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)

過去雖有文獻探討國內房地產市場泡沫化問題，卻僅從租金收益的單一角度衡量房價基值，對於自有住宅比例較高的台灣而言，家戶所得不僅代表購屋者的負擔能力，更是構成房價基值的重要因素。有鑑於此，本研究分別從租金收益及家戶所得兩者不同角度下，透過資產市場現值模型，分別建立房價基值模型分析泡沫化現象。此外，過去文獻僅從檢定價格波動穩定性與否或將殘差項視為泡沫來研究泡沫化問題，然泡沫為不可觀察之變數，故本文使用具有可估計不可觀察變數特質的狀態空間模型（STATE-SPACE MODEL），推估泡沫價格，分析在不同時期下泡沫的規模大小。 在實證方面，本研究使用台北市1973Q2至2008Q1共140筆住宅價格資料，發現由租金與所得所計算之房價泡沫規模略為一致。在1988~1990年房市泡沫化時期，所得推估之泡沫規模達到高峰，泡沫價格占市價約47%；而由租金面亦計算出泡沫價格占市價約54%的高比例。而在2008年房價持續上漲的情況下，兩者泡沫價格亦呈現相同上升之走勢，泡沫價格近市價38%，租金推估泡沫價格占市價27%；此結果表示出目前房市有泡沫化之跡象，現階段欲購屋自住者不宜進入市場，宜審慎等待時機。而本文認為房價所得比或是房價租金比皆是作為衡量台北市房地產市場泡沫化現象之重要指標，另外就總體因素分析而言，房價上漲率、貨幣供給額、貸款利率與大盤股價指數皆為影響泡沫之重要因素，且經由實證發現所得所推估之泡沫價格較具有市場代表性。 / The past literatures about Taipei housing price bubble has only been measured the fundamental price by rent. However, the housing owner ratio is so high in Taiwan that housing income is not only regarded as affordability but also an important fundamental factor of housing price. According to the above, we focus on different fundamental models that define market fundamental price to analyses the bubble price from expected present value of both rent and permanent housing income. On the other hand, different from lots of literature testing the housing price volatility or residual to measure bubble prices, because housing bubble is an unobservable variable, we apply State-Space Model which is good for testing an invisible factor to estimate bubble in the housing markets of Taipei. This paper tries to test whether there was a housing price bubble using Taipei housing price index ranged from 1973Q1 to 2008Q1. The findings indicate that there appeared bubble ratio from 1988 to 1990, 47% of the housing price based on housing income and 54 % of the housing price based on rent. In 2008 when housing price continually keeps rising, bubble price ratios are close to 38% and 27% respectively. Those results show that Taipei seems to have sign of a bubble in this moment and housing buyers should concern it with more caution. Secondly, both price-income ratio and price-rent ratio are good indicators to measure housing bubble prices. Beside, we find macro economic factors change, such as the growth rate of housing price, M2, mortgage rate, and stock price index, are important to influence the size of housing bubble. Thirdly, bubble price estimated by housing income has a better performance than rent.

本研究透過聯合系統與獨特風險綜合評估違約的強度，假設市場上經濟變數或資訊影響系統之違約強度，然若直接考慮所有經濟變數到模型中將可能會有共線性或維度過高之疑慮，因此透過狀態空間模型來設定狀態變數以及經濟變數之關係並將萃取三大狀態變數分別用以描述市場實質活動面、通貨膨脹以及信用環境。另外，將透過結構式模型來計算獨特性風險大小，當個別潛在的變數低於一定數值將導致個別的違約事件發生。而因布朗運動可能無法描述或校準市場上違約之鋒態以及偏態，將進一步考慮Variance Gamma過程用以更準確描述真實違約狀況。最後透過結合以上兩個風險綜合評估下，考慮一個聯合違約模型來評價信用違約交換之信用價差。 / Systematic and idiosyncratic risks are supposed to jointly trigger the default events. This paper identifies three fundamental risks to capture the systematic movement: real activity, inflation, and credit environment. Since most macroeconomic variables fluctuate together, the state-space model is imposed to extract the three variables from macroeconomic data series. In the idiosyncratic part, the structural model is applied. That is, idiosyncratic default is triggered by the crossing of a barrier. For improvement of the underlying lognormal distribution, we assume the process for the potential variable of the firm follows a Variance Gamma process, sufficient dimensions of which can fit the skewed and leptokurtic distributions. Under the specific setting of combinations of the two risks (the so-called joint default model), we price credit default swaps.

