Estimation of State Space Models and Stochastic Volatility

Ma thèse est composée de trois chapitres reliés à l'estimation des modèles espace-état et volatilité stochastique. Dans le première article, nous développons une procédure de lissage de l'état, avec efficacité computationnelle, dans un modèle espace-état linéaire et gaussien. Nous montrons comment exploiter la structure particulière des modèles espace-état pour tirer les états latents efficacement. Nous analysons l'efficacité computationnelle des méthodes basées sur le filtre de Kalman, l'algorithme facteur de Cholesky et notre nouvelle méthode utilisant le compte d'opérations et d'expériences de calcul. Nous montrons que pour de nombreux cas importants, notre méthode est plus efficace. Les gains sont particulièrement grands pour les cas où la dimension des variables observées est grande ou dans les cas où il faut faire des tirages répétés des états pour les mêmes valeurs de paramètres. Comme application, on considère un modèle multivarié de Poisson avec le temps des intensités variables, lequel est utilisé pour analyser le compte de données des transactions sur les marchés financières. Dans le deuxième chapitre, nous proposons une nouvelle technique pour analyser des modèles multivariés à volatilité stochastique. La méthode proposée est basée sur le tirage efficace de la volatilité de son densité conditionnelle sachant les paramètres et les données. Notre méthodologie s'applique aux modèles avec plusieurs types de dépendance dans la coupe transversale. Nous pouvons modeler des matrices de corrélation conditionnelles variant dans le temps en incorporant des facteurs dans l'équation de rendements, où les facteurs sont des processus de volatilité stochastique indépendants. Nous pouvons incorporer des copules pour permettre la dépendance conditionnelle des rendements sachant la volatilité, permettant avoir différent lois marginaux de Student avec des degrés de liberté spécifiques pour capturer l'hétérogénéité des rendements. On tire la volatilité comme un bloc dans la dimension du temps et un à la fois dans la dimension de la coupe transversale. Nous appliquons la méthode introduite par McCausland (2012) pour obtenir une bonne approximation de la distribution conditionnelle à posteriori de la volatilité d'un rendement sachant les volatilités d'autres rendements, les paramètres et les corrélations dynamiques. Le modèle est évalué en utilisant des données réelles pour dix taux de change. Nous rapportons des résultats pour des modèles univariés de volatilité stochastique et deux modèles multivariés. Dans le troisième chapitre, nous évaluons l'information contribuée par des variations de volatilite réalisée à l'évaluation et prévision de la volatilité quand des prix sont mesurés avec et sans erreur. Nous utilisons de modèles de volatilité stochastique. Nous considérons le point de vue d'un investisseur pour qui la volatilité est une variable latent inconnu et la volatilité réalisée est une quantité d'échantillon qui contient des informations sur lui. Nous employons des méthodes bayésiennes de Monte Carlo par chaîne de Markov pour estimer les modèles, qui permettent la formulation, non seulement des densités a posteriori de la volatilité, mais aussi les densités prédictives de la volatilité future. Nous comparons les prévisions de volatilité et les taux de succès des prévisions qui emploient et n'emploient pas l'information contenue dans la volatilité réalisée. Cette approche se distingue de celles existantes dans la littérature empirique en ce sens que ces dernières se limitent le plus souvent à documenter la capacité de la volatilité réalisée à se prévoir à elle-même. Nous présentons des applications empiriques en utilisant les rendements journaliers des indices et de taux de change. Les différents modèles concurrents sont appliqués à la seconde moitié de 2008, une période marquante dans la récente crise financière.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Spanning avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics: Field dependence and geometrical properties

Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at T=0 have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at T=0.

Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics.

The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.

A finite state model for on-line analytical processing in triadic contexts

About ten years ago, triadic contexts were presented by Lehmann and Wille as an extension of Formal Concept Analysis. However, they have rarely been used up to now, which may be due to the rather complex structure of the resulting diagrams. In this paper, we go one step back and discuss how traditional line diagrams of standard (dyadic) concept lattices can be used for exploring and navigating triadic data. Our approach is inspired by the slice & dice paradigm of On-Line-Analytical Processing (OLAP). We recall the basic ideas of OLAP, and show how they may be transferred to triadic contexts. For modeling the navigation patterns a user might follow, we use the formalisms of finite state machines. In order to present the benefits of our model, we show how it can be used for navigating the IT Baseline Protection Manual of the German Federal Office for Information Security.

