Thèses sur le sujet « Filtri multivariati »

This thesis includes two essays that are focused on developing multivariate filter approaches to be used for extracting common cyclical components where the common components can be used as an estimator of a business cycle. The first chapter aims to develop an optimal multivariate filter in order to extract common cyclical components of macroeconomic indicators. The filter allows macroeconomic series to be modeled as a phase shifted version of a coinciding business cycle (BC) while keeping other time series components such as the stochastic trend and idiosyncratic shocks intact (i.e. they are individually specified for each series). Earlier studies of Rünstler (2004), Valle e Azevedo et al. (2006) have applied phase shift in the form of a delay parameter when specifying lead-lag cycles. However, the lead-lag relationship is defined by rotating the baseline cycle which leads to loss of information. This deficiency is especially important if one considers working in continuous time. Therefore, this paper improves on the former technique by allowing a more flexible phase shift mechanism on the original BC. This in turn should lead to more realistic estimates and filters considering that the underlying data is generated through a continuous time framework. The study starts by presenting a structure for bi-variate time series system and then extends to model to incorporate a structure for three time series and beyond. Kalman filter and smoothing recursions are applied to compute the smoothed cycle estimates and to construct the likelihood function. Using simulated data, we test both model specifications by carrying out a grid search of the initial delay parameter to see the likelihood behavior as the parameter moves into fractional neighborhoods. Afterwards, applying the methodology to a set of EU countries and macroeconomic indicators; the study aims to shed light to the presence of cyclical heterogeneity at country level economic activity for major EU member states. A second empirical study provides analysis on how the model can be implemented for assigning a lead/lag ordering to three main economic indicators of a single country. The second chapter implements a multivariate non-parametric filtering approach; the Vertical Multivariate Singular Spectrum Analysis (V-MSSA) of Hassani and Mahmoudvand (2013) and Golyandina et al. (2013). to be applied for identifying a common economic cycle indicator. The methodology is a data-driven procedure that can decompose a time series into many sub components. By exploiting this ability of the SSA, the paper aims to first extract cyclical components based on frequency characteristics and then follow by choosing only common cyclical component pairs with-in the business cycle frequency spectrum. These components will then be aggregated for constructing an EU region wide Business cycle indicator. The chapter outlines each steps of the algorithm that will eventually identify the SSA filter to act as a band-pass filter. The study then proceeds with simulation based data where the common cycle can be controlled and extracted a priori as a benchmark to the SSA-based filter estimates. The study follows with an empirical analysis similar to the framework set in Valle e Azevedo et al. (2006) with the aim to identify a Euro region business cycle indicator. The SSA based filter estimate is compared with Euro region economic activity indicators; the EuroCoin and the quarterly GDP growth rate of the EU area. Our results presents evidence of a successful alternative for tracing the cyclical position of the EU economy from a much smaller data set. Moreover, the constructed indicator also could serve as an unobserved proxy for a monthly growth cycle. A further analysis is also conducted to reveal whether the SSA based approach can be considered as an alternative to parametric filtering methods by providing results of common cycle extraction using Unobserved component model alternatives.
This thesis includes two essays that are focused on developing multivariate filter approaches to be used for extracting common cyclical components where the common components can be used as an estimator of a business cycle. The first chapter aims to develop an optimal multivariate filter in order to extract common cyclical components of macroeconomic indicators. The filter allows macroeconomic series to be modeled as a phase shifted version of a coinciding business cycle (BC) while keeping other time series components such as the stochastic trend and idiosyncratic shocks intact (i.e. they are individually specified for each series). Earlier studies of Rünstler (2004), Valle e Azevedo et al. (2006) have applied phase shift in the form of a delay parameter when specifying lead-lag cycles. However, the lead-lag relationship is defined by rotating the baseline cycle which leads to loss of information. This deficiency is especially important if one considers working in continuous time. Therefore, this paper improves on the former technique by allowing a more flexible phase shift mechanism on the original BC. This in turn should lead to more realistic estimates and filters considering that the underlying data is generated through a continuous time framework. The study starts by presenting a structure for bi-variate time series system and then extends to model to incorporate a structure for three time series and beyond. Kalman filter and smoothing recursions are applied to compute the smoothed cycle estimates and to construct the likelihood function. Using simulated data, we test both model specifications by carrying out a grid search of the initial delay parameter to see the likelihood behavior as the parameter moves into fractional neighborhoods. Afterwards, applying the methodology to a set of EU countries and macroeconomic indicators; the study aims to shed light to the presence of cyclical heterogeneity at country level economic activity for major EU member states. A second empirical study provides analysis on how the model can be implemented for assigning a lead/lag ordering to three main economic indicators of a single country. The second chapter implements a multivariate non-parametric filtering approach; the Vertical Multivariate Singular Spectrum Analysis (V-MSSA) of Hassani and Mahmoudvand (2013) and Golyandina et al. (2013). to be applied for identifying a common economic cycle indicator. The methodology is a data-driven procedure that can decompose a time series into many sub components. By exploiting this ability of the SSA, the paper aims to first extract cyclical components based on frequency characteristics and then follow by choosing only common cyclical component pairs with-in the business cycle frequency spectrum. These components will then be aggregated for constructing an EU region wide Business cycle indicator. The chapter outlines each steps of the algorithm that will eventually identify the SSA filter to act as a band-pass filter. The study then proceeds with simulation based data where the common cycle can be controlled and extracted a priori as a benchmark to the SSA-based filter estimates. The study follows with an empirical analysis similar to the framework set in Valle e Azevedo et al. (2006) with the aim to identify a Euro region business cycle indicator. The SSA based filter estimate is compared with Euro region economic activity indicators; the EuroCoin and the quarterly GDP growth rate of the EU area. Our results presents evidence of a successful alternative for tracing the cyclical position of the EU economy from a much smaller data set. Moreover, the constructed indicator also could serve as an unobserved proxy for a monthly growth cycle. A further analysis is also conducted to reveal whether the SSA based approach can be considered as an alternative to parametric filtering methods by providing results of common cycle extraction using Unobserved component model alternatives.

