Rozprawy doktorskie na temat „AR(1) model”

In the doctoral dissertation, we consider problems of testing and estimating changed segment with unknown starting position and duration of epidemic state in the autoregressive first-order model. The proposed tests are based on partial sums of model residuals and model-parameter partial-estimator polygonal line processes. We derive asymptotic results for these processes in Holder spaces. The behavior of test statistics under the null hypothesis of no change and alternative is provided. Empirical power analysis has shown that tests are more powerful when absolute values of model parameter are quite large or autoregressive process changes from a stationary state to a nonstationary one. We prove the consistency of the least square changed-segment estimators and provide their convergence rates.
Disertacijoje nagrinėjamas pirmos eilės autoregresinio modelio pasikeitusio segmento testavimo ir vertinimo uždavinys. Aprašomo modelio epideminio pasikeitimo pradžia ir ilgis nėra žinomi. Pasiūlyti kriterijai pasikeitusio segmento testavimui, kurie pagrįsti modelio paklaidų įvertinių dalinių sumų ir modelio parametro dalinių įvertinių laužčių procesais. Šiems procesams gautos ribinės teoremos Hiolderio erdvėse. Nurodomas testų statistikų ribinis elgesys esant teisingai nulinei ir alternatyviajai hipotezėms. Iš empirinio kriterijų galios tyrimo rezultatų matyti, kad pasiūlytų testų galia didžiausia aptinkant pasikeitimus iš stacionarios būklės į nestacionarią arba esant artimoms vienetui modelio parametro reikšmėms. Taip pat įrodoma, kad mažiausių kvadratų metodu gauti pasikeitusio segmento pradžios ir ilgio įverčiai bei autoregresinio modelio su pasikeitusiu segmentu parametrų įverčiai yra suderintieji bei pateikiamas jų konvergavimo greitis.

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We considered a Bayesian analysis of first order autoregressive, AR(1), panel data model, using exact likelihood function, comparative analysis of prior distributions and predictive distributions of future observations. The methodology efficiency was evaluated by a simulation study using three prior, which were related to different Generalized Beta distributions: symmetric, asymmetric and flat prior. We applied the proposed methodology to microarray time series real data of HeLa cells. The forecast of gene expression in one future time showed high efficiency.
Considerou-se uma análise Bayesiana do modelo auto- regressivo de primeira ordem, AR(1), para dados em painel, de forma a utilizar a função de verossimilhança exata, a análise de comparação de distribuições a priori e a obtenção de distribuições preditivas de dados futuros. A eficiência da metodologia proposta foi avaliada mediante um estudo de simulação, no qual a distribuição Beta Generalizada foi usada para representar 3 diferentes prioris: simétrica, assimétrica e constante. Realizou-se uma aplicação em dados reais de expressão gênica temporal de células HeLa gerados por microarray. Os resultados mostraram alta eficiência na previsão da expressão gênica para um instante futuro.

Disertacijoje nagrinėjamas pirmos eilės autoregresinio modelio pasikeitusio segmento testavimo ir vertinimo uždavinys. Aprašomo modelio epideminio pasikeitimo pradžia ir ilgis nėra žinomi. Pasiūlyti kriterijai pasikeitusio segmento testavimui, kurie pagrįsti modelio paklaidų įvertinių dalinių sumų ir modelio parametro dalinių įvertinių laužčių procesais. Šiems procesams gautos ribinės teoremos Hiolderio erdvėse. Nurodomas testų statistikų ribinis elgesys esant teisingai nulinei ir alternatyviajai hipotezėms. Iš empirinio kriterijų galios tyrimo rezultatų matyti, kad pasiūlytų testų galia didžiausia aptinkant pasikeitimus iš stacionarios būklės į nestacionarią arba esant artimoms vienetui modelio parametro reikšmėms. Taip pat įrodoma, kad mažiausių kvadratų metodu gauti pasikeitusio segmento pradžios ir ilgio įverčiai bei autoregresinio modelio su pasikeitusiu segmentu parametrų įverčiai yra suderintieji bei pateikiamas jų konvergavimo greitis.
In the doctoral dissertation, we consider problems of testing and estimating changed segment with unknown starting position and duration of epidemic state in the autoregressive first-order model. The proposed tests are based on partial sums of model residuals and model-parameter partial-estimator polygonal line processes. We derive asymptotic results for these processes in Holder spaces. The behavior of test statistics under the null hypothesis of no change and alternative is provided. Empirical power analysis has shown that tests are more powerful when absolute values of model parameter are quite large or autoregressive process changes from a stationary state to a nonstationary one. We prove the consistency of the least square changed-segment estimators and provide their convergence rates.

Prostate cancer is the most commonly diagnosed non-skin cancer in men and the second leading cause of cancer death in the United States. Prostate cancer, like many cancers, is a disease that generally requires a long period of time to develop and grow before it becomes detectable. This long period of latency makes prostate cancer a candidate for dietary chemoprevention. Soy and selenium (Se), are associated with a decreased risk of prostate cancer. We previously showed that high dietary intake of selenium (Se) and soy isoflavones decreased the expression of the androgen receptor (AR) and AR-regulated genes in the prostates of healthy rats. In this study we hypothesized that the downregulation of AR and AR-regulated genes would inhibit tumorigenesis in the transgenic adenocarcinoma of the mouse prostate (TRAMP) mouse. Mice were fed one of two stock diets with or without a supplement of Se in a 2 X 2 factorial design. The stock diets provided high or low dietary isoflavones. Mice were exposed to the diets from conception and sacrificed at 18 or 24 weeks of age. Prostate histopathology, urogenital tract (UGT) weight, serum IGF-1 levels, and the expression of AR and AR-regulated genes in the dorsolateral prostate was examined using quantitative PCR and Western blotting. Urogenital tract (UGT) weight was reduced compared to control in all dietary groups containing high Se, isoflavones, or both at 24 weeks (p<0.005). Dietary isoflavones delayed tumor progression and downregulated protein levels of AR, AR-regulated genes, and upregulated the protective FOXO1 and FOXO3a transcription factors. High dietary isoflavones also decreased the phosphorylation of the IGF-1R. The only main effect of Se was the upregulation of AKR1C14 the enzyme that deactivates 5&aplha;-DHT.This study identifies a previously unknown effect of isoflavones in the upregulation of FOXO expression and confirms previous studies of isoflavones' anticancer effects. Further research is needed to find a protective dose or form of Se and to elucidate the mechanism of isoflavones.

In this thesis, we focus on a forecasting tool, Martingale Model of Forecast Evolution (MMFE), to model the evolution of forecasts in a production-distribution system. Additive form is performed to represent the evolution process. Variance-Covariance (VCV) matrix is defined to express the forecast updates. The selected demand pattern is stationary and it is normally distributed. It follows an Autoregressive Order-1 (AR(1)) model. Two forecasting procedures are selected to compare the MMFE with. These are MA (Moving average) and ES (Exponential smoothing) methods. A production-distribution model is constructed to represent a two-stage supply chain environment. The performance measures considered in the analyses are the total costs, fill rates and forecast accuracy observed in the operation of the production-distribution system. The goal is to demonstrate the importance of good forecasting in supply chain environments.

This paper analyzes if neighborhood income inequality has an effect on informal regulation of environmental quality, using census tract-level data on industrial air pollution exposure from EPA´s Risk Screening Environmental Indicators and income and demographic variables from the American Community Survey and EPA´s Smart Location Database. Estimating a spatial lag model and controlling for formal regulation at the states level, we find evidence that overall neighborhood inequality - as measured by the ratio between the fourth and the second income quintile or the neighborhood Gini coefficient - increases local air pollution exposure, whereas a concentration of top incomes reduces local exposure. The positive coefficient of the general inequality measure is driven by urban neighborhoods, whereas the negative coefficient of top incomes is stronger in rural areas. We explain these findings by two contradicting effects of inequality: On the one hand, overall inequality reduces collective action and thus the organizing capacities for environmental improvements. On the other hand, a concentration of income at the top enhances the ability of rich residents to negotiate with regulators or polluting plants in their vicinity. (authors' abstract)
Series: Department of Economics Working Paper Series

