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No description available.

One of the growing agricultural subsectors in developing countries is livestock. Livestock and livestock products account for a third of the agricultural gross output. However, the lack of viable livestock market information systems to increase efficiency of markets and support the decision making of traders, pastoralists, and policy makers are still an obstacle for a full development of this subsector. It is along these lines that the USAID, through the Global Livestock-Collaborative Research Support Program, supported the introduction of livestock market information systems in Kenya and Tanzania in 2003, and later in Mali in 2007. The overall objective of the dissertation is to test for cattle markets integration in three African developing countries of Mali, Kenya, and Tanzania. One way of assessing the efficiency of market and the impacts of liberalization policies is to test for market integration and price transmission. We also analyzed price leadership among the markets in each of the three case studies. Autoregressive models (vector autoregressive models and error correction model) were used to determine the level of cattle market integration. The results show a low level of cattle markets integration in Mali. The cattle markets in Mali are more-or-less independent with regard to price transmission among markets. Kenya cattle markets showed a good level of integration among the markets. Chepareria market in the Rift Valley region (west) seemed to lead other markets in price signal transmission. Tanzanian cattle markets exhibited a higher level of integration with Pugu market, in Dar es Salaam, leading other cattle markets in price signal transmission. In conclusion, the cattle markets in Tanzania and Kenya appeared to have a relatively higher level of market integration compared to the cattle markets in Mali. There is a reasonable belief that the time the livestock market information system has been in place, in each country, played a role in the market integration process. More time and better communications seem to have allowed the market actors to learn arbitrage skills and strengthen their trade relationships that ultimately led to the market integration.

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Consider a sequence of random variables which obeys a first order autoregressive model with unknown parameter alpha. Under suitable assumptions on the error structure of the model, the limiting distribution of the normalized least squares estimator of alpha is discussed. The choice of the normalizing constant depends on whether alpha is less than one, equals one, or is greater than one in absolute value. In particular, the limiting distribution is normal provided that the absolute value of alpha is less than one, but is a function of Brownian motion whenever the absolute value of alpha equals one. Some general remarks are made whenever the sequence of random variables is a first order moving average process.

In this thesis, a Bayesian approach is adopted to handle parameter estimation and model uncertainty in autoregressive moving average (ARMA) time series models and dynamic linear models (DLM). Bayesian model uncertainty is handled in a parametric fashion through the use of posterior model probabilities computed via Markov chain Monte Carlo (MCMC) simulation techniques. Attention is focused on reversible jump Markov chain Monte Carlo (RJMCMC) samplers, which can move between models of different dimensions, to address the problem of model order uncertainty and strategies for proposing efficient sampling schemes in autoregressive moving average time series models and dynamic linear models are developed. The general problem of assessing convergence of the sampler in a dimension-changing context is addressed by computing estimates of the probabilities of moving to higher and lower dimensional spaces. Graphical and numerical techniques are used to compare different updating schemes. The methodology is illustrated by applying it to both simulated and real data sets and the results for the Bayesian model selection and parameter estimation procedures are compared with the classical model selection criteria and maximum likelihood estimation.

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Spatial and temporal components play a critical role in explaining variability across geographic regions and time, and are necessary components to space-time epidemiological research. Until recent years, most spatial epidemiological studies have used simple space-time analyses, but the continuous advancements in statistical modeling software and geographic information systems have made more complex spatial analyses readily available. However, methods may be problematic and several ongoing statistical weaknesses have been documented, including failing to account for three significant correlative factors - spatial, temporal, and spatiotemporal autocorrelations. Using Eastern Equine Encephalitis (EEE) human incidence data, this Master's thesis aimed to answer the research question, is there a northeastern shift in human EEE incidence within the United States, by identifying a statistical model that adjusts for spatial, temporal, and spatiotemporal autocorrelations. This thesis introduced the spatial autoregressive distributed lag (SADL) model, a model that adjusts for spatial, temporal, and spatiotemporal autocorrelations. However, results demonstrated that EEE is too rare an event for the SADL model to be appropriate, and a non-autocorrelation model was used as the final model. Results showed that EEE incidence is significantly increasing over time for all infected regions of the United States, with a significant difference of 1.4 cases/10 million between 1964 and 2015. Results did not demonstrate a northeastern shift in EEE incidence as the northeastern US had the highest expected incidence across the entire study period (1964-1967: 2.9/10 million; 2012-2015: 6.8/10 million), but results did demonstrate that the northeastern US had the quickest increasing risk for EEE as compared to other infected regions of the US with an increase in expected incidence of 3.9/10 million between 1964 and 2015.