Mestrado em Econometria Aplicada e Previsão
This study discusses four commonly used optimal approximations to the infinite order moving average filter that ideally extracts from a time series fluctuations within a specified range of periodicities. Based on our findings, we use two of those approximations in the estimation of two macroeconomic signals: business cycle fluctuations and medium to long run component of output growth rate. This study dis-tinguishes itself from related literature by showing how to successfully incorporate in the multivariate band-pass approximations factors estimated from a large panel of time series. As illustration, we apply these approximations to U.S. data. We evaluate the real-time performance of the indicators and provide forecasting comparisons. The results suggest that the multivariate indica¬tor outperforms the competing univariate indicator across all different settings considered. Moreover, multivariate methods that target smooth growth are useful to forecast quarterly GDP growth rate at short-term and to forecast yearly GDP growth.
Este estudo discute quatro aproximações óptimas ao filtro de medias moveis infinitas que idealmente isola de uma serie temporal flutuações compreendidas num determinado intervalo de periodicidades. De acordo com as nossas conclusões, utilizamos duas dessas aproximações na estimaçao de dois sinais macroeconómicos: flutuacoes de ciclo economico no produto e a componente de medio e longo prazo da taxa de crescimento do produto. Este estudo distingue-se da literatura corrente ao mostrar como integrar nas aproximacoes do filtro banda multivariado factores estimados a partir de um largo painel de sóeries temporais. Como ilustracao, aplicamos estas aproximacoes a dados dos E.U.A.. Avaliamos o desempenho dos in¬dicadores em tempo real e apresentamos comparacoes em termos de previsao. Os resultados sugerem que o indicador multivariado tem um desempenho claramente superior ao do indicador univariado em todos os cenóarios considerados. Adicionalmente, os móetodos multivariados que aproximam o crescimento alisado sao úteis na previsao da taxa de crescimento trimestral do PIB a curto prazo e para previsao do crescimento anual do PIB.

In parametrized continuous state-space models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling step which drastically reduces the variance of the estimates also introduces discontinuities in the particles that are selected across filters when the parameters change. When the state variables are univariate, a method exists that gives an estimator of the log-likelihood that is continuous in the parameters. We present a non-trivial generalization of this method using tree-based o(N²) (and as low as O(N log N)) resampling schemes that induce significant correlation amongst the selected particles across filters. In turn, this reduces the variance of the difference between the likelihood evaluated for different values of the parameters and the resulting estimator is considerably smoother than naively running the filters with common random numbers. Importantly, in practice our methods require only a change to the resample operation in the SMC framework without the addition of any extra parameters and can therefore be used for any application in which particle filters are already used. In addition, excepting the optional use of interpolation in the schemes, there are no regularity conditions for their use although certain conditions make them more advantageous. In this thesis, we first introduce the relevant aspects of the SMC methodology to the task of likelihood estimation in continuous state-space models and present an overview of work related to the task of smooth likelihood estimation. Following this, we introduce theoretically correct resampling schemes that cannot be implemented and the practical tree-based resampling schemes that were developed instead. After presenting the performance of our schemes in various applications, we show that two of the schemes are asymptotically consistent with the theoretically correct but unimplementable methods introduced earlier. Finally, we conclude the thesis with a discussion.