The sequential estimation of the states (filtering) and the corresponding simultaneous estimation of the states and fixed parameters of a dynamic state-space model, being linear or not, is an important probleminmany fields of research, such as in the area of finance. The main objective of this research is to estimate sequ entially and efficiently –from a Bayesian perspective via the particle filtering methodology– the states and/or the fixed parameters of a nonstandard dynamic state-spacemodel: one that is possibly nonlinear, non-stationary or non-Gaussian. The present thesis consists of seven chapters and is structured into two parts. Chapter 1 introduces basic concepts, themotivation, the purpose, and the outline of the thesis. Chapters 2-4, the first part of the thesis, focus on the estimation of the states. Chapter 2 provides a comprehensive review of themost classic algorithms (non-simulation based: KF, EKF, and UKF; and simulation based: SIS, SIR, ASIR, EPF, and UPF1) used for filtering solely the states of a dynamic statespacemodel. All these filters scattered in the literature are not only described in detail, but also placed in a unified notation for the sake of consistency, readability and comparability. Chapters 3 and 4 confirm the efficiency of the well-established particle filtering methodology, via extensive Monte Carlo (MC) studies, when estimating only the latent states for a dynamic state-space model, being linear or not. Also, complementary MC studies are conducted to analyze some relevant issues within the adopted approach, such as the degeneracy problem, the resampling strategy, or the possible impact on estimation of the number of particles used and the time series length. Chapter 3 specifically illustrates the performance of the particle filtering methodology in a linear and Gaussian context, using the exact Kalman filter as a benchmark. The performance of the four studied particle filter variants (SIR, SIRopt, ASIR, KPF, the latter being a special case of the EPF algorithm) is assessed using two apparently simple, but important time series processes: the so-called Local Level Model (LLM) and the AR(1) plus noise model, which are non-stationary and stationary, respectively. An exhaustive study on the effect of the signal-to-noise ratio (SNR) over the quality of the estimation is additionally performed. ComplementaryMC studies are conducted to assess the degree of degeneracy and the possible effect of increasing the number of particles and the time series length. Chapter 4 assesses and illustrates the performance of the particle filtering methodology in a nonlinear context. Specifically, a synthetic nonlinear, non Gaussian and non-stationary state space model taken from literature is used to illustrate the performance of the four competing particle filters under study (SIR, ASIR, EPF, UPF) in contraposition to two well-known non-simulation based filters (EKF, UKF). In this chapter, the residual and stratified resampling schemes are compared and the effect of increasing the number of particles is addressed. In the second part (Chapters 5 and 6), extensive MC studies are carried out, but the main goal is the simultaneous estimation of states and fixed model parameters for chosen non-standard dynamic models. This area of research is still very active and it is within this area where this thesis contributes themost. Chapter 5 provides a partial survey of particle filter variants used to conduct the simultaneous estimation of states and fixed parameters. Such filters are an extension of those previously adopted for estimating solely the states. Additionally, a MC study is carried out to estimate the state (level) and the two fixed variance parameters of the non-stationary local level model; we use four particle filter variants (LW, SIRJ, SIRoptJ, KPFJ), six typical settings of the SNR and two settings for the discount factor needed in the jittering step. In this chapter, the SIRJ particle filter variant is proposed as an alternative to the well-established filter of Liu West (LW PF). The combined use of a Kalman-based proposal distribution and a jittering step is proposed and explored, which gives rise to the particle filter variant called: the Kalman Particle Filter plus Jittering (KPFJ). Chapter 6 focuses on estimating the states and three fixed parameters of the non-standard basic stochastic volatility model known as stochastic autoregressive volatility model of order one: SARV(1). After an introduction and detailed description of the stylized features of financial time series, the estimation ability of two competing particle filter variants (SIRJ vs LW(Liu andWest)) is shown empirically using simulated data. The chapter ends with an application to real data sets from the financial area: the Spanish IBEX 35 returns index and the Europe Brent Spot prices (in dollars). The contribution in chapters 5 and 6 is to propose new variants of particle filters, such as the KPFJ, the SIRJ, and the SIRoptJ (a special case of the SIRJ that uses an optimal proposal distribution) that have developed along this work. The thesis also suggests that the so-called EPFJ (Extended Particle Filter with Jittering) and the UPFJ (Unscented Particle Filter with Jittering) algorithms could be reasonable choices when dealingwith highly nonlinearmodels. In this part, also relevant issueswithin the particle filteringmethodology are discussed, such as the potential impact on estimation of the discount factor parameter, the time series length, and the number of particles used. Throughout this work, pseudo-codes are written for all filters studied and are implemented in RLanguage. The reported findings are obtained as the result of extensive MC studies, considering a variety of case-scenarios described in the thesis. The intrinsic characteristics of the model at hand guided -according to suitability– the choice of filters in each specific situation. The comparison of filters is based on the RMSE, the elapsed CPU-time and the degree of degeneracy. Finally, Chapter 7 includes the discussion, contributions, and future lines of research. Some complementary theoretical and practical aspects are presented in the appendix.
L’estimació seqüencial dels estats (filtratge) i la corresponent estimació simultània dels estats i els paràmetres fixos d’unmodel dinàmic formulat en forma d’espai d’estat –sigui lineal o no– constitueix un problema de rellevada importància enmolts camps, com ser a l’àrea de finances. L’objectiu principal d’aquesta tesi és el d’estimar seqüencialment i de manera eficient –des d’un punt de vista bayesià i usant lametodologia de filtratge de partícules– els estats i/o els paràmetres fixos d’unmodel d’espai d’estat dinàmic no estàndard: possiblement no lineal, no gaussià o no estacionari. El present treball consisteix de 7 capítols i s’organitza en dues parts. El Capítol 1 hi introdueix conceptes bàsics, lamotivació, el propòsit i l’estructura de la tesi. La primera part d’aquesta tesi (capítols 2 a 4) se centra únicament en l’estimació dels estats. El Capítol 2 presenta una revisió exhaustiva dels algorismes més clàssics no basats en simulacions (KF, EKF, UKF2) i els basats en simulacions (SIS, SIR, ASIR, EPF, UPF). Per a aquests filtres, tots esmentats en la literatura, amés de descriure’ls detalladament, s’ha unificat la notació amb l’objectiu que aquesta sigui consistent i comparable entre els diferents algorismes implementats al llarg d’aquest treball. Els capítols 3 i 4 se centren en la realització d’estudis Monte Carlo (MC) extensos que confirmen l’eficiència de la metodologia de filtratge de partícules per estimar els estats latents d’un procés dinàmic formulat en forma d’espai d’estat, sigui lineal o no. Alguns estudis MC complementaris es duen a terme per avaluar diferents aspectes de la metodologia de filtratge de partícules, com ser el problema de la degeneració, l’elecció de l’estratègia de remostreig, el nombre de partícules usades o la grandària de la sèrie temporal. Específicament, el Capítol 3 il·lustra el comportament de la metodologia de filtratge de partícules en un context lineal i gaussià en comparació de l’òptim i exacte filtre de Kalman. La capacitat de filtratge de les quatre variants de filtre de partícules estudiades (SIR, SIRopt, ASIR, KPF; l’últim sent un cas especial de l’algorisme EPF) es va avaluar sobre la base de dos processos de sèries temporals aparentment simples però importants: els anomenats Local Level Model (LLM) i el AR (1) plus noise, que són no estacionari i estacionari, respectivament. Aquest capítol estudia en profunditat temes rellevants dins de l’enfocament adoptat, coml’impacte en l’estimació de la relació entre el senyal i el soroll (SNR: signal-to-noise-ratio, en aquesta tesi), de la longitud de la sèrie temporal i del nombre de partícules. El Capítol 4 avalua i il·lustra el comportament de la metodologia de filtratge de partícules en un context no lineal. En concret, s’utilitza un model d’espai d’estat no lineal, no gaussià i no estacionari pres de la literatura per il·lustrar el comportament de quatre filtres de partícules (SIR, ASIR, EPF, UPF) en contraposició a dos filtres no basats en simulació ben coneguts (EKF, UKF). Aquí es comparen els esquemes de remostreig residual i estratificat i s’avalua l’efecte d’augmentar el nombre de partícules. A la segona part (capítols 5 i 6), es duen a terme també estudis MC extensos, però ara l’objectiu principal és l’estimació simultània dels estats i paràmetres fixos de certsmodels seleccionats. Aquesta àrea de recerca segueix sentmolt activa i és on aquesta tesi hi contribueixmés. El Capítol 5 proveeix una revisió parcial dels mètodes per dur a terme l’estimació simultània dels estats i paràmetres fixos a través de la metodologia de filtratge de partícules. Aquests filtres són una extensió d’aquells adoptats anteriorment només per estimar els estats. Aquí es realitza un estudi MC per estimar l’estat (nivell) i els dos paràmetres de variància del model LLM no estacionari; s’utilitzen quatre variants (LW, SIRJ, SIRoptJ, KPFJ) de filtre de partícules, sis escenaris típics del SNR i dos escenaris per a l’anomenat factor de descompte necessari en el pas de diversificació. En aquest capítol, es proposa la variant de filtre de partícules SIRJ (Sample Importance Resampling with Jittering) com a alternativa al filtre de referència de Liu iWest (LWPF). També es proposa i explora l’ús combinat d’una distribució d’importància basada en el filtre de Kalman i un pas de diversificació (jittering) que dóna lloc a la variant del filtre de partícules anomenada Kalman Particle Filteringwith Jittering (KPFJ). El Capítol 6 se centra en l’estimació dels estats i dels paràmetres fixos delmodel bàsic no estàndard de volatilitat estocàstica denominat Stochastic autoregressive model of order one: SARV (1). Després d’una introducció i descripció detallada de les característiques pròpies de sèries temporals financeres, es demostra mitjançant estudis MC la capacitat d’estimació de dues variants de filtre de partícules (SIRJ vs. LW(Liu iWest)) utilitzant dades simulades. El capítol acaba amb una aplicació a dos conjunts de dades reals dins de l’àrea financera: l’índex de rendiments espanyol IBEX 35 i els preus al comptat (en dòlars) del Brent europeu. La contribució en els capítols 5 i 6 consisteix en proposar noves variants de filtres de partícules, compoden ser el KPFJ, el SIRJ i el SIRoptJ (un cas especial de l’algorisme SIRJ utilitzant una distribució d’importància òptima) que s’han desenvolupat al llarg d’aquest treball. També se suggereix que els anomenats filtres de partícules EPFJ (Extended Particle Filter with Jittering) i UPFJ (Unscented Particle Filter with Jittering) podrien ser opcions raonables quan es tracta de models altament no lineals; el KPFJ sent un cas especial de l’algorisme EPFJ. En aquesta part, també es tracten aspectes rellevants dins de la metodologia de filtratge de partícules, com ser l’impacte potencial en l’estimació de la longitud de la sèrie temporal, el paràmetre de factor de descompte i el nombre de partícules. Al llarg d’aquest treball s’han escrit (i implementat en el llenguatge R) els pseudo-codis per a tots els filtres estudiats. Els resultats presentats s’obtenenmitjançant simulacionsMonte Carlo (MC) extenses, tenint en compte variats escenaris descrits en la tesi. Les característiques intrínseques del model baix estudi van guiar l’elecció dels filtres a comparar en cada situació específica. Amés, la comparació dels filtres es basa en el RMSE (RootMean Square Error), el temps de CPU i el grau de degeneració. Finalment, el Capítol 7 presenta la discussió, les contribucions i les línies futures de recerca. Alguns aspectes teòrics i pràctics complementaris es presenten en els apèndixs.
La estimación secuencial de los estados (filtrado) y la correspondiente estimación simultánea de los estados y los parámetros fijos de un modelo dinámico formulado en forma de espacio de estado –sea lineal o no– constituye un problema de relevada importancia enmuchos campos, como ser en el área de finanzas. El objetivo principal de esta tesis es el de estimar secuencialmente y de manera eficiente –desde un punto de vista bayesiano y usando la metodología de filtrado de partículas– los estados y/o los parámetros fijos de un modelo de espacio de estado dinámico no estándar: posiblemente no lineal, no gaussiano o no estacionario. El presente trabajo consta de 7 capítulos y se organiza en dos partes. El Capítulo 1 introduce conceptos básicos, la motivación, el propósito y la estructura de la tesis. La primera parte de esta tesis (capítulos 2 a 4) se centra únicamente en la estimación de los estados. El Capítulo 2 presenta una revisión exhaustiva de los algoritmos más clásicos no basados en simulaciones (KF, EKF,UKF3) y los basados en simulaciones (SIS, SIR, ASIR, EPF, UPF). Para todos estos filtros, mencionados en la literatura, además de describirlos en detalle, se ha unificado la notación con el objetivo de que ésta sea consistente y comparable entre los diferentes algoritmos implementados a lo largo de este trabajo. Los capítulos 3 y 4 se centran en la realización de estudios Monte Carlo (MC) extensos que confirman la eficiencia de la metodología de filtrado de partículas para estimar los estados latentes de un proceso dinámico formulado en forma de espacio de estado, sea lineal o no. Algunos estudios MC complementarios se llevan a cabo para evaluar varios aspectos de la metodología de filtrado de partículas, como ser el problema de la degeneración, la elección de la estrategia de remuestreo, el número de partículas usadas o el tamaño de la serie temporal. Específicamente, el Capítulo 3 ilustra el comportamiento de lametodología de filtrado de partículas en un contexto lineal y gaussiano en comparación con el óptimo y exacto filtro de Kalman. La capacidad de filtrado de las cuatro variantes de filtro de partículas estudiadas (SIR, SIRopt, ASIR, KPF; el último siendo un caso especial del algoritmo EPF) se evaluó en base a dos procesos de series temporales aparentemente simples pero importantes: los denominados Local Level Model (LLM) y el AR (1) plus noise, que son no estacionario y estacionario, respectivamente. Este capítulo estudia en profundidad temas relevantes dentro del enfoque adoptado, como el impacto en la estimación de la relación entre la señal y el ruido (SNR: signal-to-noise-ratio, en esta tesis), de la longitud de la serie temporal y del número de partículas. El Capítulo 4 evalúa e ilustra el comportamiento de la metodología de filtrado de partículas en un contexto no lineal. En concreto, se utiliza un modelo de espacio de estado no lineal, no gaussiano y no estacionario tomado de la literatura para ilustrar el comportamiento de cuatro filtros de partículas (SIR, ASIR, EPF, UPF) en contraposición a dos filtros no basados en simulación bien conocidos (EKF, UKF). Aquí se comparan los esquemas de remuestreo residual y estratificado y se evalúa el efecto de aumentar el número de partículas. En la segunda parte (capítulos 5 y 6), se llevan a cabo también estudios MC extensos, pero ahora el objetivo principal es la estimación simultánea de los estados y parámetros fijos de ciertos modelos seleccionados. Esta área de investigación sigue siendo muy activa y es donde esta tesis contribuye más. El Capítulo 5 provee una revisión parcial de losmétodos para llevar a cabo la estimación simultánea de los estados y parámetros fijos a través de lametodología de filtrado de partículas. Dichos filtros son una extensión de aquellos adoptados anteriormente sólo para estimar los estados. Aquí se realiza un estudio MC para estimar el estado (nivel) y los dos parámetros de varianza del modelo LLM no estacionario; se utilizan cuatro variantes (LW, SIRJ, SIRoptJ, KPFJ) de filtro de partículas, seis escenarios típicos del SNR y dos escenarios para el llamado factor de descuento necesario en el paso de diversificación. En este capítulo, se propone la variante de filtro de partículas SIRJ (Sample Importance resampling with Jittering) como alternativa al filtro de referencia de Liu y West (LW PF). También se propone y explora el uso combinado de una distribución de importancia basada en el filtro de Kalman y un paso de diversificación (jittering) que da lugar a la variante del filtro de partículas denominada Kalman Particle Filteringwith Jittering (KPFJ). El Capítulo 6 se centra en la estimación de los estados y de los parámetros fijos del modelo básico no estándar de volatilidad estocástica denominado Stochastic autoregressivemodel of order one: SARV (1). Después de una introducción y descripción detallada de las características propias de series temporales financieras, se demuestra mediante estudios MC la capacidad de estimación de dos variantes de filtro de partículas (SIRJ vs. LW (Liu y West)) utilizando datos simulados. El capítulo termina con una aplicación a dos conjuntos de datos reales dentro del área financiera: el índice de rendimientos español IBEX 35 y los precios al contado (en dólares) del Brent europeo. La contribución en los capítulos 5 y 6 consiste en proponer nuevas variantes de filtros de partículas, como pueden ser el KPFJ, el SIRJ y el SIRoptJ (Caso especial del algoritmo SIRJ utilizando una distribución de importancia óptima) que se han desarrollado a lo largo de este trabajo. También se sugiere que los llamados filtros de partículas EPFJ (Extended Particle Filter with Jittering) y UPFJ (Unscented Particle Filter with Jittering) podrían ser opciones razonables cuando se trata de modelos altamente no lineales; el KPFJ siendo un caso especial del algoritmo EPFJ. En esta parte, también se tratan aspectos relevantes dentro de lametodología de filtrado de partículas, como ser el impacto potencial en la estimación de la longitud de la serie temporal, el parámetro de factor de descuento y el número de partículas. A lo largo de este trabajo se han escrito (e implementado en el lenguaje R) los pseudo-códigos para todos los filtros estudiados. Los resultados presentados se obtienen mediante simulaciones Monte Carlo (MC) extensas, teniendo en cuenta variados escenarios descritos en la tesis. Las características intrínsecas del modelo bajo estudio guiaron la elección de los filtros a comparar en cada situación específica. Además, la comparación de los filtros se basa en el RMSE (Root Mean Square Error), el tiempo de CPU y el grado de degeneración. Finalmente, el Capítulo 7 presenta la discusión, las contribuciones y las líneas futuras de investigación. Algunos aspectos teóricos y prácticos complementarios se presentan en los apéndices.