The discipline of component-based modeling and simulation offers promising gains including reduction in development cost, time, and system complexity. This paradigm is very profitable as it promotes the use and reuse of modular components and is auspicious for effective development of complex simulations. It however is confronted by a series of research challenges when it comes to actually practice this methodology. One of such important issue is Composability verification. In modeling and simulation (M&amp;S), composability is the capability to select and assemble components in various combinations to satisfy specific user requirements. Therefore to ensure the correctness of a composed model, it is verified with respect to its requirements specifications.There are different approaches and existing component modeling frameworks that support composability however in our observation most of the component modeling frameworks possess none or weak built-in support for the composability verification. One such framework is Base Object Model (BOM) which fundamentally poses a satisfactory potential for effective model composability and reuse. However it falls short of required semantics, necessary modeling characteristics and built-in evaluation techniques, which are essential for modeling complex system behavior and reasoning about the validity of the composability at different levels.In this thesis a comprehensive verification framework is proposed to contend with some important issues in composability verification and a verification process is suggested to verify composability of different kinds of systems models, such as reactive, real-time and probabilistic systems. With an assumption that all these systems are concurrent in nature in which different composed components interact with each other simultaneously, the requirements for the extensive techniques for the structural and behavioral analysis becomes increasingly challenging. The proposed verification framework provides methods, techniques and tool support for verifying composability at its different levels. These levels are defined as foundations of a consistent model composability. Each level is discussed in detail and an approach is presented to verify composability at that level. In particular we focus on theDynamic-Semantic Composability level due to its significance in the overallcomposability correctness and also due to the level of difficulty it poses in theprocess. In order to verify composability at this level we investigate the application ofthree different approaches namely (i) Petri Nets based Algebraic Analysis (ii) ColoredPetri Nets (CPN) based State-space Analysis and (iii) Communicating SequentialProcesses based Model Checking. All the three approaches attack the problem ofverifying dynamic-semantic composability in different ways however they all sharethe same aim i.e., to confirm the correctness of a composed model with respect to itsrequirement specifications. Beside the operative integration of these approaches inour framework, we also contributed in the improvement of each approach foreffective applicability in the composability verification. Such as applying algorithmsfor automating Petri Net algebraic computations, introducing a state-space reductiontechnique in CPN based state-space analysis, and introducing function libraries toperform verification tasks and help the molder with ease of use during thecomposability verification. We also provide detailed examples of using each approachwith different models to explain the verification process and their functionality.Lastly we provide a comparison of these approaches and suggest guidelines forchoosing the right one based on the nature of the model and the availableinformation. With a right choice of an approach and following the guidelines of ourcomponent-based M&amp;S life-cycle a modeler can easily construct and verify BOMbased composed models with respect to its requirement specifications. / <p>Overseas Scholarship for PHD in selected Studies Phase II Batch I</p><p>Higher Education Commision of Pakistan.</p><p>QC 20130224</p>