O biodiesel tem sido amplamente utilizado como uma fonte de energia renovável, que contribui para a diminuição de demanda por diesel mineral. Portanto, existem várias propriedades que devem ser monitoradas, a fim de produzir e distribuir biodiesel com a qualidade exigida. Neste trabalho, as propriedades físicas do biodiesel, tais como massa específica, índice de refração e ponto de entupimento de filtro a frio foram medidas e associadas a espectrometria no infravermelho próximo (NIR) e espectrometria no infravermelho médio (Mid-IR) utilizando ferramentas quimiométricas. Os métodos de regressão por mínimos quadrados parciais (PLS), regressão de mínimos quadrados parciais por intervalos (iPLS), e regressão por máquinas de vetor de suporte (SVM) com seleção de variáveis por Algoritmo Genético (GA) foram utilizadas para modelar as propriedades mencionadas. As amostras de biodiesel foram sintetizadas a partir de diferentes fontes, tais como canola, girassol, milho e soja. Amostras adicionais de biodiesel foram adquiridas de um fornecedor da região sul do Brasil. Em primeiro lugar, o pré-processamento de correção de linha de base foi usado para normalizar os dados espectrais de NIR, seguidos de outros tipos de pré-processamentos que foram aplicados, tais como centralização dos dados na média, 1 derivada e variação de padrão normal. O melhor resultado para a previsão do ponto de entupimento de filtro a frio foi utilizando os espectros de Mid-IR e o método de regressão GA-SVM, com alto coeficiente de determinação da previsão, R2Pred=0,96 e baixo valor da Raiz Quadrada do Erro Médio Quadrático da previsão, RMSEP (C)= 0,6. Para o modelo de previsão da massa específica, o melhor resultado foi obtido utilizando os espectros de Mid-IR e regressão por PLS, com R2Pred=0,98 e RMSEP (g/cm3)= 0,0002. Quanto ao modelo de previsão para o índice de refração, o melhor resultado foi obtido utilizando os espectros de Mid-IR e regressão por PLS, com excelente R2Pred=0,98 e RMSEP= 0,0001. Para esses conjuntos de dados, o PLS e o SVM demonstraram sua robustez, apresentando-se como ferramentas úteis para a previsão das propriedades do biodiesel estudadas
Biodiesel has been widely used as a renewable energy source which contributes to the mineral diesel decrease demand. Therefore, there are several properties that must be monitored in order to produce and distribute biodiesel with the required quality. In this work, the biodiesel physical properties such as specific mass, refractive index and cold filter plugging point were measured and associated with near infrared spectroscopy (NIR) and mid-Infrared spectroscopy (mid-IR) spectra using chemometric tools. The Partial Least Squares Regression (PLS), Interval Partial Least Squares Regression (iPLS), and Support Vector Machines Regression (SVM) with variable selection by Genetic Algorithm (GA) methods were used to model the aforementioned properties. The biodiesel samples were synthesized from different sources such as canola, sunflower, corn, and soybean. Additional biodiesel samples were purchased from a Brazil South Region supplier. Firstly, the preprocessing baseline correction was used to normalize the NIR spectral data, following others preprocessing types were applied in such as the mean center, the first derivative and standard normal variate. The best result for predicting the cold filter plugging point was using Mid-IR spectra and GA-SVM regression method, with high coefficient determination of prediction, R2Pred = 0.94 and low value of the Root Mean Square Error of Prediction, RMSEP (C) = 0.7. For the specific mass prediction model, the best result was obtained using the Mid-IR spectrums and PLS regression, with the R2Pred = 0.98 and RMSEP (g/cm3) = 0.0002. As for a prediction model for the refractive index, the best result was obtained using the Mid-IR spectrums and PLS regression, with the R2Pred = 0.98 and RMSEP = 0.0001. For these datasets, the PLS and SVM models demonstrated theirs robustness, presenting themselves as useful tools for the biodiesel properties prediction studied

