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Dissertação de mestrado em Estatística para Ciência de Dados, A esperança de vida tem vindo a aumentar ao longo dos anos, sendo por isso necessário atualizar as tábuas de mortalidade da população portuguesa. Nestas constam indicadores bastante importantes como a taxa de mortalidade e a esperança média de vida e, através de algumas funções que constam nas mesmas, é também possível calcular as taxas vitalícias dos pensionistas de modo a realizar um cálculo mais correto das responsabilidades da companhia. O objetivo deste trabalho é construir tábuas geracionais, que modelem o comportamento da população portuguesa, e pretende-se também desenvolver modelos que permitam estimar os fatores a serem utilizados para o cálculo das pensões vitalícias no ramo de Acidentes de Trabalho. Inicialmente os dados a modelar são referentes à população portuguesa e, em seguida, é efetuado o ajustamento aos dados específicos do mercado segurador. Com o objetivo de construir as tábuas de mortalidade, inicialmente é necessário modelar a mortalidade, utilizando métodos como o Método Lee-Carter e o Modelo de Poisson (ou Extensão do Método Lee-Carter). Para modelar e prever as séries temporais subjacentes às taxas de mortalidade, são utilizados modelos de previsão de séries temporais paramétricos (Modelação ARIMA) e não paramétricos (Método de Holt). Por fim, são modeladas as taxas de mortalidade da população da companhia, de modo a comparar as taxas obtidas na população portuguesa e na população da companhia, para entender se o comportamento dos pensionistas é semelhante ao da população portuguesa. Esta comparação é feita através do cálculo de medidas de avaliação, nomeadamente o EQM, o REQM, o EPAM, o EAM e a estatística U de Theil., Life expectancy has been increasing over the years and it is therefore necessary to update the mortality tables for the Portuguese population. These tables contain very important indicators such as the mortality rate and the life expectancy and through some functions that are included in them, it is also possible to calculate the lifetime rates of pensioners in order to make a more accurate calculation of the company’s liabilities. The objective of this work is to build generational tables that model the behavior of the Portuguese population and also to develop models that allow estimating the factors to be used to calculate the life annuities in the Work Accidents branch. Initially, the data to be modeled refers to the Portuguese population and, then, the adjustment is made to the specific data of the insurance market. In order to construct the life tables, it is initially necessary to model mortality, using methods such as the Lee-Carter Method and the Poisson Model (or Extension of the Lee-Carter Method). To model and forecast the time series underlying the mortality rates, both parametric (ARIMA Modeling) and non parametric (Holt’s Method) time series forecasting models are used. Finally, the mortality rates of the company’s population are modeled, in order to compare the rates obtained in the Portuguese population and in the company population, to understand if the behavior of the pensioners is similar to that of the Portuguese population. This comparison is made by calculating evaluation measures, namely the MSE, the RMSE, the MAPE, the MAE and Theil’s U statistic.

Modeling and forecasting international migration are significant research areas since migration forecasts are vital in decision making and policy design regarding economy, security, society, and resource allocation. The methods for modeling and forecasting migration rely on strict subjective or statistical assumptions which may not always be met. In addition, lack of a universally accepted definition of the term “migrant” and the ambiguities in data due to recording and collection systems result in inconsistencies and vagueness in migration modeling. Considering these, in this paper, a fuzzy bi-level age-specific migration modeling method is proposed. The bi-level structure embedded in the model makes use of the well-known Lee-Carter method as well as fuzzy regression, singular value decomposition technique, and hierarchical clustering to reflect the general characteristics of the country of concern together with the distinct emigration and immigration behaviors of the age groups. Bayesian time series models are fitted to the time-variant fuzzy parameters obtained through the proposed method to forecast future migration values. The proposed method is applied on female and male age-specific emigration and immigration counts of Finland for 1990–2010 period and Germany for 1995–2012 period, and the future values are forecasted for 2011–2025 and 2013–2025 respectively. The method is compared with an existing Bayesian approach and the numerical findings display that the proposed fuzzy method is superior to the existing one in modeling and forecasting age-specific migration values within significantly narrower prediction intervals. © 2018 Elsevier Ltd