Dans cette thèse, plusieurs concepts importants liés à la théorie de la réalisation des modèles linéaires à paramètres variants (LPV) sont étudiés.Tout d’abord, nous abordons le problème de l’identifiabilité des modèles LPV affines (ALPV). Une nouvelle condition suffisante et nécessaire est introduite afin de garantir l’identifiabilité structurelle pour les paramétrages ALPV. L’identifiabilité de cette classe de paramétrages est liée à l’absence d’isomorphismes liant deux représentations d’état LPV lorsque deux modèles LPV correspondant à différentes valeurs des variables de séquencement sont considérés. Nous présentons ainsi une condition suffisante et nécessaire pour l’identifiabilité structurelle locale, et une condition suffisante pour l’identifiabilité structurelle (globale) qui sont toutes deux fonction du rang d’une matrice définie par l’utilisateur. Ces dernières conditions permettent la vérification de l’identifiabilité structurelle des modèles ALPV.Ensuite, étant donné que les techniques d’identification dites locales sont parfois inévitables, nous fournissons une expression analytique de la borne supérieure de l’erreur de comportements entrées-sorties de deux modèles LPV équivalents localement. Cette erreur se révèle être une fonction de (i) la vitesse de changement du signal de séquencement et (ii) l’écart entre les bases cohérentes de deux modèles LPV. En particulier, la différence entre les sorties des deux modèles peut être arbitrairement réduite en choisissant un signal de séquencement qui varie assez lentement.Enfin, nous présentons et étudions des propriétés importantes de la transformation des représentations d’état ALPV en Représentations Linéaires Fractionnelles (LFR). Plus précisément, nous montrons que (i) les représentations ALPV minimales conduisent à des LFR minimales, et vice versa, (ii) le comportement entrée-sortie de la représentation ALPV détermine de manière unique le comportement entrée-sortie de la LFR résultante, (iii) les modèles ALPV structurellement identifiables fournissent des LFRs structurellement identifiables et vice versa. Nous caractérisons ensuite les LFRs qui correspondent á des modèles ALPV équivalents basés sur leurs applications entrées-sorties. Comme illustré tout au long du manuscrit, ces résultats ont des conséquences importantes pour l’identification et la commande des systèmes LPV. / In this thesis, important concepts related to the identification of Linear Parameter-Varying (LPV) systems are studied.First, we tackle the problem of identifiability of Affine-LPV (ALPV) state-space parametrizations. A new sufficient and necessary condition is introduced in order to guarantee the structural identifiability for ALPV parameterizations. The identifiability of this class of parameterizations is related to the lack of state-space isomorphisms between any two models corresponding to different scheduling parameter values. In addition, we present a sufficient and necessary condition for local structural identifiability, and a sufficient condition for (global) structural identifiability which are both based on the rank of a model-based matrix. These latter conditions allow systematic verification of structural identifiability of ALPV models. Moreover, since local identification techniques are inevitable in certain applications, it is thus a priority to study the discrepancy between different LPV models obtained using different local techniques. We provide an analytic error bound on the difference between the input-output behaviors of any two LPV models which are frozen equivalent. This error bound turns out to be a function of both (i) the speed of the change of the scheduling signal and (ii) the discrepancy between the coherent bases of the two LPV models. In particular, the difference between the outputs of the two models can be made arbitrarily small by choosing a scheduling signal which changes slowly enough.Finally, we introduce and study important properties of the transformation of ALPV statespace representations into Linear Fractional Representations (LFRs). More precisely, we show that (i) state minimal ALPV representations yield minimal LFRs, and vice versa, (ii) the inputoutput behavior of the ALPV representation determines uniquely the input-output behavior of theresulting LFR, (iii) structurally identifiable ALPV models yield structurally identifiable LFRs, and vice versa. We then characterize LFRs which correspond to equivalent ALPV models based on their input-output maps. As illustrated all along the manuscript, these results have important consequences for identification and control of LPV systems.