Identifying parameters for state-space models in high dimensioned cases requires a complex methodology. We offer an example of application for hedonic prices and the hyper-parameter estimation for dynamic supply chains. An algorithm is created based on the Kalman filter-smoother and Expectation-Maximization procerures. Stopping rules for the algorithm are analyzed and compared. We detected the best stopping rule for our environment. In this way, the hedonic prices estimated can be used for any decision process. The thesis point to an application in forecast analysis for product prices. Accurate forecasting of market price developments is essential in achieving superior market performance. Especially in oligopolistic markets for durable consumer products a robust understanding of selling prices is important, as it drives pricing behavior as well as procurement, inventory and production decisions. Moreover, a supply chain perspective is indispensable for pricing forecasts since companies not only compete for product sales but also for limited resources. The thesis explores the use of dynamic multivariate hedonics-based pricing models that explicitly model selling prices with the market valuation of constituting parts. The model is applied to TAC SCM, a supply-chain trading agent competition. To find unknown component prices series we apply the Kalman filter technique to smooth and forecast implicit prices using the EM algorithm. Finally, we present results of our analysis to establish the viability of this method.

The primate hand, a biomechanical structure with over twenty kinematic degrees of freedom, has an elaborate anatomical architecture. Although the hand requires complex, coordinated neural control, it endows its owner with an astonishing range of dexterous finger movements. Despite a century of research, however, the neural mechanisms that enable finger and grasping movements in primates are largely unknown. In this thesis, we investigate statistical models of finger movement that can provide insights into the mechanics of the hand, and that can have applications in neural-motor prostheses, enabling people with limb loss to regain natural function of the hands. There are many challenges associated with (1) the understanding and modeling of the kinematics of fingers, and (2) the mapping of intracortical neural recordings into motor commands that can be used to control a Brain-Machine Interface. These challenges include: potential nonlinearities; confounded sources of variation in experimental datasets; and dealing with high degrees of kinematic freedom. In this work we analyze kinematic and neural datasets from repeated-trial experiments of hand motion, with the following contributions: We identified static, nonlinear, low-dimensional representations of grasping finger motion, with accompanying evidence that these nonlinear representations are better than linear representations at predicting the type of object being grasped over the course of a reach-to-grasp movement. In addition, we show evidence of better encoding of these nonlinear (versus linear) representations in the firing of some neurons collected from the primary motor cortex of rhesus monkeys. A functional alignment of grasping trajectories, based on total kinetic energy, as a strategy to account for temporal variation and to exploit a repeated-trial experiment structure. An interpretable model for extracting dynamic synergies of finger motion, based on Gaussian Processes, that decomposes and reduces the dimensionality of variance in the dataset. We derive efficient algorithms for parameter estimation, show accurate reconstruction of grasping trajectories, and illustrate the interpretation of the model parameters. Sound evidence of single-neuron decoding of interpretable grasping events, plus insights about the amount of grasping information extractable from just a single neuron. The Laplace Gaussian Filter (LGF), a deterministic approximation to the posterior mean that is more accurate than Monte Carlo approximations for the same computational cost, and that in an off-line decoding task is more accurate than the standard Population Vector Algorithm.

Le traitement des images satellitaires est considéré comme l'un des domaines les plus intéressants dans les domaines de traitement d'images numériques. Les images satellitaires peuvent être dégradées pour plusieurs raisons, notamment les mouvements des satellites, les conditions météorologiques, la dispersion et d'autres facteurs. Plusieurs méthodes d'amélioration et de restauration des images satellitaires ont été étudiées et développées dans la littérature. Les travaux présentés dans cette thèse se concentrent sur la restauration des images satellitaires par des techniques de filtrage statistique non linéaire. Dans un premier temps, nous avons proposé une nouvelle méthode pour restaurer les images satellitaires en combinant les techniques de restauration aveugle et non aveugle. La raison de cette combinaison est d'exploiter les avantages de chaque technique utilisée. Dans un deuxième temps, de nouveaux algorithmes statistiques de restauration d'images basés sur les filtres non linéaires et l'estimation non paramétrique de densité multivariée ont été proposés. L'estimation non paramétrique de la densité à postériori est utilisée dans l'étape de ré-échantillonnage du filtre Bayésien bootstrap pour résoudre le problème de la perte de diversité dans le système de particules. Enfin, nous avons introduit une nouvelle méthode de la combinaison hybride pour la restauration des images basée sur la transformée en ondelettes discrète (TOD) et les algorithmes proposés à l'étape deux, et nos avons prouvé que les performances de la méthode combinée sont meilleures que les performances de l'approche TOD pour la réduction du bruit dans les images satellitaires dégradées
Satellite image processing is considered one of the more interesting areas in the fields of digital image processing. Satellite images are subject to be degraded due to several reasons, satellite movements, weather, scattering, and other factors. Several methods for satellite image enhancement and restoration have been studied and developed in the literature. The work presented in this thesis, is focused on satellite image restoration by nonlinear statistical filtering techniques. At the first step, we proposed a novel method to restore satellite images using a combination between blind and non-blind restoration techniques. The reason for this combination is to exploit the advantages of each technique used. In the second step, novel statistical image restoration algorithms based on nonlinear filters and the nonparametric multivariate density estimation have been proposed. The nonparametric multivariate density estimation of posterior density is used in the resampling step of the Bayesian bootstrap filter to resolve the problem of loss of diversity among the particles. Finally, we have introduced a new hybrid combination method for image restoration based on the discrete wavelet transform (DWT) and the proposed algorithms in step two, and, we have proved that the performance of the combined method is better than the performance of the DWT approach in the reduction of noise in degraded satellite images

