Treatment of geophysical data as a non-stationary process

ABSTRACT: The Kalman-Bucy method is here analized and applied to the solution of a specific filtering problem to increase the signal message/noise ratio. The method is a time domain treatment of a geophysical process classified as stochastic non-stationary. The derivation of the estimator is based on the relationship between the Kalman-Bucy and Wiener approaches for linear systems. In the present work we emphasize the criterion used, the model with apriori information, the algorithm, and the quality as related to the results. The examples are for the ideal well-log response, and the results indicate that this method can be used on a variety of geophysical data treatments, and its study clearly offers a proper insight into modeling and processing of geophysical problems.

Stationary processes for object detection and non-rigid structure-from-motion

Stationary processes are random variables whose value is a signal and whose distribution is invariant to translation in the domain of the signal. They are intimately connected to convolution, and therefore to the Fourier transform, since the covariance matrix of a stationary process is a Toeplitz matrix, and Toeplitz matrices are the expression of convolution as a linear operator. This thesis utilises this connection in the study of i) efficient training algorithms for object detection and ii) trajectory-based non-rigid structure-from-motion.

Stationary random response of multidegree-of-freedom systems

An approximate approach is presented for determining the stationary random response of a general multidegree-of-freedom nonlinear system under stationary Gaussian excitation. This approach relies on defining an equivalent linear system for the nonlinear system. Two particular systems which possess exact solutions have been solved by this approach, and it is concluded that this approach can generate reasonable solutions even for systems with fairly large nonlinearities. The approximate approach has also been applied to two examples for which no exact or approximate solutions were previously available.

Also presented is a matrix algebra approach for determining the stationary random response of a general multidegree-of-freedom linear system. Its derivation involves only matrix algebra and some properties of the instantaneous correlation matricies of a stationary process. It is therefore very direct and straightforward. The application of this matrix algebra approach is in general simpler than that of commonly used approaches.

Estimation of evolutionary distances under stationary and nonstationary models of nucleotide substitution

Estimation of evolutionary distances has always been a major issue in the study of molecular evolution because evolutionary distances are required for estimating the rate of evolution in a gene, the divergence dates between genes or organisms, and the relationships among genes or organisms. Other closely related issues are the estimation of the pattern of nucleotide substitution, the estimation of the degree of rate variation among sites in a DNA sequence, and statistical testing of the molecular clock hypothesis. Mathematical treatments of these problems are considerably simplified by the assumption of a stationary process in which the nucleotide compositions of the sequences under study have remained approximately constant over time, and there now exist fairly extensive studies of stationary models of nucleotide substitution, although some problems remain to be solved. Nonstationary models are much more complex, but significant progress has been recently made by the development of the paralinear and LogDet distances. This paper reviews recent studies on the above issues and reports results on correcting the estimation bias of evolutionary distances, the estimation of the pattern of nucleotide substitution, and the estimation of rate variation among the sites in a sequence.

What is a linear process?

We argue that given even an infinitely long data sequence, it is impossible (with any test statistic) to distinguish perfectly between linear and nonlinear processes (including slightly noisy chaotic processes). Our approach is to consider the set of moving-average (linear) processes and study its closure under a suitable metric. We give the precise characterization of this closure, which is unexpectedly large, containing nonergodic processes, which are Poisson sums of independent and identically distributed copies of a stationary process. Proofs of these results will appear elsewhere.

Essays on Vietnam’s Financial Reforms: Foreign Exchange Statistics and Evidence of Long-Run Equilibrium

In this paper, we examine exchange rates in Vietnam’s transitional economy. Evidence of long-run equilibrium are established in most cases through a single co-integrating vector among endogenous variables that determine the real exchange rates. This supports relative PPP in which ECT of the system can be combined linearly into a stationary process, reducing deviation from PPP in the long run. Restricted coefficient vectors ß’ = (1, 1, -1) for real exchange rates of currencies in question are not rejected. This empirics of relative PPP adds to found evidences by many researchers, including Flre et al. (1999), Lee (1999), Johnson (1990), Culver and Papell (1999), Cuddington and Liang (2001). Instead of testing for different time series on a common base currency, we use different base currencies (USD, GBP, JPY and EUR). By doing so we want to know the whether theory may posit significant differences against one currency? We have found consensus, given inevitable technical differences, even with smallerdata sample for EUR. Speeds of convergence to PPP and adjustment are faster compared to results from other researches for developed economies, using both observed and bootstrapped HL measures. Perhaps, a better explanation is the adjustment from hyperinflation period, after which the theory indicates that adjusting process actually accelerates. We observe that deviation appears to have been large in early stages of the reform, mostly overvaluation. Over time, its correction took place leading significant deviations to gradually disappear.

