Uncertainty in Mortality Forecasting: An Extension to the Classical Lee-Carter Approach

2009 ◽  
Vol 39 (1) ◽  
pp. 137-164 ◽  
Author(s):  
Johnny Siu-Hang Li ◽  
Mary R. Hardy ◽  
Ken Seng Tan
Keyword(s):  
Individual Differences ◽  
Selection Criteria ◽  
Financial Risk ◽  
Goodness Of Fit ◽  
Mortality Data ◽  
Model Structure ◽  
Death Rates ◽  
Mortality Forecasting ◽  
Mortality Improvement ◽  
Carter Model

AbstractTraditionally, actuaries have modeled mortality improvement using deterministic reduction factors, with little consideration of the associated uncertainty. As mortality improvement has become an increasingly significant source of financial risk, it has become important to measure the uncertainty in the forecasts. Probabilistic confidence intervals provided by the widely accepted Lee-Carter model are known to be excessively narrow, due primarily to the rigid structure of the model. In this paper, we relax the model structure by considering individual differences (heterogeneity) in each age-period cell. The proposed extension not only provides a better goodness-of-fit based on standard model selection criteria, but also ensures more conservative interval forecasts of central death rates and hence can better reflect the uncertainty entailed. We illustrate the results using US and Canadian mortality data.

scholarly journals Modelling and Prediction of the Gross Mortality Rate in Ecuador

2018 ◽  
Vol 6 (3) ◽  
Author(s):  
Mónica Mite ◽  
Sandra Garcia-Bustos ◽  
Marcela Pincay ◽  
Ana Debón ◽  
Francisco Santoja
Keyword(s):  
Mortality Rate ◽  
Cohort Effect ◽  
Mortality Data ◽  
Arima Models ◽  
Men And Women ◽  
Mortality Forecasting ◽  
Basic Model ◽  
Adjusted Model ◽  
Age Range ◽  
Carter Model

This paper presents the results obtained from the modelling of the mortality data in Ecuador from 1990 to 2010, using the StMoMo library in the open source programming language R. This library was developed based on the Generalized Age-Period-Cohort Models (GAPC), among which is the Lee-Carter model, which has been widely applied in the actuarial area. The gross mortality rate of men and women in an age range of 1 to 85 years was modelled for the data of Ecuador, in the period 1990-2010. Of a total of eight models, two models have been selected because they present a good fit of the data for both genders. The first is the basic model of Lee-Carter and the second, the Plat model, which incorporates the cohort effect. A comparison was made with the two models to determine which one has a better forecast in a horizon of 20 years for specific ages. Both models show and predict the decrease in mortality in Ecuador of both genders, a decrease that is more pronounced, in general, for women at certain ages. In determining the uncertainty of the models, the bootstrap technique was used to define the confidence intervals of the adjusted model. The GAPC and ARIMA models were also compared; the former improve the mortality forecasting.

A quantitative comparison of simulation strategies for mortality projection

2014 ◽  
Vol 8 (2) ◽  
pp. 281-297 ◽  
Author(s):  
Jackie Li
Keyword(s):  
New Zealand ◽  
Life Expectancy ◽  
Quantitative Comparison ◽  
Mortality Data ◽  
Death Rates ◽  
Mortality Projection ◽  
Mortality Index ◽  
Carter Model

AbstractWe compare quantitatively six simulation strategies for mortality projection with the Poisson Lee–Carter model. We test these strategies on New Zealand mortality data and discuss the simulated results of the mortality index, death rates, and life expectancy.

scholarly journals Hybrid of the Lee-Carter Model with Maximum Overlap Discrete Wavelet Transform Filters in Forecasting Mortality Rates

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2295
Author(s):  
Nurul Aityqah Yaacob ◽  
Jamil J. Jaber ◽  
Dharini Pathmanathan ◽  
Sadam Alwadi ◽  
Ibrahim Mohamed
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Arima Model ◽  
Mortality Rates ◽  
Percentage Error ◽  
Mortality Data ◽  
Discrete Wavelet ◽  
Death Rates ◽  
Wavelet Filters ◽  
Carter Model

This study implements various, maximum overlap, discrete wavelet transform filters to model and forecast the time-dependent mortality index of the Lee-Carter model. The choice of appropriate wavelet filters is essential in effectively capturing the dynamics in a period. This cannot be accomplished by using the ARIMA model alone. In this paper, the ARIMA model is enhanced with the integration of various maximal overlap discrete wavelet transform filters such as the least asymmetric, best-localized, and Coiflet filters. These models are then applied to the mortality data of Australia, England, France, Japan, and USA. The accuracy of the projecting log of death rates of the MODWT-ARIMA model with the aforementioned wavelet filters are assessed using mean absolute error, mean absolute percentage error, and mean absolute scaled error. The MODWT-ARIMA (5,1,0) model with the BL14 filter gives the best fit to the log of death rates data for males, females, and total population, for all five countries studied. Implementing the MODWT leads towards improvement in the performance of the standard framework of the LC model in forecasting mortality rates.

scholarly journals Evaluation of the Kou-Modified Lee-Carter Model in Mortality Forecasting: Evidence from French Male Mortality Data

Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 123 ◽  
Author(s):  
Marie Angèle Cathleen Alijean ◽  
Jason Narsoo
Keyword(s):  
Mortality Data ◽  
Male Mortality ◽  
Forecasting Accuracy ◽  
Mortality Forecasting ◽  
Mortality Models ◽  
Double Exponential ◽  
Jump Diffusion Model ◽  
Mortality Forecasts ◽  
Death Data ◽  
Carter Model