Time series model have been used in many areas of knowledge and have become a current necessity for companies to survive in a globalized and competitive market, as well as climatic factors that have always been a concern because of the different ways they interfere in human life. In this context, this work aims to present a comparison among the performances by the following models of time series: ARIMA, ARMAX and Exponential Smoothing, adjusted to air relative humidity (UR) and also to verify the volatility present in the series through non-linear models ARCH/GARCH, adjusted to residues of the ARIMA and ARMAX models. The data were collected from INMET from October, 1st to January, 22nd, 2014. In the comparison of the results and the selection of the best model, the criteria MAPE, EQM, MAD and SSE were used. The results showed that the model ARMAX(3,0), with the inclusion of exogenous variables produced better forecast results, compared to the other models SARMA(3,0)(1,1)12 and the Holt-Winters multiplicative. In the volatility study of the series via non-linear ARCH(1), adjusted to the quadrants of SARMA(3,0)(1,1)12 and ARMAX(3,0) residues, it was observed that the volatility does not tend to influence the future long-term observations. It was then concluded that the classes of models used and compared in this study, for data of a climatologic variable, showed a good performance and adjustment. We highlight the broad usage possibility in the techniques of temporal series when it is necessary to make forecasts and also to describe a temporal process, being able to be used as an efficient support tool in decision making.
Modelos de séries temporais vêm sendo empregados em diversas áreas do conhecimento e têm surgido como necessidade atual para empresas sobreviverem em um mercado globalizado e competitivo, bem como fatores climáticos sempre foram motivo de preocupação pelas diferentes formas que interferem na vida humana. Nesse contexto, o presente trabalho tem por objetivo apresentar uma comparação do desempenho das classes de modelos de séries temporais ARIMA, ARMAX e Alisamento Exponencial, ajustados a dados de umidade relativa do ar (UR) e verificar a volatilidade presente na série por meio de modelos não-lineares ARCH/GARCH ajustados aos resíduos dos modelos ARIMA e ARMAX. Os dados foram coletados junto ao INMET no período de 01 de outubro de 2001 a 22 de janeiro de 2014. Na comparação dos resultados e na seleção do melhor modelo foram utilizados os critérios MAPE, EQM, MAD e SSE. Os resultados mostraram que o modelo ARMAX(3,0) com a inclusão de variáveis exógenas produziu melhores resultados de previsão em relação aos seus concorrentes SARMA(3,0)(1,1)12 e o Holt-Winters multiplicativo. No estudo da volatilidade da série via modelo não-linear ARCH(1), ajustado aos quadrados dos resíduos dos modelos SARMA(3,0)(1,1)12 e ARMAX(3,0), observou-se que a volatilidade não tende a influenciar as observações futuras em longo prazo. Conclui-se que as classes de modelos utilizadas e comparadas neste estudo, para dados de uma variável climatológica, demonstraram bom desempenho e ajuste. Destaca-se a ampla possibilidade de utilização das técnicas de séries temporais quando se deseja fazer previsões e descrever um processo temporal, podendo ser utilizadas como ferramenta eficiente de apoio nas tomadas de decisão.

