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建構台灣壽險業解約率期限結構 / Construction of the Term Structure of Lapse Rates - Experiences from Taiwan.杜於叡 Unknown Date (has links)
過去有相當多的文獻針對解約率建立模型,但由於資料取得之困難,鮮少文獻針對不同保單年度之解約率進行分析,本研究將以台灣壽險業資料分析不同保單年度之解約率行為,期望能找出解約率之期限結構,提供壽險業者訂價或風險管理之參考依據。
本研究使用台灣壽險業1987年至2011年間之生死合險及終身壽險資料,透過資料分析顯示兩險種之解約率關聯性不大,且應將繳別分為三類進行分析,分別為不分繳別、月繳及年繳和半年繳及季繳三類,針對各保單年度進行主成分分析,結果顯示皆需6至8個主成分方可達到90%之解釋力,並透過ARMA模型檢驗選定之主成分與總體經濟變數間之關聯性,進而觀察是否符合利率假說及緊急資金假說,最後透過VAR模型或ARMA模型模擬總體經濟變數和各主成分之分數,並利用主成分分析之結果將主成分分數轉換回保單年度變數,完成各保單年度解約率之模擬,建構出台灣壽險業解約率之期限結構。
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GARMA models, a new perspective using Bayesian methods and transformationsAndrade, Breno Silveira de 16 December 2016 (has links)
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Previous issue date: 2016-12-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Generalized autoregressive moving average (GARMA) models are
a class of models that was developed for extending the univariate
Gaussian ARMA time series model to a flexible observation-driven
model for non-Gaussian time series data. This work presents
the GARMA model with discrete distributions and application of
resampling techniques to this class of models. We also proposed The
Bayesian approach on GARMA models. The TGARMA (Transformed
Generalized Autoregressive Moving Average) models was proposed,
using the Box-Cox power transformation. Last but not least we
proposed the Bayesian approach for the TGARMA (Transformed
Generalized Autoregressive Moving Average). / Modelos Autoregressivos e de médias móveis generalizados
(GARMA) são uma classe de modelos que foi desenvolvida para
extender os conhecidos modelos ARMA com distribuição Gaussiana
para um cenário de series temporais não Gaussianas. Este trabalho
apresenta os modelos GARMA aplicados a distribuições discretas,
e alguns métodos de reamostragem aplicados neste contexto. É
proposto neste trabalho uma abordagem Bayesiana para os modelos
GARMA. O trabalho da continuidade apresentando os modelos
GARMA transformados, utilizando a transformação de Box-Cox. E por
último porém não menos importante uma abordagem Bayesiana para
os modelos GARMA transformados.
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Sur les tests lisses d'ajustement dans le context des series chronologiquesTagne Tatsinkou, Joseph Francois 12 1900 (has links)
La plupart des modèles en statistique classique repose sur une hypothèse sur
la distribution des données ou sur une distribution sous-jacente aux données. La
validité de cette hypothèse permet de faire de l’inférence, de construire des intervalles
de confiance ou encore de tester la fiabilité du modèle. La problématique
des tests d’ajustement vise à s’assurer de la conformité ou de la cohérence de
l’hypothèse avec les données disponibles. Dans la présente thèse, nous proposons
des tests d’ajustement à la loi normale dans le cadre des séries chronologiques
univariées et vectorielles. Nous nous sommes limités à une classe de séries chronologiques
linéaires, à savoir les modèles autorégressifs à moyenne mobile (ARMA
ou VARMA dans le cas vectoriel).
Dans un premier temps, au cas univarié, nous proposons une généralisation du
travail de Ducharme et Lafaye de Micheaux (2004) dans le cas où la moyenne est
inconnue et estimée. Nous avons estimé les paramètres par une méthode rarement
utilisée dans la littérature et pourtant asymptotiquement efficace. En effet, nous
avons rigoureusement montré que l’estimateur proposé par Brockwell et Davis
(1991, section 10.8) converge presque sûrement vers la vraie valeur inconnue du
paramètre. De plus, nous fournissons une preuve rigoureuse de l’inversibilité de
la matrice des variances et des covariances de la statistique de test à partir de
certaines propriétés d’algèbre linéaire. Le résultat s’applique aussi au cas où la
moyenne est supposée connue et égale à zéro. Enfin, nous proposons une méthode
de sélection de la dimension de la famille d’alternatives de type AIC, et nous
étudions les propriétés asymptotiques de cette méthode. L’outil proposé ici est
basé sur une famille spécifique de polynômes orthogonaux, à savoir les polynômes
de Legendre.