Mortality forecasting has always been a target of study by academics and practitioners. Since the introduction and rising significance of securitization of risk in mortality and longevity, more in-depth studies regarding mortality have been carried out to enable the fair pricing of such derivatives. In this article, a comparative analysis is performed on the mortality forecasting accuracy of four mortality models. The methodology employs the Age-Period-Cohort model, the Cairns-Blake-Dowd model, the classical Lee-Carter model and the Kou-Modified Lee-Carter model. The Kou-Modified Lee-Carter model combines the classical Lee-Carter with the Double Exponential Jump Diffusion model. This paper is the first study to employ the Kou model to forecast French mortality data. The dataset comprises death data of French males from age 0 to age 90, available for the years 1900–2015. The paper differentiates between two periods: the 1900–1960 period where extreme mortality events occurred for French males and the 1961–2015 period where no significant jump is observed. The Kou-modified Lee-Carter model turns out to give the best mortality forecasts based on the RMSE, MAE, MPE and MAPE metrics for the period 1900–1960 during which the two World Wars occurred. This confirms that the consideration of jumps and leptokurtic features conveys important information for mortality forecasting.

scholarly journals Spatiotemporal Econometrics Models for Old Age Mortality in Europe

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1061
Author(s):  
Patricia Carracedo ◽  
Ana Debón
Keyword(s):  
Panel Data ◽  
Goodness Of Fit ◽  
Population Aging ◽  
European Population ◽  
Data Models ◽  
European Countries ◽  
Mortality Data ◽  
Panel Data Models ◽  
Estimation Of Parameters ◽  
Advantages And Disadvantages

In the past decade, panel data models using time-series observations of several geographical units have become popular due to the availability of software able to implement them. The aim of this study is an updated comparison of estimation techniques between the implementations of spatiotemporal panel data models across MATLAB and R softwares in order to fit real mortality data. The case study used concerns the male and female mortality of the aged population of European countries. Mortality is quantified with the Comparative Mortality Figure, which is the most suitable statistic for comparing mortality by sex over space when detailed specific mortality is available for each studied population. The spatial dependence between the 26 European countries and their neighbors during 1995–2012 was confirmed through the Global Moran Index and the spatiotemporal panel data models. For this reason, it can be said that mortality in European population aging not only depends on differences in the health systems, which are subject to national discretion but also on supra-national developments. Finally, we conclude that although both programs seem similar, there are some differences in the estimation of parameters and goodness of fit measures being more reliable MATLAB. These differences have been justified by detailing the advantages and disadvantages of using each of them.

scholarly journals Do Different Models Induce Changes in Mortality Indicators? That Is a Key Question for Extending the Lee-Carter Model

2021 ◽  
Vol 18 (4) ◽  
pp. 2204
Author(s):  
Ana Debón ◽  
Steven Haberman ◽  
Francisco Montes ◽  
Edoardo Otranto
Keyword(s):  
Historical Data ◽  
Mortality Rates ◽  
Parametric Model ◽  
Mortality Data ◽  
Block Bootstrap ◽  
Functional Anova ◽  
Model Block ◽  
The Usa ◽  
Data Constraints ◽  
Carter Model

The parametric model introduced by Lee and Carter in 1992 for modeling mortality rates in the USA was a seminal development in forecasting life expectancies and has been widely used since then. Different extensions of this model, using different hypotheses about the data, constraints on the parameters, and appropriate methods have led to improvements in the model’s fit to historical data and the model’s forecasting of the future. This paper’s main objective is to evaluate if differences between models are reflected in different mortality indicators’ forecasts. To this end, nine sets of indicator predictions were generated by crossing three models and three block-bootstrap samples with each of size fifty. Later the predicted mortality indicators were compared using functional ANOVA. Models and block bootstrap procedures are applied to Spanish mortality data. Results show model, block-bootstrap, and interaction effects for all mortality indicators. Although it was not our main objective, it is essential to point out that the sample effect should not be present since they must be realizations of the same population, and therefore the procedure should lead to samples that do not influence the results. Regarding significant model effect, it follows that, although the addition of terms improves the adjustment of probabilities and translates into an effect on mortality indicators, the model’s predictions must be checked in terms of their probabilities and the mortality indicators of interest.

scholarly journals MODELLING SOCIO-ECONOMIC DIFFERENCES IN MORTALITY USING A NEW AFFLUENCE INDEX

2019 ◽  
Vol 49 (03) ◽  
pp. 555-590 ◽  
Author(s):  
Andrew J.G. Cairns ◽  
Malene Kallestrup-Lamb ◽  
Carsten Rosenskjold ◽  
David Blake ◽  
Kevin Dowd
Keyword(s):  
Mortality Data ◽  
National Register ◽  
Death Rates ◽  
Modelling Framework ◽  
Projection Properties ◽  
Key Features ◽  
Using Data ◽  
Model Fits

AbstractWe introduce a new modelling framework to explain socio-economic differences in mortality in terms of an affluence index that combines information on individual wealth and income. The model is illustrated using data on older Danish males over the period 1985–2012 reported in the Statistics Denmark national register database. The model fits the historical mortality data well, captures their key features, generates smoothed death rates that allow us to work with a larger number of sub-groups than has previously been considered feasible, and has plausible projection properties.

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