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O objetivo principal deste trabalho foi avaliar a influência das condições de contorno nas simulações com o modelo CMAQ sobre a Região Metropolitana da Grande Vitória (RMGV) para os poluentes, ozônio (O3) e material particulado inalável (MP10). Foram feitos quatro cenários de simulação para o mês de agosto de 2010 com diferentes condições de contorno. O primeiro cenário (M1) utilizando condições de contorno fixas, invariáveis com o tempo com concentrações nulas (zero) para todos os poluentes; um segundo cenário (M2) com valores fixos de concentração, invariável com o tempo com valores médios obtidos através do monitoramento das estações de qualidade da RMGV e de estações de Aracruz ao Norte e Anchieta ao sul; o terceiro cenário (M3) utilizou condições de contorno variáveis com o tempo provenientes de uma simulação prévia do CMAQ com um domínio maior, centralizado sobre a mesma área (RMGV); e por fim o quarto cenário (M4) que utilizou valores de concentrações variáveis com o tempo para as bordas oriundas de simulações com o modelo global GEOS-Chem. Todos os cenários utilizaram as mesmas condições de meteorológicas e emissões de poluentes, com condições meteorológicas geradas pelo modelo WRF versão 3.6.1 e emissões atmosféricas provenientes do inventário de emissões oficial da RMGV. As simulações de qualidade do ar foram feitas com domínio 61 x79 km centrado nas coordenadas -20,25ºS; -40,28ºW com resolução de 1 km, utilizando o CB05 e Aero6 e ainda o analisador de processos do CMAQ (PROCAN). Os resultados das simulações foram comparados com os dados medidos em estações de monitoramento da RMGV. Os resultados mostraram que para MP10 as condições de contorno não foram tão influentes nas concentrações simuladas, com pequenas variações das concentrações entre eles, porém, de um modo geral, os métodos M3 e M4 alcançaram os melhores resultados para estatística, entretanto o método M2 não está totalmente equivocado, porém deve-se ter cautela em usar esse método. Foram observados comportamentos diferentes entre as estações de monitoramento onde houve umas com valores superestimados em algumas horas e outras com valores subestimados, ocorrido provavelmente, por causa do tamanho da grade associado com as condições meteorológicas e variação temporal das emissões. Para o ozônio, notou-se que as condições de contorno influenciam diretamente nas concentrações modeladas, podendo inclusive influenciar no aumento da produção do O3 não apenas por reações químicas, mas também por processos de advecção e difusão atmosférica. Foi observado que cenário M1 faz com que as concentrações de O3 modeladas sejam bem pequenas, não representando a realidade. No cenário M2 as concentrações foram superestimadas, tanto nas estações quanto nas áreas próximas aos limites do domínio, principalmente na porção Oeste. Os cenários M3 e M4 alcançaram os melhores resultados de concentrações e estatística, sendo estes os mais aconselháveis quando o objetivo é avaliar o ozônio. Como o domínio final utilizado na modelagem do CMAQ foi de apenas 61 x 79km, observou-se que as condições de fronteira influenciam diretamente em toda grade do domínio, principalmente para ozônio, ao utilizar o processador de analises (PROCAN). Quando as concentrações de contorno são altas, independentes de serem fixas ou variantes com o tempo, os processos de advecção e difusão turbulenta promovem um incremento muito maior nas regiões de fronteira com a RMGV, aumentando a concentração.

In recent years, two estimators have been proposed to correct the bias exhibited by the leastsquares (LS) estimator of the lagged dependent variable (LDV) coefficient in dynamic regression models when the sample is finite. They have been termed as &lsquo
mean-unbiased&rsquo
and &lsquo
medianunbiased&rsquo
estimators. Relative to other similar procedures in the literature, the two locationbased estimators have the advantage that they offer an exact and uniform methodology for LS estimation of the LDV coefficient in a first order autoregressive model with or without exogenous regressors i.e. ARX(1).

However, no attempt has been made to accurately establish and/or compare the statistical properties among these estimators, or relative to those of the LS estimator when the LDV coefficient is restricted to realistic values. Neither has there been an attempt to 
compare their performance in terms of their mean squared error (MSE) when various forms of the exogenous regressors are considered. Furthermore, only implicit confidence intervals have been given for the &lsquo
medianunbiased&rsquo
estimator. Explicit confidence bounds that are directly usable for inference are not available for either estimator. In this study a new estimator of the LDV coefficient is proposed
the &lsquo
most-probably-unbiased&rsquo
estimator. Its performance properties vis-a-vis the existing estimators are determined and compared when the parameter space of the LDV coefficient is restricted. In addition, the following new results are established: (1) an explicit computable form for the density of the LS estimator is derived for the first time and an efficient method for its numerical evaluation is proposed
(2) the exact bias, mean, median and mode of the distribution of the LS estimator are determined in three specifications of the ARX(1) model
(3) the exact variance and MSE of LS estimator is determined
(4) the standard error associated with the determination of same quantities when simulation rather than numerical integration method is used are established and the methods are compared in terms of computational time and effort
(5) an exact method of evaluating the density of the three estimators is described
(6) their exact bias, mean, variance and MSE are determined and analysed
and finally, (7) a method of obtaining the explicit exact confidence intervals from the distribution functions of the estimators is proposed.