[pt] Esta Dissertação procura, sob um enfoque freqüentista, discutir tecnologias para que se imponham restrições no processo de estimação de componentes não observáveis associadas a um modelo em Espaço de Estado (EE) arbitrário. O escopo do texto abrange desde procedimentos propostos pioneiramente por Howard Doran para restrições de igualdade, lineares e/ou não lineares, invariantes ou variantes no tempo, em modelos em EE lineares, até a adoção e o ajuste de estruturas mais delicadas, como os modelos em EE não lineares. Entende-se que estes últimos se constituem em uma alternativa relevante, caso seja requerida, por exemplo, a imposição de restrições de desigualdade. Técnicas e estratégias de implementação são apresentadas, debatidas e comparadas, incluindo-se também o processo de estimação de parâmetros desconhecidos e a questão de diagnósticos. Ao final, são apresentados exercícios empíricos com base nas tecnologias discutidas. Os modelos propostos para esta ilustração visam à realização da análise dinâmica de estilo baseado no retorno para carteiras de investimento brasileiras (a versão estática desses modelos fora introduzida por William Sharpe, para carteiras norte-americanas), os quais devem, eventualmente, abranger dois tipos de restrições nas componentes de interesse, quais sejam, um de igualdade e outro de desigualdade. / [en] This Dissertation aims, in a frequentist way, to discuss technologies for imposing restrictions in non-observable components associated with an arbitrary State Space (SS) model. The text scope ranges from procedures proposed originally by Howard Doran for equality, linear or non- linear, time invariant or time varying restrictions in a linear SS model, to adoption and estimation of more complicated structures like non-linear SS models. It is understood that these last ones are a relevant alternative, in cases of, for instance, inequality restrictions requirement. Implementation techniques and strategies are given, debated and compared, also including unknown parameters estimation and diagnostics analysis. At the end, empirical exercises are presented based on discussed methodologies. The proposed models for this illustration aim at dynamic return based style analysis for Brazilian investment portfolios (the static version of these models had been introduced by William Sharpe, for American portfolios), which shall eventually satisfy two kinds of restrictions on components of interest, namely one of equality and other of inequality.

Nous considérions des modèles à espace d'état où les observations sont multicatégorielles et longitudinales, et l'état est décrit par des modèles du type CHARN. Nous estimons l'état au moyen des récursivités de Kalman généralisées. Celles-ci reposent sur l'application d'une variété de filtres particulaires et de l’algorithme EM. Nos résultats sont appliqués à l'estimation du trait latent en qualité de vie. Ce qui fournit une alternative et une généralisation des méthodes existantes dans la littérature. Ces résultats sont illustrés par des simulations numériques et une application aux données réelles sur la qualité de vie des femmes ayant subi une opération pour cause de cancer du sein / We consider state space models where the observations are multicategorical and longitudinal, and the state is described by CHARN models. We estimate the state by generalized Kalman recursions, which rely on a variety of particle filters and EM algorithm. Our results are applied to estimating the latent trait in quality of life, and this furnishes an alternative and a generalization of existing methods. These results are illustrated by numerical simulations and an application to real data in the quality of life of patients surged for breast cancer