Dans un second temps, dans le cas vectoriel, nous proposons un test d’ajustement
pour les modèles autorégressifs à moyenne mobile avec une paramétrisation
structurée. La paramétrisation structurée permet de réduire le nombre élevé de paramètres dans ces modèles ou encore de tenir compte de certaines contraintes
particulières. Ce projet inclut le cas standard d’absence de paramétrisation. Le
test que nous proposons s’applique à une famille quelconque de fonctions orthogonales.
Nous illustrons cela dans le cas particulier des polynômes de Legendre
et d’Hermite. Dans le cas particulier des polynômes d’Hermite, nous montrons
que le test obtenu est invariant aux transformations affines et qu’il est en fait
une généralisation de nombreux tests existants dans la littérature. Ce projet peut
être vu comme une généralisation du premier dans trois directions, notamment le
passage de l’univarié au multivarié ; le choix d’une famille quelconque de fonctions
orthogonales ; et enfin la possibilité de spécifier des relations ou des contraintes
dans la formulation VARMA.
Nous avons procédé dans chacun des projets à une étude de simulation afin
d’évaluer le niveau et la puissance des tests proposés ainsi que de les comparer
aux tests existants. De plus des applications aux données réelles sont fournies.
Nous avons appliqué les tests à la prévision de la température moyenne annuelle
du globe terrestre (univarié), ainsi qu’aux données relatives au marché du travail
canadien (bivarié).
Ces travaux ont été exposés à plusieurs congrès (voir par exemple Tagne,
Duchesne et Lafaye de Micheaux (2013a, 2013b, 2014) pour plus de détails). Un
article basé sur le premier projet est également soumis dans une revue avec comité
de lecture (Voir Duchesne, Lafaye de Micheaux et Tagne (2016)). / Several phenomena from natural and social sciences rely on distribution’s assumption
among which the normal distribution is the most popular. The validity
of that assumption is useful to setting up forecast intervals or for checking model
adequacy of the underlying model. The goodness-of-fit procedures are tools to
assess the adequacy of the data’s underlying assumptions. Autoregressive and moving
average time series models are often used to find the mathematical behavior
of these phenomena from natural and social sciences, and especially in the finance
area. These models are based on some assumptions including normality distribution
for the innovations. Normality assumption may be helpful for some testing
procedures. Furthermore, stronger conclusions can be drawn from the adjusted
model if the white noise can be assumed Gaussian. In this work, goodness-of-fit
tests for checking normality for the innovations from autoregressive moving average
time series models are proposed for both univariate and multivariate cases
(ARMA and VARMA models).
In our first project, a smooth test of normality for ARMA time series models
with unknown mean based on a least square type estimator is proposed.
We derive the asymptotic null distribution of the test statistic. The result here
is an extension of the paper of Ducharme et Lafaye de Micheaux (2004), where
they supposed the mean known and equal to zero. We use the least square type
estimator proposed by Brockwell et Davis (1991, section 10.8) and we provide a
rigorous proof that it is almost surely convergent. We show that the covariance
matrix of the test is nonsingular regardless if the mean is known. We have also
studied a data driven approach for the choice of the dimension of the family and
we gave a finite sample approximation of the null distribution. Finally, the finite
and asymptotic sample properties of the proposed test statistic are studied via a
small simulation study.
In the second project, goodness-of-fit tests for checking multivariate normality
for the innovations from vector autoregressive moving average time series
models are proposed. Since these time series models may rely on a large number
of parameters, structured parameterization of the functional form is allowed. The
methodology also relies on the smooth test paradigm and on families of orthonormal
functions with respect to the multivariate normal density. It is shown that
the smooth tests converge to convenient chi-square distributions asymptotically.
An important special case makes use of Hermite polynomials, and in that situation
we demonstrate that the tests are invariant under linear transformations.
We observed that the test is not invariant under linear transformations with Legendre
polynomials. A consistent data driven method is discussed to choose the
family order from the data. In a simulation study, exact levels are studied and
the empirical powers of the smooth tests are compared to those of other methods.
Finally, an application to real data is provided, specifically on Canadian labour
market data and annual global temperature.
These works were exposed at several meeting (see for example Tagne, Duchesne
and Lafaye de Micheaux (2013a, 2013b, 2014) for more details). A paper
based on the first project is submitted in a refereed journal (see Duchesne, Lafaye
de Micheaux et Tagne (2016)).