The discussion and results show that the estimators are still biased in the usual sense: &lsquo
in expectation&rsquo
. However the bias is substantially reduced compared to that of the LS estimator. The findings are important in the specification of time-series regression models, point and interval estimation, decision theory, and simulation.

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Universidade Federal Fluminense. Instituto de Química. Programa de Pós-Graduação em Geoquímica, Niterói, RJ
Este estudo analisa os fluxos de óxido nitroso (N 2 O) e amônia (NH 3 ) no Sistema Lagunar de Maricá-Guarapina (SLMG). O N 2 O é um dos gases do efeito estufa e está envolvido no consumo de ozônio (O 3 ) na estratosfera. A NH 3 pode levar a acidificação de ambientes terrestres e aquáticos, a eutrofização de sistemas aquáticos e produção de N 2 O. O SLMG vem sofrendo degradação da qualidade de suas á guas devido à urbanização e às atividades agropecuárias na região. Este sistema la gunar é composto por quatro lagoas interligadas entre si através de canais: Maricá, Ba rra, Padre e Guarapina. Para a análise de N 2 O foi utilizada a técnica da câmara estática flutua nte e 4 modelos de predição de fluxos (MPF). No caso da NH 3 foram feitas estimativas de fluxos também através de MPF. Os resultados deste estudo mostram que as quatro lagoa s do SLMG apresentam comportamentos distintos com relação aos fluxos dos dois gases ana lisados. As estimativas de taxas de emissão do sistema lagunar mostram que, apesar do sistema a presentar lagoas que parecem atuar como sorvedouro de N 2 O ou de NH 3 , num balanço geral, ele emite N para a atmosfera s ob uma ou outra forma. A taxa de emissão estimada variou entr e 92,15 g N dia -1 e 104,77 g N dia -1 . Outra informação que esta estimativa trouxe foi a d e que a maior parte das emissões ocorre sob a forma de NH 3 com emissão estimada de 84,79 g N dia -1 a 97,41 g N dia -1 .
This study examines the nitrous oxide (N 2 O) and ammonia (NH 3 ) fluxes in Maricá- Guarapina’s system. The N 2 O is a greenhouse gas and is involved in the consum ption of the ozone (O 3 ) in the stratosphere. The NH 3 can lead to acidification of terrestrial and aquat ic environments, eutrophication of aquatic systems and production of N 2 O. The SLMG is suffering degradation in the water’s quality due to urbanization and agricultural activities in the region. This system is composed for four lagoon interconnected between themselves through channels: Maricá, Barra, Father and Guarapi na. For the analysis of N 2 O was used the technique of the static chamber and 4 models predic tion fluxes (MPF). In the case of NH 3 were made estimates of fluxes through MPF too. The results of this study show that the four lagoons in the SLMG have different behaviors with r espect to the fluxes of the two gases analyzed. Estimates of the rates of emission in th e system lagoon show that despite the present system lagoons that seem act as sink of N 2 O and NH 3 , in a general balance, it gives N to the atmosphere in one form or another. The estim ated emission rate ranged between 92,15 g N -1 day -1 and 104,77 g N -1 day -1 . Other information that brought this estimate was that the majority of emissions occur in the form of NH 3 with estimated emission of 84,79 g N -1 day -1 to 97,41 g N -1 day -1 .

Les travaux de la thèse portent sur les théorèmes limites pour des modèles stochastiques à forte dépendance. Dans la première partie, nous considérons des modèles AR(1) à coefficient aléatoire. Nous identifions trois régimes asymptotiques différents pour le schéma d’agrégation conjointe temporelle-contemporaine lorsque les processus AR sont indépendants et lorsque les AR possède des innovations communes. Ensuite, on discute de l’estimation non paramétrique de la fonction de répartition du coefficient autorégressif à partir d’un panel de séries AR(1) à coefficient aléatoire. Nous prouvons la convergence faible du processus empirique basé sur des estimations des coefficients autorégressifs non observables vers un pont brownien généralisé. Ce résultat est ensuite appliqué pour valider différents outils d’inférence statistique à partir des données du panel AR(1). Dans la deuxième partie de la thèse, nous nous concentrons sur les modèles spatiaux en dimension 2. Nous considérons des champs aléatoires construits à partir des polynômes Appell et de champs aléatoires linéaires. Pour ce modèle non linéaire, nous étudions la limite de ses sommes partielles normalisées prises sur des rectangles et prouvons l’existence d’une transition d’échelle. Enfin, nous abordons la même question pour le modèle de germes-grains aléatoire. Nous mettons en évidence l’existence de deux points de transition dans les limites de ces modèles
The thesis is devoted to limit theorems for stochastic models with long-range dependence. We first consider a random-coefficient AR(1) process, which can have long memory provided the distribution of autoregressive coefficient concentrates near the unit root. We identify three different limit regimes in the scheme of joint temporal-contemporaneous aggregation for independent copies of random-coefficient AR(1) process and for its copies driven by common innovations. Next, we discuss nonparametric estimation of the distribution of the autoregressive coefficient given multiple random-coefficient AR(1) series. We prove the weak convergence of the empirical process based on estimates of unobservable autoregressive coefficients to a generalized Brownian bridge and apply this result to draw statistical inference from panel AR(1) data. In the second part of the thesis we focus on spatial models in dimension 2. We define a nonlinear random field as the Appell polynomial of a linear random field with long-range dependence. For the nonlinear random field, we investigate the limit of its normalized partial sums over rectangles and prove the existence of scaling transition. Finally, we study such like scaling of the random grain model and obtain two-change points in its limits

CAPES
Este estudo teve por objetivo sugerir locais para o monitoramento da qualidade do ar no município de Paranaguá-PR. Para tal, foi utilizada modelagem matemática de dispersão de poluentes atmosféricos, associada ao levantamento de informações sobre adensamento populacional e distribuição de equipamentos urbanos nos bairros do município. Com o uso do software de modelagem AERMOD foram simuladas as concentrações de CO, NOX, SO2, PTS e HCT, considerando emissão veicular, industrial e do Porto de Paranaguá. Os dados meteorológicos utilizados nas simulações consistiram em uma série horária de três anos. As concentrações máximas horárias para CO, NOX, SO2, PTS e HCT foram 5572 μg m-3, 5741 μgm-3, 1539 μg m-3, 3368 μg m-3 e 247 μg m-3, respectivamente. Para a média do período modelado as concentrações para CO, NOX, SO2, PTS e HCT foram 340 μg m-3, 343 μg m-3, 94μg m-3, 116 μg m-3 e 38,6 μg m-3, respectivamente. Foram sugeridos para a instalação de estações de monitoramento da qualidade do ar os seguintes bairros: Alboit para estação industrial, por pertencer à Zona de Interesse Portuário, que abriga atividades potencialmente poluidoras; Costeira para estação residencial devido a sua relativa proximidade à zona portuária; Vila Horizonte para estação veicular, por estar localizado entre vias de tráfego intenso; Parque São Jorge para estação de fundo, por estar distantes de fontes de emissão significativas e os bairros Porto dos Prades e Bockmann para estação comercial, por serem bairros com características comercias e de centralidade, nos quais se supõe haver intensa circulação de pedestres.
This study aimed to suggest locations for the monitoring of air quality in the city of Paranagua. For this, mathematical modeling of air pollutants dispersion was used, associated with the collection of information on population density and distribution of urban facilities in the city's neighborhoods. The concentration of different air pollutants (CO, NOX, SO2, PTS e HCT) on space and time were simulated using the modeling software AERMOD, considering vehicular, industrial and the Port of Paranagua emission. The meteorological data used in the simulations consisted of an hourly series of three years. The hourly maximum concentration to CO, NOX, SO2, PTS e HCT were 5572 μg m-3, 5741 μg m-3, 1539 μg m-3, 3368 μg m-3 e 247 μg m-3, respectively. The average concentration during the period considered to CO, NOX, SO2, PTS e HCT were 340 μg m-3, 343 μg m-3, 94 μg m-3, 116 μg m-3 e 38,6 μg m-3, respectively. For the installation of the air quality monitoring stations, the following neighborhoods were suggested: Alboit for industrial station, because it belongs to the Zone of Interest Port, which has potentially polluting activities; Coast for residential station due to its relative proximity to the port area; Vila Horizonte to serve station, to be located between high-traffic roads; Parque Sao Jorge to background station, to be far from significant emission sources and Port neighborhoods of Prades and Bockmann to commercial station because they are neighborhoods with commercial features and centrality, in which it is supposed be intense circulation of pedestrians.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
No planejamento dos gráficos de controle destinados ao monitoramento da média do processo, assume-se que esta permanece fixa em seu valor alvo até a ocorrência de uma causa especial, que a desloca. Em muitos processos, contudo, é mais razoável supor que a média oscila mesmo na ausência de causas especiais. Para descrever este comportamento oscilatório, tem-se utilizado o modelo autoregressivo de 1ª ordem, AR (1). Quando esta oscilação é grande, o melhor desempenho do gráfico de X é obtido com amostras unitárias. O mesmo não se observa com a carta de EWMA (exceto quando o parâmetro de ponderação  é próximo de um); os melhores desempenhos são obtidos com a adoção de amostras de tamanho n>1 e  pequeno, mesmo quando o objetivo é a detecção rápida de grandes deslocamentos da média. Neste estudo, utiliza-se como medida de desempenho o TES – tempo médio entre a ocorrência de uma mudança na posição em torno da qual a média oscila e sua sinalização pelo gráfico de controle. Quando a média do processo oscila, o TES passa a ser uma função do número esperado de visitas aos estados transientes de uma cadeia de Markov
The design of the control charts for the process mean, assumes that this parameter remains fixed on its target value until the occurrence of a special cause that shifts it. In many cases, however, it is more reasonable to assume that the mean wanders even in the absence of special causes. To describe this wandering behavior, has used the AR(1) model. When the wandering behavior is responsible for significant proportion of the data variability, the best performance of the X chart is obtained with samples of size one (n=1). The same is not true with the EWMA control chart (except when the smoothing parameter  is very close to one), its best performance is achieved with the adoption of n>1 and small , even to detect large changes in the process mean position. In this study, the average time between the occurrence of a change in the process mean position and the signal (TES) - is used to assess the chart’s performance. With the process mean wandering, this measure of performance becomes function of the expected number of visits to the transient states of a Markov chain

