A General Procedure for Constructing Mortality Models

Backtesting stochastic mortality models by prediction interval-based metrics

Human lifespan increments represent one of the main current risks for governments and pension and health benefits providers. Longevity societies imply financial sustainability challenges to guarantee adequate socioeconomic conditions for all individuals for a longer period. Consequently, modelling population dynamics and projecting future longevity scenarios are vital tasks for policymakers. As an answer, the demographic and the actuarial literature have been introduced and compared to several stochastic mortality models, although few studies have thoroughly tested the uncertainty concerning mortality projections. Forecasting mortality uncertainty levels have a central role since they reveal the potential, unexpected longevity rise and the related economic impact. Therefore, the present study poses a methodological framework to backtest uncertainty in mortality projections by exploiting uncertainty metrics not yet adopted in mortality literature. Using the data from the Human Mortality Database of the male and female populations of five countries, we present some numerical applications to illustrate how the proposed criterion works. The results show that there is no mortality model overperforming the others in all cases, and the best model choice depends on the data considered.

Machine-Learning-Based Functional Time Series Forecasting: Application to Age-Specific Mortality Rates

We propose a functional time series method to obtain accurate multi-step-ahead forecasts for age-specific mortality rates. The dynamic functional principal component analysis method is used to decompose the mortality curves into dynamic functional principal components and their associated principal component scores. Machine-learning-based multi-step-ahead forecasting strategies, which automatically learn the underlying structure of the data, are used to obtain the future realization of the principal component scores. The forecasted mortality curves are obtained by combining the dynamic functional principal components and forecasted principal component scores. The point and interval forecast accuracy of the proposed method is evaluated using six age-specific mortality datasets and compared favorably with four existing functional time series methods.

Projecting Mortality Rates to Extreme Old Age with the CBDX Model

We introduce a simple extension to the CBDX model to project cohort mortality rates to extreme old age. The proposed approach fits a polynomial to a sample of age effects, uses the fitted polynomial to project the age effects to ages beyond the sample age range, then splices the sample and projected age effects, and uses the spliced age effects to obtain mortality rates for the higher ages. The proposed approach can be used to value financial instruments such as life annuities that depend on projections of extreme old age mortality rates.

Robust Non-Parametric Mortality and Fertility Modelling and Forecasting: Gaussian Process Regression Approaches

A rapid decline in mortality and fertility has become major issues in many developed countries over the past few decades. An accurate model for forecasting demographic movements is important for decision making in social welfare policies and resource budgeting among the government and many industry sectors. This article introduces a novel non-parametric approach using Gaussian process regression with a natural cubic spline mean function and a spectral mixture covariance function for mortality and fertility modelling and forecasting. Unlike most of the existing approaches in demographic modelling literature, which rely on time parameters to determine the movements of the whole mortality or fertility curve shifting from one year to another over time, we consider the mortality and fertility curves from their components of all age-specific mortality and fertility rates and assume each of them following a Gaussian process over time to fit the whole curves in a discrete but intensive style. The proposed Gaussian process regression approach shows significant improvements in terms of forecast accuracy and robustness compared to other mainstream demographic modelling approaches in the short-, mid- and long-term forecasting using the mortality and fertility data of several developed countries in the numerical examples.

A Comparison of Forecasting Mortality Models Using Resampling Methods

The accuracy of the predictions of age-specific probabilities of death is an essential objective for the insurance industry since it dramatically affects the proper valuation of their products. Currently, it is crucial to be able to accurately calculate the age-specific probabilities of death over time since insurance companies’ profits and the social security of citizens depend on human survival; therefore, forecasting dynamic life tables could have significant economic and social implications. Quantitative tools such as resampling methods are required to assess the current and future states of mortality behavior. The insurance companies that manage these life tables are attempting to establish models for evaluating the risk of insurance products to develop a proactive approach instead of using traditional reactive schemes. The main objective of this paper is to compare three mortality models to predict dynamic life tables. By using the real data of European countries from the Human Mortality Database, this study has identified the best model in terms of the prediction ability for each sex and each European country. A comparison that uses cobweb graphs leads us to the conclusion that the best model is, in general, the Lee–Carter model. Additionally, we propose a procedure that can be applied to a life table database that allows us to choose the most appropriate model for any geographical area.

Model confidence sets and forecast combination: an application to age-specific mortality

Background

Model averaging combines forecasts obtained from a range of models, and it often produces more accurate forecasts than a forecast from a single model.

Objective

The crucial part of forecast accuracy improvement in using the model averaging lies in the determination of optimal weights from a finite sample. If the weights are selected sub-optimally, this can affect the accuracy of the model-averaged forecasts. Instead of choosing the optimal weights, we consider trimming a set of models before equally averaging forecasts from the selected superior models. Motivated by Hansen et al. (Econometrica 79(2):453–497, 2011), we apply and evaluate the model confidence set procedure when combining mortality forecasts.

Data and methods

The proposed model averaging procedure is motivated by Samuels and Sekkel (International Journal of Forecasting 33(1):48–60, 2017) based on the concept of model confidence sets as proposed by Hansen et al. (Econometrica 79(2):453–497, 2011) that incorporates the statistical significance of the forecasting performance. As the model confidence level increases, the set of superior models generally decreases. The proposed model averaging procedure is demonstrated via national and sub-national Japanese mortality for retirement ages between 60 and 100+.

Results

Illustrated by national and sub-national Japanese mortality for ages between 60 and 100+, the proposed model-averaged procedure gives the smallest interval forecast errors, especially for males.

Conclusion

We find that robust out-of-sample point and interval forecasts may be obtained from the trimming method. By robust, we mean robustness against model misspecification.

Electronic supplementary material

The online version of this article (10.1186/s41118-018-0043-9) contains supplementary material, which is available to authorized users.

Leprosy in a Lombard-Avar cemetery in central Italy (Campochiaro, Molise, 6th-8th century AD): ancient DNA evidence and demography

BACKGROUND

The study of past infectious diseases increases knowledge of the presence, impact and spread of pathogens within ancient populations.

AIM

Polymerase chain reaction (PCR) was used to examine bones for the presence of Mycobacterium leprae ancient DNA (aDNA) as, even when leprosy is present, bony changes are not always pathognomonic of the disease. This study also examined the demographic profile of this population and compared it with two other populations to investigate any changes in mortality trends between different infectious diseases and between the pre-antibiotic and antibiotic eras.

SUBJECTS AND METHODS

The individuals were from a site in Central Italy (6th-8th CE) and were examined for the presence of Mycobacterium leprae aDNA. In addition, an abridged life mortality table was constructed.

RESULTS

Two individuals had typical leprosy palaeopathology, and one was positive for Mycobacterium leprae aDNA. However, the demographic profile shows a mortality curve similar to that of the standard, in contrast to a population that had been subjected to bubonic plague.

CONCLUSIONS

This study shows that, in the historical population with leprosy, the risk factors for health seem to be constant and distributed across all age classes, similar to what is found today in the antibiotic era. There were no peaks of mortality equivalent to those found in fatal diseases such as the plague, probably due to the long clinical course of leprosy.