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Tests d'ajustement reposant sur les méthodes d'ondelettes dans les modèles ARMA avec un terme d'erreur qui est une différence de martingales conditionnellement hétéroscédastiqueLiou, Chu Pheuil 09 1900 (has links)
No description available.
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MODELO BETA AUTORREGRESSIVO DE MÉDIAS MÓVEIS: CRITÉRIOS DE SELEÇÃO E APLICAÇÕESGuerra, Renata Rojas 27 February 2015 (has links)
Time series modeling and forecasting has many applicability in scientific and technological
researchs. Specifically about variables restricted to the interval (0; 1), which includes
rates and proportions, the classical regression models could not be suitable because they assume
normality. In this context, Rocha and Cribari-Neto (2009) proposed the beta autoregressive
moving average (βARMA) model. It admits that the variable of interest is beta distributed. The
beta distribution is more flexible than the normal distribution and also assumes that de dependent
variable is restricted to the interval (0; 1). Through βARMA is possible to obtain results
closer to the nature of the data. But just choose the better parametric model does not guarantee
the accuracy of the fitted model. To identify the lags is also relevant to ensure the accuracy of
the adjusted model. It is in this purpose that the model selection criteria, or information criteria,
were developed. They compare the explanatory capacity of a group of models and select,
among this group, the model which minimizes the information loss. In this context, this paper
aims to evaluate by Monte Carlo simulations the performance of different selection criteria in
βARMA model. Considering several scenarios and sample sizes, the selection criteria evaluated
was AIC, BIC, HQ, AICc, BICc and HQc. The results indicate that BICc, HQ and HQc had the
better performance identifying the true model among the candidate models. Using the selection
criteria indicated by the simulation study, were also adjusted βARMA models to real data. It
were considered the credit delinquency and the relationship between payroll loan and individual
credit, both variables are from national financial system. It was adjusted the classical ARIMA
models too. This models were compared with βARMA in applications. For both variables was
found a reasonable proximity between the original data and the predicted by the models, with
advantage for βARMA, as much inside as outside the sample. / A modelagem e a previsão de séries temporais é um campo de ampla aplicabilidade em diversas áreas científicas e tecnológicas. No âmbito específico de variáveis restritas ao intervalo
(0; 1), como taxas e proporções, a utilização de modelos clássicos, que supõem normalidade da variável de interesse, pode não ser adequada. Neste contexto, Rocha e Cribari-Neto (2009)
propuseram o modelo beta autorregressivo de médias móveis (β
ARMA). Por assumir que a variável de interesse possui distribuição beta, que é uma distribuição mais flexível que a normal
e com suporte restrito ao intervalo (0; 1), o βARMA possibilita modelagens e previsões mais condizentes com a natureza desses dados. Contudo, apenas a escolha do modelo paramétrico
mais adequado não garante a acurácia do modelo ajustado. A identificação das defasagens a serem incluídas também exerce um papel de relevância neste sentido. É neste propósito que foram
desenvolvidos os critérios de seleção de modelos, ou critérios de informação. Estes comparam as capacidades de explicação entre um grupo de modelos candidatos e selecionam, dentro deste
grupo, o modelo que minimiza a perda de informações. Diante do exposto, este trabalho tem o objetivo de avaliar, via simulações de Monte Carlo, o desempenho de diferentes critérios de seleção
no modelo βARMA. Por meio de um extenso estudo de simulação, considerando diversos cenários e tamanhos amostrais, foram avaliados os desempenhos em amostras de tamanho finito
dos critérios AIC, BIC, HQ, AICc, BICc e HQc. Como resultados numéricos gerais, destaca-se que os critérios HQ, BICc e HQc foram os que alcançaram os melhores níveis de identificação
do modelo verdadeiro. Utilizando os critérios de seleção sugeridos no estudo de simulação também foram ajustados modelos βARMA a dados reais. Para isso, foram considerados o índice
de inadimplência de crédito e a relação entre o crédito consignado e o crédito total pessoa física, ambos do Sistema Financeiro Nacional. Também foram ajustados os clássicos modelos
ARIMA comparativamente ao modelo βARMA na realização de previsões e posterior comparação entre os resultados de ambas as aplicações. Para as duas variáveis há um grau razoável de
proximidade entre os dados originais e previstos, com superioridade do βARMA tanto dentro quanto fora do conjunto de observações utilizado para estimação dos modelos.
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