Resumo: No planejamento dos gráficos de controle destinados ao monitoramento da média do processo, assume-se que esta permanece fixa em seu valor alvo até a ocorrência de uma causa especial, que a desloca. Em muitos processos, contudo, é mais razoável supor que a média oscila mesmo na ausência de causas especiais. Para descrever este comportamento oscilatório, tem-se utilizado o modelo autoregressivo de 1ª ordem, AR (1). Quando esta oscilação é grande, o melhor desempenho do gráfico de X é obtido com amostras unitárias. O mesmo não se observa com a carta de EWMA (exceto quando o parâmetro de ponderação  é próximo de um); os melhores desempenhos são obtidos com a adoção de amostras de tamanho n>1 e  pequeno, mesmo quando o objetivo é a detecção rápida de grandes deslocamentos da média. Neste estudo, utiliza-se como medida de desempenho o TES - tempo médio entre a ocorrência de uma mudança na posição em torno da qual a média oscila e sua sinalização pelo gráfico de controle. Quando a média do processo oscila, o TES passa a ser uma função do número esperado de visitas aos estados transientes de uma cadeia de Markov
Abstract: The design of the control charts for the process mean, assumes that this parameter remains fixed on its target value until the occurrence of a special cause that shifts it. In many cases, however, it is more reasonable to assume that the mean wanders even in the absence of special causes. To describe this wandering behavior, has used the AR(1) model. When the wandering behavior is responsible for significant proportion of the data variability, the best performance of the X chart is obtained with samples of size one (n=1). The same is not true with the EWMA control chart (except when the smoothing parameter  is very close to one), its best performance is achieved with the adoption of n>1 and small , even to detect large changes in the process mean position. In this study, the average time between the occurrence of a change in the process mean position and the signal (TES) - is used to assess the chart's performance. With the process mean wandering, this measure of performance becomes function of the expected number of visits to the transient states of a Markov chain
Orientador: Antonio Fernando Branco Costa
Coorientador: Marcela Aparecida Guerreiro Machado
Banca: Mauro Hugo Mathias
Banca: Fernando Antonio Elias Claro
Mestre

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This study was developed in Serra do Sudeste and Encosta do Sudeste physiographic regions of Rio Grande do Sul state. The objective was to identify the physical and hydraulic soil properties related to forest yield sites in two distinct areas, including physical-structural properties and soil available water capacity (AW) of Argissolo Vermelho-Amarelo Distrófico típico, Argissolo Vermelho-Amarelo Distrófico latossólico (ARG) and Neossolo Quartzarênico Órtico típico (NEO), as well as perform parameterization of the Physiological Principles to Predicting Growth model (3-PG). In the two sites with high (ARG) and low (NEO) productive potential capacity, the growth and productivity of stands characterization was based on data from forest inventories and from destructive sampling and cube by Smalian method of 30 trees of medium quadratic mean diameter (dg). Soil properties were determined in undisturbed and disturbed soil samples, taken from 0.00-0.10, 0.10-0.20, 0.20-0.40, 0.40-0.60, 0.60-0.80, 0.80-1.00 e 1.00-1.20 m soil depths, in 12 sampling points. Eucalyptus yield was different in the ARG (from clay loam to clay texture) and NEO (sandy texture) areas, characterized by mean values of 373.9 m³ ha-1 and 272.3 m³ ha-1, for 89-months-old stands. In the ARG, AW ranged from 0.100 up to 0.304 cm3 cm-3. The highest soil bulk density (BD; 1.64 Mg m-3) was observed in the 0.00-0.10 and 0.10-0.20 m soil layers. Multiple regression analysis with BD and macroporosity (Mac) of the 0.40-0.60 m soil layer had r2 ~ 0.22 in variance estimation of mean annual volume increment (MAIV). Soil air permeability (Kar) was the main soil property related to productivity in ARG stands. In the NEO (sandy texture) areas, AW ranged from 0.025 up to 0.04 cm3 cm-3 and BD had the highest values (1.60 Mg m-3) in the 0.80-1.00 m soil layer. The BD determined from surface up to 0.60 m explained 14% of MAIV variance and 27% of the total height variance (h). Multiple regression that included BD and Kar of the surface layers explained around 23% of mean annual stem biomass increment (MAISB) variance. In the parameterization of the model 3-PG we obtained estimates characterized by r2 higher than 0.9 for the wood volume with bark (V; m3 ha-1), wood biomass (BL; Mg ha-3) and total height (h), and equal to 0.78 for the diameter at breast high (dbh; cm). The statistical efficiency described by the Nash-Sutcliffe indicator had values higher than 0.8, while the PBIAS indicator showed a tendency of underestimation of less than 12%. In the validation process of the model, performed in unused portions in the parameterization, the results were similar to those obtained in the efficiency evaluation, except for the variable dbh, which was underestimated at the lowest ages. The results showed that the soils with high water availability have their physical quality, based on productivity, determined by the properties that represent the flow of solutes and gases, while coarse soils, highly drainable, have their productive capacity inversely related to BD. The 3-PG model was efficient and accurate for the estimation of E. saligna productivity in the observed climatic conditions, with a higher sensitivity for coarse textured soils.
O presente estudo foi realizado nas regiões fisiográficas da Serra do Sudeste e Encosta do Sudeste do estado do Rio Grande do Sul. O objetivo do estudo foi identificar as propriedades físico-hídricas dos solos relacionadas à produtividade dos sítios florestais, distintos quanto às propriedades físico-estruturais e à água disponível (AD), caracterizados pela presença de Argissolo Vermelho-Amarelo Distrófico típico e Argissolo Vermelho-Amarelo Distrófico latossólico (ARG) e de Neossolo Quartzarênico Órticos típicos (NEO), e ainda, realizar a parametrização do modelo Physiological Principles to Predicted Growth (3-PG). A caracterização do crescimento e produtividade dos povoamentos foi realizada por meio de inventários florestais e pela amostragem destrutiva e cubagem, pelo método de Smalian, de 30 árvores de diâmetro médio quadrático (dg). As propriedades físico-hídricas dos solos foram determinadas em amostras de solos de estrutura preservada e alterada, coletadas nas camadas de 0,00-0,10, 0,10-0,20, 0,20-0,40, 0,40-0,60, 0,60-0,80, 0,80-1,00 e 1,00-1,20 m, em 12 pontos amostrais. A produtividade foi distinta nas áreas ARG e NEO, com média de 373,9 m³ ha-1 e 272,3 m3 ha-1, aos 89 meses de idade. Nos solos ARG (classe textural franco arenosa a muito argilosa), a AD variou entre 0,100 e 0,304 m3 m-3, e os maiores valores de densidade do solo (Ds; 1,64 Mg m-3) foram observados nas camadas 0,00-0,10 e 0,10-0,20 m. Pela análise de regressão múltipla a Ds e a macroporosidade (Mac) da camada 0,40-0,60 m tiveram eficiência estatística com r2 ~ 0,22 na estimativa da variância do incremento médio anual em volume (IMAV). A permeabilidade do solo ao ar (Kar) foi a principal propriedade do solo relacionada à produtividade dos povoamentos das áreas ARG. Nas áreas NEO (classe textural areia) a AD variou entre 0,025 e 0,04 m3 m-3 e a maior Ds foi observada na camada 0,80-1,00 m (1,60 Mg m-3). A Ds determinada nas camadas acima de 0,60 m de profundidade explicou 14% da variância observada no IMAV e 27% da variância da altura total (h). Pela regressão múltipla a Ds e a Kar das camadas superficiais explicaram em torno de 23% da variância observada no incremento médio anual em biomassa de lenho (IMABL). Na parametrização do modelo 3-PG foram obtidas estimativas caracterizadas por r2 superior a 0,9 para o volume com casca (V; m3 ha-1), biomassa de lenho (BL; Mg ha-3) e altura total (h; m), e igual a 0,78 para o dap (cm). O indicador estatístico Nash-Sutcliffe teve valores superiores a 0,8, enquanto o indicador Bias percentual (PBIAS) apontou tendência de subestimativa inferior a 12%. No processo de validação do modelo, realizado em parcelas não utilizadas na parametrização, os resultados foram semelhantes aos obtidos na avaliação da eficiência, com exceção para a variável dap, que foi subestimada nas menores idades. Solos com alta disponibilidade de água podem ter sua qualidade física, com base na produtividade, determinada pelas propriedades que representam o fluxo de solutos e gases, enquanto solos de textura grossa, altamente drenáveis, têm sua capacidade produtiva inversamente relacionada a Ds. O modelo 3-PG foi eficiente e preciso para a estimativa da produtividade do E. saligna nas condições climáticas observadas, com maior sensibilidade para os solos de textura grossa.