Made available in DSpace on 2017-07-10T19:24:46Z (GMT). No. of bitstreams: 1 Marcio Paulo de Oliveira.pdf: 1960743 bytes, checksum: 7438fe00d388d47b01b27d6cfdf2e229 (MD5) Previous issue date: 2010-02-04 / The knowledge about soil and plant attributes is important for the improvement of agricultural management. Intense tillage activities may induce not only alterations in the soil attributes but also decrease in productivity. Studies directed to the soil and plant spatial variability identification and the relations amid these variables are tools for agriculture, with the potential to increase productivity. The data set for this study was sampled in a Rhodic Acrudox soil, at a farmland that has been being cultivated for over five years under no-tillage system, with soybean and wheat in crop succession. At 252 m long transect, 84 points were demarcated, with 3 m of spacing between each of them. The relations between soybean productivity and soil water content, micro, macro and total porosity, soil density and soil resistance to penetration at 0,0-0,10 m and 0,10-0,20 m deep layers, were evaluated, as well as the respective variabilities. The relations between soybean productivity and soil attributes were determined using simple and cross correlations, followed by the state space models determinations, compared to linear and multiple regression models. The results have shown that the soybean productivity and soil mechanical resistance variables presented not only autocorrelation structure but also crosscorrelation structure. The state space models, relating to the soybean productivity at a point i, with the same attribute at point i-1, at the two layers, were more efficient than the equivalent models in simple and multiple regression. With geoestatistics, the spatial dependence structure was determined with envelopes and models for the semivariograms, allowing identification and classification of the spatial dependence for the variables under study. The thematic maps were obtained with simple kriging and indicated the soil attributes behavior, related to the soybean productivity. / O conhecimento do comportamento dos atributos do solo e da planta é importante para a melhoria das práticas agrícolas. A intensa atividade de cultivo pode provocar modificações dos atributos do solo e reduzir a produtividade de uma cultura em determinada região. Os estudos que visam identificar a variabilidade espacial dos atributos do solo e da planta e a relação entre esses atributos surgem como um recurso para a agricultura, podendo ser utilizados para realização de um manejo adequado dos recursos disponíveis, ampliando a produtividade e preservando o meioambiente. Os dados para a realização deste estudo foram obtidos em um Latossolo Vermelho distroférrico, em uma área cultivada há mais de cinco anos com alternância entre as culturas de soja e trigo, com o sistema de plantio direto. Em uma transeção de 252 m de comprimento foram demarcados 84 elementos amostrais, espaçados de 3 m entre si. As relações da produtividade da soja com os seguintes atributos físicos e hídricos do solo: teor de água no solo, microporosidade, macroporosidade e porosidade total do solo, densidade do solo e resistência mecânica do solo à penetração, nas camadas 0,0-0,10 m e 0,10-0,20 m, foram avaliadas bem como a variabilidade espacial desses atributos. A relação entre a produtividade da soja e os atributos do solo foi determinada através das correlações simples e cruzada entre os elementos amostrais de cada atributo, seguida da estimação dos modelos em espaço de estados, comparados aos modelos equivalentes em regressão linear múltipla. Os resultados mostraram que as variáveis produtividade da soja e resistência do solo a penetração apresentaram estrutura de autocorrelação e de correlação cruzada entre si. Os modelos estimados em espaço de estados, relacionando a produtividade da soja em um ponto i com a produtividade da soja e resistência do solo a penetração nas duas camadas no ponto i -1 mostraram-se mais eficientes do que os modelos equivalentes estimados em regressão linear simples e múltipla. Por meio da geoestatística, a estrutura de dependência espacial foi avaliada por meio dos envelopes e modelos para os semivariogramas experimentais, permitindo identificar e classificar a dependência espacial das variáveis em estudo. Os mapas temáticos foram obtidos por meio de interpolação por krigagem ordinária e indicaram o comportamento dos atributos do solo ligadas a produtividade da soja.