BACKGROUNDWith the rapid aging of the population, mortality forecasting becomes increasingly important, especially for the insurance and pension industries. However, a wide variety of projection methods are in use, both between and within countries, that produce different outcomes.OBJECTIVEWe review the different mortality forecasting methods and their assumptions in Europe, and assess their impact on projections of future life expectancy for the Netherlands.METHODSFor the Netherlands, we assess the projections of life expectancy at birth (e0) and at age 65 (e65) up to 2050 resulting from different methods using similar explicit assumptions regarding the historical period and the jump-off rates. We compare direct linear extrapolation, the Lee-Carter model, the Li-Lee model, a cohort model, separate projections of smoking-and non-smoking-related mortality, and the official forecast.RESULTSIn predicting mortality, statistical offices in Europe mostly use simple linear extrapolation methods. Countries with less linear trends employ other approaches or different assumptions. The approaches used in the Netherlands include explanatory models, the separate projection of smoking-and non-smoking-related mortality, and the projection of the age profile of mortality. There are clear differences in the explicit assumptions used, including assumptions regarding the historical period. The resulting e0 in 2050 varies by approximately six years. Using the same historical period (1970-2009) and the observed jump-off rates, the findings generated by different methods result in a range of 2.1 years for women and of 1.8 years for men. For e65, the range is 1.4 and 1.9 years, respectively.CONCLUSIONSAs the choice of the explicit assumptions proved to be more important than the choice of the forecasting method, the assumptions should be carefully considered when forecasting mortality.

The increase in life expectancy registered in the last decades in Brazil was one of the most important achievements of society and brought new challenges in several areas of human knowledge. In order to know the future behavior of life expectancy, the goal of this work was to project the mortality of the Brazilian Semi-Arid from 2015 to 2050. The following methodological steps were performed: obtaining the correction factors of the deaths. Construction of complete Mortality Tables, assembling of databases with the age structure of annual mortality rates from 1980 to 2014, application of the Lee-Carter method for projection of mortality levels and patterns. This method combines a demographic model with a time series model. The projected life expectancies for the year 2050 for the Semi-arid States ranged from 78.25 to 83.82 years. It was concluded that the method produced plausible estimates of mortality levels and standards for most of the geographical areas of the Semi-Arid States, whose Mortality Tables produced may constitute important subsidies in the planning of health and welfare actions and in decision making for the populations of the Semiarid. O aumento da expectativa de vida registrada nas últimas décadas no Brasil foi uma das mais importantes conquistas da sociedade e trouxe novos desafios em diversas áreas do conhecimento humano. Com o intuito de conhecer o comportamento futuro da expectativa de vida, o objetivo deste trabalho consistiu em projetar a mortalidade do Semiárido brasileiro de 2015 a 2050. Os seguintes passos metodológicos foram executados: obtenção dos fatores de correção dos óbitos; construção de Tábuas de Mortalidade completa; montagem dos bancos de dados com a estrutura etária das taxas de mortalidade anual de 1980 a 2014; aplicação do método de Lee-Carter para projeção dos níveis e padrões de mortalidade. Este método combina um modelo demográfico com um modelo de séries temporais. As expectativas de vida projetadas para o ano 2050 para os Estados do Semiárido variaram de 78,25 a 83,82 anos. Concluiu-se que o método produziu estimativas plausíveis dos níveis e padrões de mortalidade para a maioria dos espaços geográficos dos Estados do Semiárido, cujas Tábuas de Mortalidade produzidas podem se constituir em importantes subsídios no planejamento das ações em saúde e previdência e na tomada de decisão para as populações do Semiárido.

Mortality is different across countries, states and regions. Several empirical research works however reveal that mortality trends exhibit a common pattern and show similar structures across populations. The key element in analyzing mortality rate is a time-varying indicator curve. Our main interest lies in validating the existence of the common trends among these curves, the similar gender differences and their variability in location among the curves at the national level. Motivated by the empirical findings, we make the study of estimating and forecasting mortality rates based on a semi-parametric approach, which is applied to multiple curves with the shape-related nonlinear variation. This approach allows us to capture the common features contained in the curve functions and meanwhile provides the possibility to characterize the nonlinear variation via a few deviation parameters. These parameters carry an instructive summary of the time-varying curve functions and can be further used to make a suggestive forecast analysis for countries with barren data sets. In this research the model is illustrated with mortality rates of Japan and China, and extended to incorporate more countries. All numerical procedures are transparent and reproduced on www.quantlet.de.