Volume, volatility, and leverage: A dynamic analysis

This paper uses dynamic impulse response analysis to investigate the interrelationships among stock price volatility, trading volume, and the leverage effect. Dynamic impulse response analysis is a technique for analyzing the multi-step-ahead characteristics of a nonparametric estimate of the one-step conditional density of a strictly stationary process. The technique is the generalization to a nonlinear process of Sims-style impulse response analysis for linear models. In this paper, we refine the technique and apply it to a long panel of daily observations on the price and trading volume of four stocks actively traded on the NYSE: Boeing, Coca-Cola, IBM, and MMM.

Short run and long run causality in time series: Inference

We propose methods for testing hypotheses of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression methods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the U.S. economy.

Characterization of microalgae native to Quebec for biofuel production.

La production de biodiésel par des microalgues est intéressante à plusieurs niveaux. Dans le premier chapitre, un éventail de pour et contres concernant l’utilisation de microalgues pour la production de biocarburant sont ici révisés. La culture d’algues peut s'effectuer en utilisant des terres non-arables, de l’eau non-potable et des nutriments de base. De plus, la biomasse produite par les algues est considérablement plus importante que celle de plantes vasculaires. Plusieurs espèces on le contenu lipidique en forme de triacylglycérols (TAGs), qui peut correspondre jusqu'à 30% - 40% du poids sec de la biomasse. Ces proportions sont considérablement plus élevées que celui des huiles contenues dans les graines actuellement utilisées pour le biodiésel de première génération. Par contre, une production pratique et peu couteuse de biocarburant par des microalgues requiert de surpasser plusieurs obstacles. Ceci inclut le développement de systèmes de culture efficace à faible coût, de techniques de récupération requérant peu d’énergie, et de méthodes d’extraction et de conversion de l’huile non-dommageables pour l’environnement et peu couteuses. Le deuxième chapitre explore l'une des questions importantes soulevées dans le premier chapitre: la sélection d'une souche pour la culture. Une collection de souches de microalgues d'eau douce indigène au Québec a été établi et examiné au niveau de la diversité physiologique. Cette collection est composée de cent souches, que apparaissaient très hétérogènes en terme de croissance lorsque mises en culture à 10±2 °C ou 22±2 °C sur un effluent secondaire d’une usine municipale de traitement des eaux usées (EU), défini comme milieu Bold's Basal Medium (BBM). Des diagrammes de dispersion ont été utilisés pour étudier la diversité physiologique au sein de la collection, montrant plusieurs résultats intéressants. Il y avait une dispersion appréciable dans les taux de croissance selon les différents types de milieux et indépendamment de la température. De manière intéressante, en considérant que tous les isolats avaient initialement été enrichis sur milieu BBM, la distribution était plutôt symétrique autour de la ligne d’iso-croissance, suggérant que l’enrichissement sur BBM n’a pas semblé biaiser la croissance des souches sur ce milieu par rapport aux EU. Également, considérant que les isolats avaient d’abord été enrichis à 22°C, il est assez surprenant que la distribution de taux de croissance spécifiques soit aussi symétrique autour de la ligne d’iso-croissance, avec grossièrement des nombres égaux d’isolats de part et d’autre. Ainsi, l’enrichissement à 22°C ne semble pas biaiser les cellules vers une croissance à cette température plutôt que vers 10°C. Les diagrammes de dispersion obtenus lorsque le pourcentage en lipides de cultures sur BBM ont été comparées à des cultures ayant poussé sur EU soit à 10°C ou 22°C rendent évident que la production de lipides est favorisée par la culture sur EU aux deux températures, et que la production lipidique ne semble pas particulièrement plus favorisée par l’une ou l’autre de ces températures. Lorsque la collection a été examinée pour y déceler des différences avec le site d’échantillonnage, une analyse statistique a montré grossièrement que le même degré de diversité physiologique était retrouvé dans les échantillons des deux différents sites. Le troisième chapitre a poursuivi l'évaluation de la culture d'algues au Québec. L’utilisation de déchets industriels riches en nutriments minéraux et en sources de carbone pour augmenter la biomasse finale en microalgues et le produit lipidique à faible coût est une stratégie importante pour rendre viable la technologie des biocarburants par les algues. Par l’utilisation de souches de la collection de microalgues de l’Université de Montréal, ce rapport montre pour la première fois que des souches de microalgues peuvent pousser en présence de xylose, la source de carbone majoritairement retrouvée dans les eaux usées provenant des usines de pâte et papier, avec une hausse du taux de croissance de 2,8 fois par rapport à la croissance photoautotrophe, atteignant jusqu’à µ=1,1/jour. En présence de glycérol, les taux de croissance atteignaient des valeurs aussi élevées que µ=1,52/jour. La production lipidique augmentait jusqu’à 370% en présence de glycérol et 180% avec le xylose pour la souche LB1H10, démontrant que cette souche est appropriée pour le développement ultérieur de biocarburants en culture mixotrophe. L'ajout de xylose en cultures d'algues a montré certains effets inattendus. Le quatrième chapitre de ce travail a porté à comprendre ces effets sur la croissance des microalgues et la production de lipides. Quatre souches sauvages indigènes ont été obersvées quotidiennement, avant et après l’ajout de xylose, par cytométrie en flux. Avec quelques souches de Chlorella, l’ajout de xylose induisait une hausse rapide de l’accumulation de lipide (jusqu’à 3,3 fois) pendant les premières six à douze heures. Aux temps subséquents, les cellules montraient une diminution du contenu en chlorophylle, de leur taille et de leur nombre. Par contre, l’unique membre de la famille des Scenedesmaceae avait la capacité de profiter de la présence de cette source de carbone sous culture mixotrophe ou hétérotrophe sans effet négatif apparent. Ces résultats suggèrent que le xylose puisse être utilisé avant la récolte afin de stimuler l’augmentation du contenu lipidique de la culture d’algues, soit en système de culture continu ou à deux étapes, permettant la biorestauration des eaux usées provenant de l’industrie des pâtes et papiers. Le cinquième chapitre aborde une autre déché industriel important: le dioxyde de carbone et les gaz à effet de serre. Plus de la moitié du dioxyde de carbone qui est émis dans l'atmosphère chaque jour est dégagé par un processus stationnaire, soit pour la production d’électricité ou pour la fabrication industrielle. La libération de CO2 par ces sources pourrait être atténuée grâce à la biorestauration avec microalgues, une matière première putative pour les biocarburants. Néanmoins, toutes les cheminées dégagent un gaz différent, et la sélection des souches d'algues est vitale. Ainsi, ce travail propose l'utilisation d’un état de site particulier pour la bioprospection de souches d'algues pour être utilisé dans le processus de biorestauration. Les résultats montrent que l'utilisation d'un processus d'enrichissement simple lors de l'étape d'isolement peut sélectionner des souches qui étaient en moyenne 43,2% mieux performantes dans la production de biomasse que les souches isolées par des méthodes traditionnelles. Les souches isolées dans ce travail étaient capables d'assimiler le dioxyde de carbone à un taux supérieur à la moyenne, comparées à des résultats récents de la littérature.