A pronta detecção da ocorrência de falhas em sistemas de engenharia é de grande significância. Nas últimas quatro décadas a área de detecção de falhas tem feito grandes avanços, principalmente pela melhoria dos sistemas computacionais. Devido ao grande escopo da área de detecção de falhas e às dificuldades de soluções em tempo real, várias técnicas foram desenvolvidas ao longo dos anos. Este trabalho apresenta duas técnicas distintas de detecção de falhas, as inovações de um Filtro de Kalman e o cálculo da distância de Mahalanobis; estas são aplicadas a uma planta didática que representa o comportamento de um helicóptero com três graus de liberdade. Foram simuladas falhas abruptas e incipientes nos dois motores do helicóptero, além de perturbações abruptas e incipientes. As técnicas são implementadas de forma separada e num esquema híbrido; apresenta-se o desempenho destas tanto sozinhas quanto usadas em conjunto no esquema híbrido proposto. A técnica das inovações do Filtro de Kalman mostrou-se melhor em relação à rejeição aos distúrbios e o esquema híbrido proposto apresenta um desempenho superior na detecção das falhas, mas não tão bom na rejeição aos distúrbios. Como continuidade do trabalho é proposta a implementação de uma terceira técnica no esquema híbrido.

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Universidade Federal de Sao Carlos
Several studies cite the pollution of stormwater as equivalent and sometimes even superior to those found in the sewers. According to this premise and thinking about environmental issues, especially in the contamination of groundwater and the spread of waterborne diseases, the quality of rainwater has become an important focus of study. This work concerns the monitoring of an infiltration system consisting of grass filter, trench and infiltration trench, built in full scale on the campus of University Federal of São Carlos - UFSCar, located in São Carlos - SP, from the assessment water quality of runoff directly before and after passing through the proposed infiltration system, parallel to monitoring the quality of rain water, through analysis of the physico-chemical and bacteriological established in legislation and international experiences, compared the conditions of the study area, and exploratory data analysis by two chemometric techniques: Principal Component Analysis (PCA) and Hierarchical Cluster Analysis (HCA). According to the analysis of the results variation, especially the quality of atmospheric water and quality of direct runoff results were obtained as concentrations low significantly to parameters Turbidity, Color, ST, STD, Nitrate, Nitrite, Ammonia nitrogen, Sulfate, Chloride, Cadmium, Copper, Lead and Zinc in the water samples analyzed directly from rain, compared with previous studies in the literature and standards and legislation existing about water resources, and the efficiency of the infiltration trench in the removal of Zinc (90,89%), Cooper (88,31%), Electrical Conductivity (31,40%), Ammonial nitrogen (24,32%) and Chloride (5,88%) compared with the predial direct runnof in the channel. With regard to PCA analysis, proves the characteristics between samples according to the conditions of sampling (day, month, place and time) and analysed variables, dividing into groups of samples and contributing to the extraction and interpretation of information unlikely to be viewed directly in the data matrix. The analysis complemented by HCA analysis by PCA.
Diversos estudos citam a poluição das águas pluviais como equivalente e, às vezes, até superior àquelas presentes nos esgotos. De acordo com tal premissa e pensando na problemática ambiental, especialmente na contaminação de águas subterrâneas e disseminação de doenças por veiculação hídrica, a qualidade da água pluvial tornou-se um foco importante de estudo. Este trabalho visa o monitoramento de um sistema de infiltração constituído de filtro de grama, vala e trincheira de infiltração, construído em escala real no campus da Universidade Federal de São Carlos UFSCar, localizado na cidade de São Carlos SP, a partir da avaliação da qualidade da água do escoamento superficial direto predial antes e após passar pelo sistema de infiltração proposto, paralelo ao monitoramento da qualidade da água de chuva, mediante análise de parâmetros físico-químicos e microbiológicos estabelecidos em legislação e em experiências nacionais e internacionais, comparadas às condições da área de estudo, e análise exploratória dos dados por duas técnicas quimiométricas: Análise de Componentes Principais (PCA) e Análise Hierárquica de Agrupamentos (HCA). De acordo com a análise da variação dos resultados obtidos, sobretudo, da qualidade da água atmosférica e da qualidade da água do escoamento superficial direto, obtiveram-se como resultados concentrações sensivelmente menores dos parâmetros Turbidez, Cor, ST, STD, Nitrato, Nitrito, Nitrogênio Amoniacal, Sulfato, Cloreto, Cádmio, Cobre, Chumbo e Zinco analisados nas amostras de água diretamente da chuva, comparando-se com estudos precedentes na literatura e normas e legislações de recursos hídricos vigentes. O sistema filtro-vala-trincheira de infiltração removeu os seguintes parâmetros analisados, comparando-se com a água do escoamento superficial direto predial no canal: Zinco (90,89%), Cobre (88,31%), Condutividade Elétrica (31,40%), Nitrogênio Amoniacal (24,32%) e Cloreto (5,88%). Com relação às análises por PCA, evidenciaram-se as características entre as amostras de acordo com as condições de amostragem (dia, mês, local e tempo) e variáveis analisadas, dividindo em grupos de amostras e contribuindo para a extração e interpretação das informações que dificilmente seriam visualizadas diretamente na matriz de dados. As análises por HCA complementaram as análises por PCA.