Dans l’analyse des séries temporelles multivariées, la plupart des modèles existants sont utilisés à des fins de prévision, c’est-à-dire pour estimer les valeurs futures du système étudié à partir d’un historique de valeurs observées dans le passé. Une autre tâche consiste à extraire des causalités entre les variables d’un système dynamique. C’est pour ce dernier problème à visée explicative que nous développons une série d’outils. À cette fin, nous définissons dans cette thèse une nouvelle famille de modèles autorégressifs vectoriels non paramétriques construits à partir de noyaux à valeur opérateur. En faisant l’hypothèse d’une structure sous-jacente creuse, la parcimonie du modèle est contrôlée en imposant dans la fonction de coût des contraintes de parcimonie aux paramètres du modèle (qui sont en l’occurrence des vecteurs qui pondèrent une combinaison linéaire de noyaux). Les noyaux étudiés possèdent parfois des hyperparamètres qui doivent être appris selon la nature du problème considéré. Lorsque des hypothèses de travail ou des connaissances expertes permettent de fixer les paramètres du noyau, le problème d’apprentissage se réduit à la seule estimation des paramètres du modèle. Pour optimiser la fonction de coût correspondante, nous développons un algorithme proximal. A contrario, lorsqu’aucune hypothèse relative aux variables n’est disponible, les paramètres de certains noyaux ne peuvent être fixés a priori. Il est alors nécessaire d’apprendre conjointement les paramètres du modèle et ceux du noyau. Pour cela, nous faisons appel à un schéma d’optimisation alterné qui met en jeu des méthodes proximales. Nous proposons ensuite d’extraire un estimateur de la matrice d’adjacence encodant le réseau causal sous-jacent en calculant une statistique des matrices jacobiennes instantanées. Dans le cas de la grande dimension, c’est-à-dire un nombre insuffisant de données par rapport au nombre de variables, nous mettons en oeuvre une approche d’ensemble qui partage des caractéristiques du boosting et des forêts aléatoires. Afin de démontrer l’efficacité de nos modèles, nous les appliquons à deux jeux de données : des données simulées à partir de réseaux de régulation génique et des données réelles sur le climat. / In multivariate time series analysis, existing models are often used for forecasting, i.e. estimating future values of the observed system based on previously observed values. Another purpose is to find causal relationships among a set of state variables within a dynamical system. We focus on the latter and develop tools in order to address this problem. In this thesis, we define a new family of nonparametric vector autoregressive models based on operator-valued kernels. Assuming a sparse underlying structure, we control the model’s sparsity by defining a loss function that includes sparsity-inducing penalties on the model parameters (which are basis vectors within a linear combination of kernels). The selected kernels sometimes involve hyperparameters that may need to be learned depending on the nature of the problem. On the one hand, when expert knowledge or working assumptions allow presetting the parameters of the kernel, the learning problem boils down to estimating only the model parameters. To optimize the corresponding loss function, we develop a proximal algorithm. On the other hand, when no prior knowledge is available, some other kernels may exhibit unknown parameters. Consequently, this leads to the joint learning of the kernel parameters in addition to the model parameters. We thus resort to an alternate optimization scheme which involves proximal methods. Subsequently, we propose to build an estimate of the adjacency matrix coding for the underlying causal network by computing a function of the instantaneous Jacobian matrices. In a high-dimensional setting, i.e. insufficient amount of data compared to the number of variables, we design an ensemble methodology that shares features of boosting and random forests. In order to emphasize the performance of the developed models, we apply them on two tracks : simulated data from gene regulatory networks and real climate data.

We study in this dissertation Generalized Autoregressive Conditionally Heteroskedastic (GARCH) time series. The research focuses on squared GARCH sequences. Our main results are as follows: 1. We compare three methods of constructing confidence intervals for sample autocorrelations of squared returns modeled by models from the GARCH family. We compare the residual bootstrap, block bootstrap and subsampling methods. The residual bootstrap based on the standard GARCH(l,1) model is seen to perform best. Confidence intervals for cross-correlations of a bivariate GARCH model are also studied. 2. We study a test to discriminate between long memory and volatility changes in financial returns data. Finite sample performance of the test is examined and compared using various variance estimators. The Bartlett kernel estimator with truncation lag determined by a calibrated bandwidth selection procedure is seen to perform best. The testing procedure is robust to various GARCH-type models. 3. We propose several methods of on-line detection of a change in unconditional variance in a conditionally heteroskedastic time series. We follow a paradigm in which the first m observations are assumed to follow a stationary process and the monitoring scheme has asymptotically controlled probability of falsely rejecting the null hypothesis of no change. Our theory is applicable to broad classes of GARCH-type time series and relies on a strong invariance principle which holds for the squares of observations generated by such models. Practical implementation of the procedures is proposed and the performance of the methods is investigated by a simulation study.