Using the age- and sex-specific data of 14 developed countries, we compare the point and interval forecast accuracy and bias of ten principal component methods for forecasting mortality rates and life expectancy. The ten methods are variants and extensions of the Lee-Carter method. Based on one-step forecast errors, the weighted Hyndman-Ullah method provides the most accurate point forecasts of mortality rates and the Lee-Miller method is the least biased. For the accuracy and bias of life expectancy, the weighted Hyndman-Ullah method performs the best for female mortality and the Lee-Miller method for male mortality. While all methods underestimate variability in mortality rates, the more complex Hyndman-Ullah methods are more accurate than the simpler methods. The weighted Hyndman-Ullah method provides the most accurate interval forecasts for mortality rates, while the robust Hyndman-Ullah method provides the best interval forecast accuracy for life expectancy.

Mortality is different across countries, states and regions. Several empirical research works however reveal that mortality trends exhibit a common pattern and show similar structures across populations. The key element in analyzing mortality rate is a time-varying indicator curve. Our main interest lies in validating the existence of the common trends among these curves, the similar gender differences and their variability in location among the curves at the national level. Motivated by the empirical findings, we make the study of estimating and forecasting mortality rates based on a semi-parametric approach, which is applied to multiple curves with the shape-related nonlinear variation. This approach allows us to capture the common features contained in the curve functions and meanwhile provides the possibility to characterize the nonlinear variation via a few deviation parameters. These parameters carry an instructive summary of the time-varying curve functions and can be further used to make a suggestive forecast analysis for countries with barren data sets. In this research the model is illustrated with mortality rates of Japan and China, and extended to incorporate more countries. All numerical procedures are transparent and reproduced on www.quantlet.de.

Human mortality modeling and forecasting are important study fields since mortality rates are ebential in financial and social policy making. Among many others, Lee Carter (LC) model is one of the most popular stochastic method in mortality forecasting. Koibi and Shapiro fuzzified the standard LC model and eliminated the abumptions of homoscedasticity and the ambiguity on the size of the error term variances. In this study, a modified version of fuzzy LC model incorporating singular value decomposition (SVD) technique is proposed. Utilizing SVD instead of ordinary least squares in the fuzzy LC model allows the model to capture existing fluctuations in mortality rates and yields a better fit. The proposed method is applied to Finland mortality data for years 1925 to 2009. The results are compared with Koibi and Shapiro's fuzzy LC method and the standard LC method. Numerical findings show that proposed method gives statistically better results in generating small spreads and in estimating mortality rates when compared with Koibi and Shapiro's method. © Copyright 2015 by SCITEPRESS - Science and Technology Publications, Lda. Institute for Systems and Technologies of Information, Control and Communication (INSTICC) 7th International Joint Conference on Computational Intelligence, IJCCI 2015 -- 12 November 2015 through 14 November 2015 -- -- 117187

We present a new mortality projection methodology that distinguishes smoking- and non-smoking-related mortality and takes into account mortality trends of the opposite sex and in other countries. We evaluate to what extent future projections of life expectancy at birth (e 0) for the Netherlands up to 2040 are affected by the application of these components. All-cause mortality and non-smoking-related mortality for the years 1970–2006 are projected by the Lee-Carter and Li-Lee methodologies. Smoking-related mortality is projected according to assumptions on future smoking-attributable mortality. Projecting all-cause mortality in the Netherlands, using the Lee-Carter model, leads to high gains in e 0 (4.1 for males; 4.4 for females) and divergence between the sexes. Coherent projections, which include the mortality experience of the other 21 sex- and country-specific populations, result in much higher gains for males (6.4) and females (5.7), and convergence. The separate projection of smoking and non-smoking-related mortality produces a steady increase in e 0 for males (4.8) and a nonlinear trend for females, with lower gains in e 0 in the short run, resulting in temporary sex convergence. The latter effect is also found in coherent projections. Our methodology provides more robust projections, especially thanks to the distinction between smoking- and non-smoking-related mortality.

