modélisation des co-mouvements au sein des marchés financiers internationaux. La thèse s'articule autour de six chapitres équitablement répartis entre contributions économétriques et économiques. Concernant l'approche économétrique, un intérêt particulier est donné à l'estimation de ces systèmes en absence d'information sur les paramètres d'intérêts. Dans cette optique, plusieurs techniques d'estimation sont analysées et développées, essentiellement dans le domaine des fréquences car celui-ci permet un traitement semi-paramétrique des paramètres de nuisances. Les performances de ses estimateurs sont étudiés à travers des simulations mais également à travers l'étude des propriétés asymptotiques. Concernant l'approche économique, une première contribution exploite la cointégration fractionnaire pour révéler l'existence d'un système de taux de change entre certains pays Asiatiques. Une deuxième contribution porte sur l'analyse des interdépendances entre le marché du pétrole et divers taux de change au niveau de la volatilité. Une troisième contribution introduit un processus d'apprentissage adaptatif dans un modèle monétaire à plusieurs pays afin d'étudier sous quelles conditions un système de taux de change peut émerger. / The aim of the thesis is to study a triangular form of fractional cointegration systems and to investigate whether these systems allow to model the comovements in international financial markets. The thesis is organized around six chapters. Three of them are theory-oriented and the three others are empirics-oriented. Concerning the econometric approach, a particular interest is devoted to the estimation of these systems when all parameters of interest are unknown. To this extent, several estimation techniques are investigated and introduced, essentially in frequency domain as it allows a semi-parametric treatment of the nuisance parameters. Most of times, the performance of these estimators are studied by means of simulations but the asymptotic theory is also developed. Concerning the economic approach, a first contribution applies the fractional cointegration theory to reveal the existence of an exchange rate system between several Asian countries. A second contribution deals with the risk interdependences between the crude oil market and several exchange rates. A third contribution considers an adaptive learning mechanism in a multi-country monetary model to investigate the conditions under which an exchange rate system is likely to emerge.

Le premier chapitre consiste en une brève revue de littérature dont les éléments sont repris dans les différentes introductions des études empiriques proposées dans la suite de la thèse. L'objet de cet état des lieux est de fixer le cadre général des analyses macro-économétriques opérées dans la thèse. Ce cadre nous permet d'une part, d'envisager une adéquate intégration des anticipations des agents économiques dans le raisonnement ayant mené aux modèles keynésiens actuels et d'autre part, d'effectuer des estimations des principales versions de la courbe de Phillips introduites dans la littérature macro-économique post-seconde guerre mondiale. Dans cette optique, la thèse est constituée de trois études empiriques. Dans la première de ces études, nous nous plaçons au sein d'un cadre uni-varié et tentons de discriminer entre plusieurs spécifications, proposant différentes caractérisations économétriques de la dynamique du taux d'inflation U.S. Essentiellement, trois types de spécifications, théoriquement associés à trois évolutions possibles du taux d'inflation espéré (anticipé), sont mis à l'épreuve. Les résultats de cette première étude montrent que la dynamique du taux d'inflation peut être pertinemment décrite à l'aide d'un modèle à changements de (trois) régimes markoviens dans les dérives (Intercepts) d'un processus autorégressif (d'ordre deux), soit le modèle MSI(3)-AR(2). La deuxième étude s'opère dans le cadre multi-varié d'une Nouvelle Courbe de Phillips Keynésienne à Inflation tendancielle Positive (NKPC-PI). Au sein de ce cadre, la relation d'arbitrage Inflation/Activité réelle est estimée suivant une procédure en deux étapes. Dans la première, nous identifions des régimes distincts du taux d'inflation U.S. à l'aide d'un modèle à changements de (trois) régimes markoviens dans les dérives d'un processus vectoriel autorégressif (d'ordre deux), soit le modèle MSI(3)-VAR(2). Dans la seconde étape, nous estimons les paramètres structurels de cette économie keynésienne afin d'extraire la courbe de Phillips résultante des changements de régimes initialement identifiés. Les résultats de cette deuxième étude nous amènent à conclure à une non-négligeable instabilité de la courbe de Phillips au cours de la période post-seconde guerre mondiale. La troisième étude