Com a evolução dos projetos de multirotores e dos seus componentes, os projetistas vem tendo inúmeras opções de combinações de componentes na fase de projeto do multirotor, buscando melhor performance e menor custo. Isto deixa um problema em aberto: como atingir o multirotor pode atingir uma boa performance ainda na fase de projeto. A motivação para realização deste estudo se justifica no fato que não há trabalhos relacionado ao levantamento de métricas e análise de performance dos multirotores. Assim como o fator de não haver formas de mensurar a qualidade dos projetos e ter possibilidade de comparação, uma vez que tem-se várias formas de projetar um multirotor para diferentes aplicações. Este trabalho propõe uma abordagem para a análise do projeto de multirotores em termos de sua capacidade de voo (definida como voabilidade), levando em consideração as características de seus rotores, peso e topologia. O principal objetivo é apresentar uma forma de qualificar e quantificar uma aeronave multirotor para otimizar seu projeto. A abordagem discutida tem como objetivo analisar as habilidades de voo dos multirotores em seu projeto teórico para suportar os requisitos de projeto (como tamanho da hélice, torque do motor, topologia de armação), garantindo as capacidades de voo exigidas pela tarefa. Como resultado deste trabalhos, um conjunto de índices foi proposto para avaliar a qualidade de projeto de multirotores, sendo eles: voo, estabilidade, posicionamento e flutuação. A soma destes índices compõem o índice de voabilidade. Este índice oferece a possibilidade de comparação da análise do veículo em função das especificações do conjunto motor, hélice, topologia e tamanho do quadro. Para a validação destas métricas, uma análise das topologias tradicionais foi realizada, permitindo uma comparação em função do desempenho e esforço delas.
With an evolution of the multi-curral projects and their components, the designers have been having numerous options of combinations of components in the multirotor design phase, seeking better performance and lower cost. This leaves an open problem: as what the multirotor can achieve a good performance still in the design phase. One motivation to carry out this study is justified in that there are no works related to the survey of metrics and analysis of the performance of multirotors. As well as the factor there are no ways to measure a quality of projects and possibility of comparison, since there are several ways to design a multirotor for different applications. This work proposes an approach for an analysis of the design of multirotors in terms of their flight capacity, defining as characteristics of their rotors, weight and topology. The main objective is to present a way to qualify and quantify a multirotor aircraft to optimize its design. An approach approached for design design to support design requirements (such as power size, engine torque, frame topology), ensuring as required flight capabilities. As a result of this work, a set of indexes proposed to evaluate a multirole project quality, being: flight, stability, hover and heading. The sum of these indices compose the voleability index. This index offers a possibility of comparing the vehicle analysis according to the specifications of the engine assembly, propeller, topology and frame size. For a metric validation, an analysis of the topologies was performed, allowing a comparison for the performance function and their effort.

In time series models, autoregressive processes are one of the most popular stochastic processes, which are stationary under certain conditions. In this study we consider nonstationary autoregressive models of order one, which have iid random errors. One of the important nonstationary time series models is the unit root process in AR (1), which simply implies that a shock to the system has permanent effect through time. Therefore, testing unit root is a very important problem. However, under nonstationarity, any estimator of the autoregressive coefficient does not have a known exact distribution and the usual t &ndash
statistic is not accurate even if the sample size is very large. Hence,Wiener process is invoked to obtain the asymptotic distribution of the LSE under normality. The first four moments of under normality have been worked out for large n. In 1998, Tiku and Wong proposed the new test statistics and whose type I error and power values are calculated by using three &ndash
moment chi &ndash
square or four &ndash
moment F approximations. The test statistics are based on the modified maximum likelihood estimators and the least square estimators, respectively. They evaluated the type I errors and the power of these tests for a family of symmetric distributions (scaled Student&rsquo
s t). In this thesis, we have extended this work to skewed distributions, namely, gamma and generalized logistic.

Binomial AR(1) process is a model for integer-valued time series with a fi- nite range and discrete time. It has the binomial marginal distribution and the AR(1)-like autocorrelation structure. This thesis deals with deriving some ba- sic properties of this process, methods of parameter estimation and goodness of fit testing. Three methods of parameter estimation are presented: Yule-Walker, the conditional least squares and the maximum likelihood method together with proofs of their asymptotical properties. Next, the goodness of fit testing is pre- sented. At first, two known methods based on the marginal distribution and the autocorrelation function are summarized. Then our own method is added, based on the probability generating function. Several simulations are provided to show the properties of all tests. The application of this model is illustrated on a real dataset. 1

碩士
國立高雄大學
統計學研究所
101
In this article, a portfolio selection problem with spectral risk measure is considered. The dynamics of the returns of each underlying asset is modeled by an autoregressive model of order 1. The tail dependence structure of the underlying asset-return vector is depicted by a copula function. The technique of linear programming is employed to solve the optimal asset allocation. Empirical studies are conducted for investigating the impact of the degree of risk aversion, the level of autocorrelation and the tail dependence for underlying assets on the portfolio selection problem based on the component stocks of the Taiwan 50 Index. Numerical results indicate that less risk aversion investors have higher income during a period of economic prosperity while conservative investments have less losses during a recession. However, these phenomena are unapparent if the tail dependence for underlying assets is large. In addition, a less risk aversion investment strategy receives higher earnings in an economic recovery if underlying returns are negatively autocorrelated.

碩士
國立交通大學
統計學研究所
93
For the linear regression with AR(1) errors model, a robust type generalized and feasible generalized estimators of Lai et al. (2003) of regression parameters are shown to have the desired property of robust type Gauss Markov theorem. It is done by shown that these two estimators are, respectively, the best among classes of linear trimmed means. Monte Carlo and data analysis for this technique have been performed.

碩士
淡江大學
財務金融學系碩士在職專班
95
Because of the high liquidity and lower fee, the index futures become the favorable tools for the purpose of hedging, arbitraging and speculating. In this paper, we use the weekly data of spot price and futures price from the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and the MSCI Taiwan Index to investigate the behavior of the relative price between the spot and futures. We also check the relationship between the volatility of return of both spot and futures and the relative price. The empirical results indicated that : (1) Both relative price represent high and low volatility state of the Markov process. (2) At high volatility state, the relative price represent more negative effect in the Taiwan market and more positive effect in the Singapore market. (3) The probabilities of state persistence are very high in both markets. (4) The relationship between the volatility of return and the relative price are different in both markets.