Made available in DSpace on 2017-05-12T14:48:09Z (GMT). No. of bitstreams: 1 Marcio Paulo de Oliveira.pdf: 1960743 bytes, checksum: 7438fe00d388d47b01b27d6cfdf2e229 (MD5) Previous issue date: 2010-02-04 / The knowledge about soil and plant attributes is important for the improvement of agricultural management. Intense tillage activities may induce not only alterations in the soil attributes but also decrease in productivity. Studies directed to the soil and plant spatial variability identification and the relations amid these variables are tools for agriculture, with the potential to increase productivity. The data set for this study was sampled in a Rhodic Acrudox soil, at a farmland that has been being cultivated for over five years under no-tillage system, with soybean and wheat in crop succession. At 252 m long transect, 84 points were demarcated, with 3 m of spacing between each of them. The relations between soybean productivity and soil water content, micro, macro and total porosity, soil density and soil resistance to penetration at 0,0-0,10 m and 0,10-0,20 m deep layers, were evaluated, as well as the respective variabilities. The relations between soybean productivity and soil attributes were determined using simple and cross correlations, followed by the state space models determinations, compared to linear and multiple regression models. The results have shown that the soybean productivity and soil mechanical resistance variables presented not only autocorrelation structure but also crosscorrelation structure. The state space models, relating to the soybean productivity at a point i, with the same attribute at point i-1, at the two layers, were more efficient than the equivalent models in simple and multiple regression. With geoestatistics, the spatial dependence structure was determined with envelopes and models for the semivariograms, allowing identification and classification of the spatial dependence for the variables under study. The thematic maps were obtained with simple kriging and indicated the soil attributes behavior, related to the soybean productivity. / O conhecimento do comportamento dos atributos do solo e da planta é importante para a melhoria das práticas agrícolas. A intensa atividade de cultivo pode provocar modificações dos atributos do solo e reduzir a produtividade de uma cultura em determinada região. Os estudos que visam identificar a variabilidade espacial dos atributos do solo e da planta e a relação entre esses atributos surgem como um recurso para a agricultura, podendo ser utilizados para realização de um manejo adequado dos recursos disponíveis, ampliando a produtividade e preservando o meioambiente. Os dados para a realização deste estudo foram obtidos em um Latossolo Vermelho distroférrico, em uma área cultivada há mais de cinco anos com alternância entre as culturas de soja e trigo, com o sistema de plantio direto. Em uma transeção de 252 m de comprimento foram demarcados 84 elementos amostrais, espaçados de 3 m entre si. As relações da produtividade da soja com os seguintes atributos físicos e hídricos do solo: teor de água no solo, microporosidade, macroporosidade e porosidade total do solo, densidade do solo e resistência mecânica do solo à penetração, nas camadas 0,0-0,10 m e 0,10-0,20 m, foram avaliadas bem como a variabilidade espacial desses atributos. A relação entre a produtividade da soja e os atributos do solo foi determinada através das correlações simples e cruzada entre os elementos amostrais de cada atributo, seguida da estimação dos modelos em espaço de estados, comparados aos modelos equivalentes em regressão linear múltipla. Os resultados mostraram que as variáveis produtividade da soja e resistência do solo a penetração apresentaram estrutura de autocorrelação e de correlação cruzada entre si. Os modelos estimados em espaço de estados, relacionando a produtividade da soja em um ponto i com a produtividade da soja e resistência do solo a penetração nas duas camadas no ponto i -1 mostraram-se mais eficientes do que os modelos equivalentes estimados em regressão linear simples e múltipla. Por meio da geoestatística, a estrutura de dependência espacial foi avaliada por meio dos envelopes e modelos para os semivariogramas experimentais, permitindo identificar e classificar a dependência espacial das variáveis em estudo. Os mapas temáticos foram obtidos por meio de interpolação por krigagem ordinária e indicaram o comportamento dos atributos do solo ligadas a produtividade da soja.

長久以來,人類在萬物中獨具的高智慧特質吸引了無數的哲學家和科學家 投入對其研究,除了醫學的原因之外,由於人腦所具有卓越的辨識系統及學 習能力,為數不少的科學家們相信人腦存在許多最適化系統與設計,因此如 何模仿人類腦神經的組織與運作,一直是很多人努力及夢寐以求的.因此類 神經網路就是依據這些理念而在各研究領域上廣為發展與應用,其中本文 所探討的倒傳遞神經網路模型更是目前類神經網路模型中最具代表性,應 用最廣的模型.而結構性時間數列模型則是將可被觀察的變數分解成趨勢, 季節性,不規則性等不可被觀察項,故其對經濟意義的解釋是相當明當明顯 的,藉由狀態空間模式的轉換,我們將很容易地利用卡門濾器來作估計與預 測.而本文所欲探的重點在於比較有學習機能的倒傳遞神經網及可利用最 新的資訊更新之結構性時間數列何者之預測能利較佳,藉此瞭解二者之一 些特性.