Further investigation of the uncertain trend in U.S. GDP

The presence of deterministic or stochastic trend in U.S. GDP has been a continuing debate in the literature of macroeconomics. Ben-David and Papell (1995) found evindence in favor of trend stationarity using the secular sample of Maddison (1995). More recently, Murray and Nelson (2000) correctly criticized this nding arguing that the Maddison data are plagued with additive outliers (AO), which bias inference towards stationarity. Hence, they propose to set the secular sample aside and conduct inference using a more homogeneous but shorter time-span post-WWII sample. In this paper we re-visit the Maddison data by employing a test that is robust against AO s. Our results suggest the U.S. GDP can be modeled as a trend stationary process.

A new perspective on the PPP hypothesis

This paper the stastistical properties of the real exchange rates of G-5 countries for the Bretton-Woods peiod, and draw implications on the purchasing power parity (PPP) hypothesis. In contrast to most previous studies that consider only unit root and stationary process to describe the real exchange tae, this paper also considers two in-between processes, the locally persistent process ans the fractionally integrated process, to complement past studies. Seeking to be consistent with tha ample evidence of near unit in the real exchange rate movements very well. This finding implies that: 1) the real exchange movement is more persistent than the stationary case but less persistent than the unit root case; 2) the real exchange rate is non-stationary but the PPP reversion occurs and the PPP holds in the long run; 3) the real exchange rate does not exhibit the secular dependence of the fractional integration; 4) the real exchange rate evolves over time in a way that there is persistence over a range of time, but the effect of shocks will eventually disappear over time horizon longer than order O (nd), that is, at finite time horizon; 5) shocks dissipation is fasters than predicted by the fractional integracion, and the total sum of the effects of a unit innovation is finite, implying that a full PPP reversion occurs at finite horizons. These results may explain why pasrt empirical estudies could not provide a clear- conclusion on the real exchange rate processes and the PPP hypothesis.