se présente comme un prolongement et/ou un approfondissement des deux premières. Aussi, dans sa première partie, nous revenons sur les dynamiques tendancielles individuelles des quatre variables intervenant dans le cadre de modélisation NKPC-PI. Les résultats issus de ces premières estimations en contextes uni-variés montrent que seule la dynamique du taux d'inflation et, dans une moindre mesure, celle du coût marginal réel semble obéir à des changements de régimes. La spécification retenue pour l'inflation est celle de la première étude (MSI(3)-AR(2)), tandis que la dynamique du coût marginal réel pourrait être approchée à l'aide d'un modèle à changements de (deux) régimes dans les dérives d'un processus autorégressif (d'ordre deux), soit le modèle MSI(2)-AR(2). Les dynamiques du taux d'actualisation nominal et du taux de croissance de l'output (les deux autres variables du modèle NKPC-PI) semblent, quant à elles, être assez bien caractérisées par des spécifications linéaires autorégressives à deux retards (AR(2)). Sur la base de ces premiers résultats, nous estimons, dans la deuxième partie de l'étude, la nouvelle courbe de Phillips keynésienne en considérant que les processus générateurs des quatre séries du modèle peuvent répondre à de possibles intégrations fractionnelles. Les résultats de ces dernières estimations montrent que la prise en compte simultanée des changements de régimes et de la longue mémoire dans les dynamiques des variables du modèle apporte certains éclairages sur l'évolution du débat mené autour de la relation d'arbitrage post-seconde guerre mondiale. / This PhD thesis proposes, through her three articles, a macro-econometric framework of integrating, in the most adequate way to our sense, the expectations of the economic agents in the reasoning having led to current New-Keynesian models. Upon this specified frame of analysis, we evaluate the effectiveness of various versions of the Phillips curve introduced into the macroeconomic literature. The first study of this thesis takes place in a univariate context and we seek to determine an econometric model leading to best characterize the U.S inflation rate dynamic. In order to achieve this, three types of specifications, associated with three possible evolutions of the expected rate are considered. The first allows an overall instability of the trend or the expected inflation rate. The second considers an alternative specification in which the expected inflation rate is unstable in periodic segments of the sample. Finally, the last specification allows instability of a "mixed type" in which the trend inflation rate is assumed to be random or subject to a probability schema. The results of our study indicate that this last specification is the one that gives the most adequate characterization of the inflation rate dynamic. The inflation rate then appears generated by a second order autoregressive process with, on the one hand, unchanging lag coefficients and, on the other, an unconditional mean which switch between three global regimes of different frequencies of accession. Based on these first results, we extend the analysis in a multivariate framework. The main topics of the second paper are to challenge the rational nature of the agents expectations and the structural effectiveness of the behaviorally micro-based New Keynesian Phillips Curve with a Positive steady state Inflation (NKPC-PI). We then model the trade-off between the U.S inflation rate and a Unit Labor Cost-based measure of the real activity through Markov Switching - Vectorial AutoRegressive (MS-VAR) specifications. These specifications allow to adequately capturing the rationality in the agents expectations process as they underlie a finite number of expected inflation rate regimes, which highlight the agents adaptive beliefs on the achievements of these regimes. Moreover, the results confirm the structural stability of the NKPC-PI over the inflation rate regimes as its deep parameters seem to be unaffected by the regimes switching (Cogley & Sbordone (2005) and Groen & Mumtaz (2008)). In the third study, we extend the analysis of the Phillips curve trade-off. First, we look at determining econometrics models leading to characterize the dynamics of all the variables underlying the trade-off in univariate contexts. As a result, it appears that an adequate way to characterize the agents expectations regarding the dynamics of these variables is to consider a combination of some fixed levels (regimes) in the variables evolutions with an agents adaptive beliefs notion. Finally, based on the implied expectations values of the variables, we show that the Phillips curve seems to disappear when the impact of the expected inflation rate on its current value converges to its long-term value.