State Policies, Territories and Rights of Indigenous Peoples in Ecuador (1983-2012)

This work seeks to reconstruct the dynamics of the agreements and disagreements between the State and the indigenous peoples in Ecuador, emphasising particularly on two key elements: first, the indigenous peoples participation and exercise of their political rights, in particular the right to self-government and autonomy within their jurisdictions; and secondly, indigenous peoples’ degree of direct influence on public policies’ formulation and implementation, specially those directly affecting their territories, including the exploitation of natural resources. In Ecuador, during this historical period, the state has gone through three major moments in its relationship with indigenous peoples: neo - indigenism associated to developmentalism (1980-1984); multiculturalism associated to neoliberalism (1984- 2006) as one of the dominant trends over the period; and the crisis of neoliberalism and the search for national diversity and interculturalism associated to post- neoliberalism (2007-2013). Each has had a particular connotation, as to the scope and methods to respond to indigenous demands. In this context, this research aims to answer the central question: how has the Ecuadorian State met the demands of the indigenous movement in the last three decades, and how has it ensured the validity of their gradually recognized rights? And how and to what extent by doing so, it contradicts and alters the existing economic model based on the extraction of primary resources?

A Demographic Model to Evaluate Population Declines in the Endangered Streaked Horned Lark

The Streaked Horned Lark (Eremophila alpestris strigata) is listed as endangered by the State of Washington, USA and by Canada under the Species at Risk Act and is also classified as a federal candidate for listing under the Endangered Species Act in the USA. A substantial portion of Streaked Horned Lark habitat has been lost or degraded, and range contraction has occurred in Oregon, Washington, and British Columbia. We estimate the vital rates (fecundity, adult and juvenile survival) and population growth rate (λ) for Streaked Horned Larks breeding in Washington, USA and conduct a Life-Stage Simulation Analysis (LSA) to evaluate which vital rate has the greatest influence on λ. We simulated changes in the three vital rates to examine how much they would need to be adjusted either independently or in concert to achieve a stable Streaked Horned Lark population (λ = 1). We also evaluated which fecundity component (the number of fledglings per egg laid or renesting interval) had the greatest impact on λ. The estimate of population growth suggests that Streaked Horned Larks in Washington are declining rapidly (λ = 0.62 ± 0.10) and that local breeding sites are not sustainable without immigration. The LSA results indicate that adult survival had the greatest influence on λ, followed by juvenile survival and fecundity. However, increases in vital rates led to λ = 1 only when adult survival was raised from 0.47 to 0.85, juvenile survival from 0.17 to 0.58, and fecundity from 0.91 to 3.09. Increases in breeding success and decreases in the renesting interval influenced λ similarly; however, λ did not reach 1 even when breeding success was raised to 100% or renesting intervals were reduced to 1 day. Only when all three vital rates were increased simultaneously did λ approach 1 without requiring highly unrealistic increases in each vital rate. We conclude that conservation activities need to target all or multiple vital rates to be successful. The baseline data presented here and subsequent efforts to manage Streaked Horned Larks will provide valuable information for management of other declining Horned Lark subspecies and other grassland songbirds across North America.

Model-based vehicle detection and classification using orthographic approximations

This paper reports the current state of work to simplify our previous model-based methods for visual tracking of vehicles for use in a real-time system intended to provide continuous monitoring and classification of traffic from a fixed camera on a busy multi-lane motorway. The main constraints of the system design were: (i) all low level processing to be carried out by low-cost auxiliary hardware, (ii) all 3-D reasoning to be carried out automatically off-line, at set-up time. The system developed uses three main stages: (i) pose and model hypothesis using 1-D templates, (ii) hypothesis tracking, and (iii) hypothesis verification, using 2-D templates. Stages (i) & (iii) have radically different computing performance and computational costs, and need to be carefully balanced for efficiency. Together, they provide an effective way to locate, track and classify vehicles.

The effect of doubled CO2 and model basic state biases on the monsoon-ENSO system. II: Changing ENSO regimes

Integrations of a fully-coupled climate model with and without flux adjustments in the equatorial oceans are performed under 2×CO2 conditions to explore in more detail the impact of increased greenhouse gas forcing on the monsoon-ENSO system. When flux adjustments are used to correct some systematic model biases, ENSO behaviour in the modelled future climate features distinct irregular and periodic (biennial) regimes. Comparison with the observed record yields some consistency with ENSO modes primarily based on air-sea interaction and those dependent on basinwide ocean wave dynamics. Simple theory is also used to draw analogies between the regimes and irregular (stochastically forced) and self-excited oscillations respectively. Periodic behaviour is also found in the Asian-Australian monsoon system, part of an overall biennial tendency of the model under these conditions related to strong monsoon forcing and increased coupling between the Indian and Pacific Oceans. The tropospheric biennial oscillation (TBO) thus serves as a useful descriptor for the coupled monsoon-ENSO system in this case. The presence of obvious regime changes in the monsoon-ENSO system on interdecadal timescales, when using flux adjustments, suggests there may be greater uncertainty in projections of future climate, although further modelling studies are required to confirm the realism and cause of such changes.