碩士
國立交通大學
統計學研究所
83
In this paper we consider Bayesian analysis of the unbalanced (general) growth curve model with AR(1) dependence, while applying the Box-Cox power transformations. We propose both parameter estimation and prediction of future values. Meanwhile, Bayesian inference by means of Gibbs sampling is also studied. Numerical results are illustrated with several sets of real and simulated data.

碩士
國立交通大學
統計學類
86
In this paper we devote ourselves to a general growth curve modelwith power transformation, random effects and AR(1) dependence via aBayesian approach. Two priors are proposed and both parameters estimationand prediction of future values are considered. Some numerical resultswith a set of real data are also given.

The hidden state Markov (HSM) model is introduced as a new conceptual framework for modelling long-term persistence in hydrological time series. Unlike the stochastic models currently used, the conceptual basis of the HSM model can be related to the physical processes that influence long-term hydrological time series in the Australian climatic regime. A Bayesian approach was used for model calibration. This enabled rigourous evaluation of parameter uncertainty, which proved crucial for the interpretation of the results. Applying the single site HSM model to rainfall data from selected Australian capital cities provided some revealing insights. In eastern Australia, where there is a significant influence from the tropical Pacific weather systems, the results showed a weak wet and medium dry state persistence was likely to exist. In southern Australia the results were inconclusive. However, they suggested a weak wet and strong dry persistence structure may exist, possibly due to the infrequent incursion of tropical weather systems in southern Australia. This led to the postulate that the tropical weather systems are the primary cause of two-state long-term persistence. The single and multi-site HSM model results for the Warragamba catchment rainfall data supported this hypothesis. A strong two-state persistence structure was likely to exist in the rainfall regime of this important water supply catchment. In contrast, the single and multi-site results for the Williams River catchment rainfall data were inconsistent. This illustrates further work is required to understand the application of the HSM model. Comparisons with the lag-one autoregressive [AR(1)] model showed that it was not able to reproduce the same long-term persistence as the HSM model. However, with record lengths typical of real data the difference between the two approaches was not statistically significant. Nevertheless, it was concluded that the HSM model provides a conceptually richer framework than the AR(1) model.
PhD Doctorate

The hidden state Markov (HSM) model is introduced as a new conceptual framework for modelling long-term persistence in hydrological time series. Unlike the stochastic models currently used, the conceptual basis of the HSM model can be related to the physical processes that influence long-term hydrological time series in the Australian climatic regime. A Bayesian approach was used for model calibration. This enabled rigourous evaluation of parameter uncertainty, which proved crucial for the interpretation of the results. Applying the single site HSM model to rainfall data from selected Australian capital cities provided some revealing insights. In eastern Australia, where there is a significant influence from the tropical Pacific weather systems, the results showed a weak wet and medium dry state persistence was likely to exist. In southern Australia the results were inconclusive. However, they suggested a weak wet and strong dry persistence structure may exist, possibly due to the infrequent incursion of tropical weather systems in southern Australia. This led to the postulate that the tropical weather systems are the primary cause of two-state long-term persistence. The single and multi-site HSM model results for the Warragamba catchment rainfall data supported this hypothesis. A strong two-state persistence structure was likely to exist in the rainfall regime of this important water supply catchment. In contrast, the single and multi-site results for the Williams River catchment rainfall data were inconsistent. This illustrates further work is required to understand the application of the HSM model. Comparisons with the lag-one autoregressive [AR(1)] model showed that it was not able to reproduce the same long-term persistence as the HSM model. However, with record lengths typical of real data the difference between the two approaches was not statistically significant. Nevertheless, it was concluded that the HSM model provides a conceptually richer framework than the AR(1) model.
PhD Doctorate

碩士
銘傳大學
應用統計資訊學系碩士班
93
We study the Bayesian analysis of AR(1) models. The priors discussed by James O. Berger & Ruo-Yong Yang (1994) and Domenico Marinucci & Lea Petrella (1999) are compared along with a new one which seems more appealing to us. Two criteria are used for the evaluation of the performance of the priors, i.e., the posterior mean square error (MSE) and frequentist coverage probability based on posterior quantiles. Our simulated results are in very close agreement with the results by James O. Berger & Ruo-Yong Yang (1994) and Marinucci & Lea Petrella (1999) for the priors considered by them. The new one, which we proposed here, seems to have a better performance than the others in view of the two criteria we used. Model selections between stationary and non-stationary models, proposed by O’Hagan (1995), is also considered for the priors. Results by Marinucci & Lea Petrella (1999) are duplicated, and we expect the new prior will demonstrate a better performance in terms of typeⅠand typeⅡerrors.

My final thesis firstly addresses basic knowledge of the theory of stochastic processes. This is firstly due to the author's effort to make the thesis more comprehensible, and also due to the need for introduction of key concepts. The autoregressive model AR(1) is defined in the thesis through basic linear time series models, and in this model, the estimation of model parameter by the method of least squares is introduced. For this estimation, the theoretical findings of the thesis are extended through the classical limit theory. Furthermore, the models with their parameter dependent on number of observations are introduced and models of NIAR (1) are defined. Classical limit theory for least squares estimation is then enriched by the limit theory in these models. The category of more general models is introduced and using the acquired knowledge, the features for the model AR (1) are derived. This thesis deals with this issue in models of NIAR (1) and its area of interest is also the bootstrap. The theoretical part of the thesis is supplemented by a practical part represented by numerical studies.

碩士
國立交通大學
統計學研究所
84
In this paper we consider a Bayesian analysis of unbalanced (general) growth curve model with random effects and AR(1) errors. Three priors are proposed and put into comparisons in parameter estimation and prediction problems.

This thesis develops the theory of continuous-time generalized AR(1) processes and presents their use for non-normal time series models. The theory is of dual interest in probability and statistics. From the probabilistic viewpoint, this study generalizes a type of Markov process which has a similar representation structure to the Ornstein-Uhlenbeck process (or continuous-time Gaussian AR(1) process). However, the stationary distributions can now have support on non-negative integers, or positive reals, or reals; the dependence structures are no longer restricted to be linear. From the statistical viewpoint, this study is dedicated to modelling unequally-spaced or equallyspaced non-normal time series with non-negative integer, or positive, or real-valued observations. The research on both the probabilistic and statistical sides contribute to a complete modelling procedure which consists of model construction, choice and diagnosis. The main contributions in this thesis include the following new concepts: self-generalized distributions, extended-thinning operators, generalized Ornstein-Uhlenbeck stochastic differential equations, continuous-time generalized AR(1) processes, generalized self-decomposability, generalized discrete self-decomposability, P-P plots and diagonal P-P plots. These concepts play crucial roles in the newly developed theory. We take a dynamic view to construct the continuous-time stochastic processes. Part II is devoted to the construction of the continuous-time generalized AR(1) process, which is obtained from the generalized Ornstein-Uhlenbeck stochastic differential equation, and the proposed stochastic integral. The resulting continuous-time generalized AR(1) process consists of a dependent term and an innovation term. The dependent term involves an extended-thinning stochastic operation which generalizes the commonly used operation of constant multiplier. Such a Markov process can have a simple interpretation in modelling non-normal time series. In addition, the family of continuoustime generalized AR(1) processes is surprisingly rich. Both stationary and non-stationary situations of the process are considered. In Part III, we answer the question of what kind of stationary distributions are obtained from the family of continuous-time generalized AR(1) processes, as well as the converse question of whether a specific distribution can be the stationary distribution of a continuous-time generalized AR(1) process. This leads to the characterization of distributions according to the extendedthinning operations. The characterization results are meaningful in statistical modelling, because under steady state, the marginal distributions of a Markov process are the same as the stationary distribution. They will guide us to choose appropriate processes to model a non-normal time series. The probabilistic study also shows that the autocorrelation function is of exponential form in the time difference, like that of the Ornstein-Uhlenbeck or Ornstein-Uhlenbeck-type process. Part IV deals with statistical inference and modelling. We have studied parameter estimation for various situations such as equally-spaced time, unequally-spaced time, finite marginal mean, infinite marginal mean, and so on. The graphical tools, the P-P plot and diagonal P-P plot, are proposed for use in identifying the marginal distribution and serial dependence, and diagnosing the fitted model. Three data examples are given to illustrate the new modelling procedure, and the application capacity of this theory of continuous-time generalized AR(1) processes. These time series are non-negative integer or positive-valued, with equally-spaced or unequally-spaced time observations.