Dissertation thesis creates a complex and modern scheme for stochastic modeling of demographic processes, which is universally applicable to any population in the world. All calculations are described in detail on the data of the Czech Republic. Throughout the work the attention is drawn to the issues, that every analyst must necessarily take into account in order to obtain correct results. Data comes mostly from the Czech Statistical Office database. However, some data matrices had to be calculated for the purposes of the thesis. Particular demographic processes (mortality, fertility and migration) are modeled using selected modern approaches (ARIMA models, Lee-Carter method) and based on the constructed models these processes are forecasted to the future. Using partially projected results a comprehensive demographic projection of the population of the Czech Republic is created up to the year 2050. However, not on the basis of the current state and expert expectations of the future development, but based on sophistically projected demographic events, which are explained using the trends and main components of their previous development. This demographic projection is created in three scenarios (marked SC1, SC2 and SC3), which are made from selected optimal models, presented in particular sections of the work. One part of the thesis is also the backward retropolation of age-specific number of net migrants by sex in the Czech Republic since 1948. On its basis the analysis and prediction of the migration can be done. The thesis is a synthesis of the projections of demographic processess of mortality, fertility, and migration. Final results are confronted with three scenarios of population projections of the Czech Republic created by the Czech Statistical Office and five scenarios of population projections by Eurostat. The purely statistical approach of demographic forecasting in comparison with deterministic models and expert expectations has its positives and negatives. Therefore, the different results due to various methodological approaches are discussed and compared in the conclusion of the thesis.

China's life expectancy at birth is currently being debated; the 2010 census data may exaggerate the figure and its rate of increase. In this paper, with an extension of the Lee-Carter method for limited data, we use China's 1982, 1990 and 2000 censuses to forecast the mortality pattern and life expectancy for the 2000 to 2030 period. We find that the annual increase in life expectancy from 2000 to 2030 is predicted to be 0.18 years for males, and 0.23 years for females, and the infant mortality rate is predicted to decline to 10.39‰ in 2030 for males, and to 20.32‰ for females. This work is jointly supported by the 985-3 Project of Xi’an Jiaotong University and the Spanish Ministry of Economy and Competitiveness (CSO2012-31206)

Ölüm oranı tahminleri özellikle sosyal güvenlik ile emeklilik sistemlerinin, özel sigorta planlarının gelecekteki finansal durumunun değerlendirilmesinde kullanılmakta, aktüeryal hesaplamaların başlıca bileşeni olarak bu planların finansal istikrarının sağlanmasında önemli bir yer teşkil etmektedir. Oldukça eski bir geçmişe sahip olan ölüm oranı tahmin yöntemleri deterministik ve stokastik yöntemler olarak sınıflandırılabilmektedir. Deterministik modellerin ardından son yıllarda yaşanan demografik değişimle paralel olarak ölümlülük düzeylerinin daha sağlıklı değerlendirilerek, doğru ve güvenilir ölüm oranı projeksiyon modellerinin oluşturulması amacıyla stokastik modellerin ortaya çıktığı görülmektedir. Çalışmada, deterministik ölüm oranı tahmin yöntemlerinden Trend yöntemi ve stokastik yöntemlerden Lee-Carter yöntemi kullanılarak Türkiye il ve ilçe merkezlerinin nüfus ve ölüm istatistiklerine dayanan ölüm oranı tahminleri elde edilmiş ve sonuçlar karşılaştırılmıştır., Mortality forecasts are especially used to evaluate the future security of retirement and social security systems, private insurance plans etc. These forecasts are taking an important place providing a financial stability as a principal component of actuarial calculations. Mortality forecasting methods having a considerably old history can be categorized as deterministic and stochastic methods. After deterministic models, it is seen that stochastic models have emerged with a view to constituting a more accurate and reliable mortality forecasting models making a more robust assessment of mortality profile in parallel with the demographic change in recent years. In this study, mortality forecasts based on population and death statistics special to province and district centers of Turkey are obtained using one of the deterministic methods called as Trend method and one of the stochastic methods called as Lee-Carter method.