Electroencephalographic data recorded on the human scalp can be modeled as a linear mixture of underlying dipolar source generators. The characterization of such generators is the aim of several families of signal processing methods. In this HDR we consider in several details three of such families, namely 1) EEG distributed inverse solutions, 2) diagonalization methods, including spatial filtering and blind source separation and 3) Riemannian geometry. We highlight our contributions in each of this family, we describe algorithms reporting all necessary information to make purposeful use of these methods and we give numerous examples with real data pertaining to our published studies. Traditionally only the single-subject scenario is considered; here we consider in addition the extension of some methods to the simultaneous multi-subject recording scenario. This HDR can be seen as an handbook for EEG source analysis. It will be particularly useful to students and other colleagues approaching the field.

碩士
國立高雄第一科技大學
環境與安全衛生工程研究所
103
Because of receiving lots of municipal, industrial and livestock wastewater, the An-Shun Drainage, a tributary of the Yan-Shoei Creek in southern Taiwan, is often severely polluted. For water pollution control, the riverwater of An-Shun Drainage is pumped and treated with contact filters before flowing into the Yan-Shoei Creek. The purposes of this study are to apply the multivariate statistical analysis to evaluate the significant parameters of contact filter for treating river water and to investigate treatability of this contact filter for various input loadings of pollutants in the river water. In this study, the parameters (pH, DO, SS, COD, BOD and temperature) with high factor loading were investigated by the factor analysis during the multivariate statistical analysis. Based on the results of multivariate statistical analysis, the primary significant parameters, called as organic pollution factors, were found to be pH, BOD and COD. Besides, SS and COD, called as climate factors, belonged to the secondary significant parameters. After the evaluation of significant parameters by multivariate analysis, the situations of low efficiency of contact filter were obtained from the further linear regression of influent and effluent parameters.

Exponential smoothing algorithms are very attractive for the practical world such as in industry. When considering bivariate exponential smoothing methods, in addition to the properties of univariate methods, additional properties give insight to relationships between the two components of a process, and also to the overall structure of the model. It is important to study these properties, but even with the merits the bivariate exponential smoothing algorithms have, exponential smoothing algorithms are nonstatistical/nonstochastic and to study the properties within exponential smoothing may be worthless. As an alternative approach, the (bivariate) ARIMA and the structural models which are classes of statistical models, are shown to generalize the exponential smoothing algorithms. We study these properties within these classes as they will have implications on exponential smoothing algorithms. Forecast properties are studied using the state space model and the Kalman filter. Comparison of ARIMA and structural model completes the study.
Mathematical Sciences
M. Sc. (Statistics)