The effect of doubled CO2 and model basic state biases on the monsoon-ENSO system. I: Mean response and interannual variability

The impact of doubled CO2 concentration on the Asian summer monsoon is studied using a coupled ocean-atmosphere model. Both the mean seasonal precipitation and interannual monsoon variability are found to increase in the future climate scenario presented. Systematic biases in current climate simulations of the coupled system prevent accurate representation of the monsoon-ENSO teleconnection, of prime importance for seasonal prediction and for determining monsoon interannual variability. By applying seasonally varying heat flux adjustments to the tropical Pacific and Indian Ocean surface in the future climate simulation, some assessment can be made of the impact of systematic model biases on future climate predictions. In simulations where the flux adjustments are implemented, the response to climate change is magnified, with the suggestion that systematic biases may be masking the true impact of increased greenhouse gas forcing. The teleconnection between ENSO and the Asian summer monsoon remains robust in the future climate, although the Indo-Pacific takes on more of a biennial character for long periods of the flux-adjusted simulation. Assessing the teleconnection across interdecadal timescales shows wide variations in its amplitude, despite the absence of external forcing. This suggests that recent changes in the observed record cannot be distinguished from internal variations and as such are not necessarily related to climate change.

A semi-quantitative approach to deriving a model structure for the uptake of organic chemicals by vegetation

An expert elicitation exercise was undertaken to determine those components and processes that are most important for modeling plant uptake of organic chemicals. The state of our knowledge of these processes was also assessed. This semi-quantitative analysis allowed the construction of an idealized model with seven compartments; soil bulk, soil water, roots, stem, leaves, fruit, and air. Three main areas were identified further research: 1) the uptake of organic chemicals by fruit; 2) the internal transfer of organic chemicals between plant structures (e.g., stem and leaves); and 3) the transfer via the soil-air-plant pathway. Until new data becomes available to quantify these processes, it is proposed that an equilibrium partitioning approach is used between plant components other than fruit or that models consist of both an edible and inedible compartment.

El Nino-mean state-seasonal cycle interactions in a multi-model ensemble

The modelled El Nino-mean state-seasonal cycle interactions in 23 coupled ocean-atmosphere GCMs, including the recent IPCC AR4 models, are assessed and compared to observations and theory. The models show a clear improvement over previous generations in simulating the tropical Pacific climatology. Systematic biases still include too strong mean and seasonal cycle of trade winds. El Nino amplitude is shown to be an inverse function of the mean trade winds in agreement with the observed shift of 1976 and with theoretical studies. El Nino amplitude is further shown to be an inverse function of the relative strength of the seasonal cycle. When most of the energy is within the seasonal cycle, little is left for inter-annual signals and vice versa. An interannual coupling strength (ICS) is defined and its relation with the modelled El Nino frequency is compared to that predicted by theoretical models. An assessment of the modelled El Nino in term of SST mode (S-mode) or thermocline mode (T-mode) shows that most models are locked into a S-mode and that only a few models exhibit a hybrid mode, like in observations. It is concluded that several basic El Nino-mean state-seasonal cycle relationships proposed by either theory or analysis of observations seem to be reproduced by CGCMs. This is especially true for the amplitude of El Nino and is less clear for its frequency. Most of these relationships, first established for the pre-industrial control simulations, hold for the double and quadruple CO2 stabilized scenarios. The models that exhibit the largest El Nino amplitude change in these greenhouse gas (GHG) increase scenarios are those that exhibit a mode change towards a T-mode (either from S-mode to hybrid or hybrid to T-mode). This follows the observed 1976 climate shift in the tropical Pacific, and supports the-still debated-finding of studies that associated this shift to increased GHGs. In many respects, these models are also among those that best simulate the tropical Pacific climatology (ECHAM5/MPI-OM, GFDL-CM2.0, GFDL-CM2.1, MRI-CGM2.3.2, UKMO-HadCM3). Results from this large subset of models suggest the likelihood of increased El Nino amplitude in a warmer climate, though there is considerable spread of El Nino behaviour among the models and the changes in the subsurface thermocline properties that may be important for El Nino change could not be assessed. There are no clear indications of an El Nino frequency change with increased GHG.