Predecir adecuadamente el proceso de envejecimiento de la población es una preocupación no sólo de países desarrollados sino también de naciones en desarrollo que observan con preocupación el acelerado proceso de transición demográca de los últimos 50 años. La inquietud se origina en las repercusiones económicas y sociales que se derivan de una población que envejece. El sostenimiento de las personas mayores es un tema central que no da espera. Este trabajo realiza una proyección del gasto fiscal en pensiones para un horizonte de 50 años a través de la estimación de la población colombiana basada en la proyección de las tasas de mortalidad y fecundidad bajo dos escenarios diferentes, con y sin sobre-mortalidad masculina. Se proyecta el costo en pensiones en aumento superando 10% del PIB para 2050, siendo menor en el escenario sin sobre mortalidad. Lo que implica que disminuir la sobre mortalidad e incentivar el mercado laboral formal se constituyen en retos para la política social si el objetivo es controlar el gasto en pensiones. / Abstract. The right prediction of aging process concerns not only developed countries but also developing nations because of the accelerated process of demographic transition occurred in the last 50 years. The support of elderly people is a central issue that can not wait. The economic and social impacts from an aging population is the cause of the concern. This work makes a projection of fiscal expenditure on pensions based on an estimate of mortality rates in Colombia under two dierent settings, with and without male overmortality, nding that the expected expenditure increases with time exceeding 10% of GDP in 2050. Without overmortality the expenditure decreases. Therefore, whether the objective is to control the expenditure in public pensions, some challenges for social politics are reducing over mortality and stimulating formal employment. Maestría

After a comparative study of the Lee-Carter forecasting method and looking into the direct extrapolation of mortality by age and sex, this paper advocates the use of the latter method. The method is, however, supplemented by additional procedures in order to improve its efficiency in the short run and preclude implausible mortality patterns in the long run. The short-run efficiency is improved by building the forecast on data from the most recent periods of age/sex-specific duration, when the mortality dynamics exhibit a steady trend. In the long run, the rates of the decline in mortality are assumed to converge to a plausible function of age and sex, which is derived from the data based on the assumption that it is a monotonic function of age. The framework proposed also provides a natural basis for developing multi-regional projection methods and also for introducing uncertainty into the projection.

Summary The Lee–Carter method for modeling and forecasting mortality has been shown to work quite well given long time series of data. Here we consider how it can be used when there are few observations at uneven intervals. Assuming that the underlying model is correct and that the mortality index follows a random walk with drift, we find the method can be used with sparse data. The central forecast depends mainly on the first and last observation, and so can be generated with just two observations, preferably not too close in time. With three data points, uncertainty can also be estimated, although such estimates of uncertainty are themselves highly uncertain and improve with additional observations. We apply the methods to China and South Korea, which have 3 and 20 data points, respectively, at uneven intervals. Resume La methode Lee–Carter de modelisation et de prevision de la mortalite a prouve son bon fonctionnement avec des series de donnees existant sur une longue periode. Nous envisageons ici son utilisation lorsqu'on ne dispose que de quelques observations a intervalles irreguliers. En supposant que le modele sous-jacent est correct et que l'indice de mortalite suit une marche aleatoire avec derive, nous trouvons que cette methode peut eetre utilisee avec des donnees eparses. La prevision centrale depend alors principalement de la premiere et de la derniere observation. Elle peut donc eetre generee a partir de deux observations seulement, de preference pas trop proches dans le temps. Avec trois points, on peut aussi estimer l'alea, bienqu'un tel estimateur de l'alea soit lui-meeme tres aleatoire. Il s'ameliore cependant lorsqu'on dispose d'observations supplementaires. Nous appliquons notre methode ala Chine et a la Coree du Sud, pour lesquelles nous avons respectivement 3 et 20 points aintervalles irreguliers.

We compare the short- to medium- term accuracy of five variants or extensions of the Lee-Carter method for mortality forecasting. These include the original Lee-Carter, the Lee-Miller and Booth-Maindonald-Smith variants, and the more flexible Hyndman-Ullah and De Jong-Tickle extensions. These methods are compared by applying them to sex-specific populations of 10 developed countries using data for 1986–2000 for evaluation. All variants and extensions are more accurate than the original Lee-Carter method for forecasting log death rates, by up to 61%. However, accuracy in log death rates does not necessarily translate into accuracy in life expectancy. There are no significant differences among the five methods in forecast accuracy for life expectancy.