SECAGEM DE SEMENTES DE SOJA em SILO COM DISTRIBUIÇÃO RADIAL do FLUXO DE AR: I. MONITORAMENTO FÍSICO

O trabalho foi desenvolvido com o objetivo de avaliar a evolução física do processo de remoção de água das sementes em secador estacionário, com cilindro central perfurado e distribuição radical de ar. A pesquisa foi conduzida com sementes de soja, variando o fluxo (26,9, 28,4 e 33,2 m³/minuto/t) e a temperatura do ar insuflado (42, 46 e 50ºC), considerando a posição das sementes (17, 34 e 51 cm em relação ao cilindro de insuflação) e o tempo de secagem (zero a doze horas, com intervalos de duas horas). Foram caracterizados o ar ambiente, o ar insuflado, as temperaturas e os teores de água da massa, as velocidades e curvas de secagem. As avaliações realizadas destacaram vantagens físicas operacionais da combinação de 28,4 m³/minuto/t com 46ºC e o contrário, com a combinação de 26,9 m³/minuto/t com 42ºC.

Multiresolution spherical wavelet analysis in global seismic tomography

Every seismic event produces seismic waves which travel throughout the Earth. Seismology is the science of interpreting measurements to derive information about the structure of the Earth. Seismic tomography is the most powerful tool for determination of 3D structure of deep Earth's interiors. Tomographic models obtained at the global and regional scales are an underlying tool for determination of geodynamical state of the Earth, showing evident correlation with other geophysical and geological characteristics. The global tomographic images of the Earth can be written as a linear combinations of basis functions from a specifically chosen set, defining the model parameterization. A number of different parameterizations are commonly seen in literature: seismic velocities in the Earth have been expressed, for example, as combinations of spherical harmonics or by means of the simpler characteristic functions of discrete cells. With this work we are interested to focus our attention on this aspect, evaluating a new type of parameterization, performed by means of wavelet functions. It is known from the classical Fourier theory that a signal can be expressed as the sum of a, possibly infinite, series of sines and cosines. This sum is often referred as a Fourier expansion. The big disadvantage of a Fourier expansion is that it has only frequency resolution and no time resolution. The Wavelet Analysis (or Wavelet Transform) is probably the most recent solution to overcome the shortcomings of Fourier analysis. The fundamental idea behind this innovative analysis is to study signal according to scale. Wavelets, in fact, are mathematical functions that cut up data into different frequency components, and then study each component with resolution matched to its scale, so they are especially useful in the analysis of non stationary process that contains multi-scale features, discontinuities and sharp strike. Wavelets are essentially used in two ways when they are applied in geophysical process or signals studies: 1) as a basis for representation or characterization of process; 2) as an integration kernel for analysis to extract information about the process. These two types of applications of wavelets in geophysical field, are object of study of this work. At the beginning we use the wavelets as basis to represent and resolve the Tomographic Inverse Problem. After a briefly introduction to seismic tomography theory, we assess the power of wavelet analysis in the representation of two different type of synthetic models; then we apply it to real data, obtaining surface wave phase velocity maps and evaluating its abilities by means of comparison with an other type of parametrization (i.e., block parametrization). For the second type of wavelet application we analyze the ability of Continuous Wavelet Transform in the spectral analysis, starting again with some synthetic tests to evaluate its sensibility and capability and then apply the same analysis to real data to obtain Local Correlation Maps between different model at same depth or between different profiles of the same model.

Looking for a more comprehensive approach

The necessity/convenience for improving accuracy in determining the flood frequency is widely accepted further than among hydrologists, and is increasingly deepened in relationship with the statement of different thresholds related to the respective management systems. And both Scientific and Management Communities fully accept the necessity of living with determined levels of flood risk. Most of the approaches for “Advancing Methods” improving concentrate on the statistical ways, even since Climate in fact is not a Stationary process. The question is here reflected since the SMARTeST research and final highlights, policy and recommendations. The paper looks at a better agreement between Hydrology and the whole Climate as the result of the Global Thermal Machine and takes mainly into account a historical approach, trying to show the necessity of a wider collection and analysis of climate data for statistical approaches.