FORECASTING MORTALITY: SOME RECENT DEVELOPMENTS

Modeling and forecasting human mortality are significant research topics in several disciplines because mortality rates are fundamental in planning and policy decisions. Among various techniques, Lee Carter (LC) model is one of the most popular stochastic method in human mortality modeling. The original LC model was fuzzified to eliminate the assumptions related with homoscedasticity. The existing fuzzy model makes use of ordinary least squares (OLS) technique, which prevents the model to capture the existing fluctuations in data. In this study, a revised version of fuzzy LC model utilizing singular value decomposition (SVD) technique is proposed to overcome this issue. After modeling the mortality rates, their future values are forecasted by a modified first order fuzzy time series technique. For illustration purposes, proposed method is applied to mortality data of Finland. Numerical outputs show that proposed method is statistically better in modeling mortality compared to the existing fuzzy method. In addition, the modified fuzzy time series technique generates better forecasts than the original version.

Motivated by a recent discovery that the two-step inference for the Lee–Carter mortality model may be inconsistent when the mortality index does not follow from a nearly integrated AR(1) process, we propose a test for a unit root in a Lee–Carter model with an AR(p) process for the mortality index. Although testing for a unit root has been studied extensively in econometrics, the method and asymptotic results developed in this paper are unconventional. Unlike a blind application of existing R packages for implementing the two-step inference procedure in Lee and Carter (1992) to the U.S. mortality rate data, the proposed test rejects the null hypothesis that the mortality index follows from a unit root AR(1) process, which calls for serious attention on using the future mortality projections based on the Lee–Carter model in policy making, pricing annuities and hedging longevity risk. A simulation study is conducted to examine the finite sample behavior of the proposed test too.

Age coherence describes the property that forecast mortality rates across ages will not diverge in the long run. Although intuitively and biologically reasonable, this property is lost when the seminal Lee–Carter (LC) model and almost all its existing extensions are employed. In this paper, we propose two effective extensions of the LC model, allowing for the geometric (LC-G) and hyperbolic (LC-H) decayed relative speed of mortality decline at each age, over the out-of-sample forecasting steps. Those approaches are based on the original in-sample estimates of LC, which are easy to obtain. An inversed Epanechnikov kernel is employed to model the geometric and hyperbolic parameters across ages, and unknown parameters are selected via a data-driven method. With little added computational cost to LC, our approaches incorporate the dynamic and rotating relative speeds of mortality decline over ages, recognize the growing difficulty of such declines at older ages, provide age-coherent forecasts of mortality rates in the long run, and is easily extensible to multi-population cases. Using a large sample of 15 countries, we demonstrate that LC-G and LC-H, as well as their multi-population counterparties, consistently improve the forecasting accuracy of the competing LC model and its single- and multi-population extensions.Feng, L., Shi, Y., & Chang, L. (2021). Forecasting mortality with a hyperbolic spatial temporal VAR model. International Journal of Forecasting, 37(1), 255–273.

This study investigated the performance of the Lee-Carter (LC) method and it variants in modeling and forecasting Malaysia mortality. These include the original LC, the Lee-Miller (LM) variant and the Booth-Maindonald-Smith (BMS) variant. These methods were evaluated using Malaysia’s mortality data which was measured based on age specific death rates (ASDR) for 1971 to 2009 for overall population while those for 1980–2009 were used in separate models for male and female population. The performance of the variants has been examined in term of the goodness of fit of the models and forecasting accuracy. Comparison was made based on several criteria namely, mean square error (MSE), root mean square error (RMSE), mean absolute deviation (MAD) and mean absolute percentage error (MAPE). The results indicate that BMS method was outperformed in in-sample fitting for overall population and when the models were fitted separately for male and female population. However, in the case of out-sample forecast accuracy, BMS method only best when the data were fitted to overall population. When the data were fitted separately for male and female, LCnone performed better for male population and LM method is good for female population.

Multivariate Long Memory Cohort Mortality Models

The Lee–Carter model could be considered as one of the most important mortality prediction models among stochastic models in the field of mortality. With the recent developments of machine learning and deep learning, many studies have applied deep learning approaches to time series mortality rate predictions, but most of them only focus on a comparison between the Long Short-Term Memory and the traditional models. In this study, three different recurrent neural networks, Long Short-Term Memory, Bidirectional Long Short-Term Memory, and Gated Recurrent Unit, are proposed for the task of mortality rate prediction. Different from the standard country level mortality rate comparison, this study compares the three deep learning models and the classic Lee–Carter model on nine divisions’ yearly mortality data by gender from 1966 to 2015 in the United States. With the out-of-sample testing, we found that the Gated Recurrent Unit model showed better average MAE and RMSE values than the Lee–Carter model on 72.2% (13/18) and 67.7% (12/18) of the database, respectively, while the same measure for the Long Short-Term Memory model and Bidirectional Long Short-Term Memory model are 50%/38.9% (MAE/RMSE) and 61.1%/61.1% (MAE/RMSE), respectively. If we consider forecasting accuracy, computing expense, and interpretability, the Lee–Carter model with ARIMA exhibits the best overall performance, but the recurrent neural networks could also be good candidates for mortality forecasting for divisions in the United States.

The paper presents the results of study about the influence of the initial weights choice on the long-term forecast accuracy in the problem of multi-step forecast with a neural network based on long short-term memory (LSTM-net) for time series, composed of time-ordered samples of a harmonic, an amplitude-modulated signal and a frequency-modulated signal. The recursive forecast has been estimated on model time series data providing the means to measure the actual accuracy of the forecast while controlling influence of different characteristics. The analysis of the results show that a necessary condition for obtaining a high-quality long-term forecast is the correct choice of the LSTM-net parameters, especially the initialization of weights for neural network layers. At the same time the use of LSTM-net parameters, which provide high accuracy of short-term forecast, does not guarantee the accuracy of the long-term forecast, and vice-versa. In this regard it is concluded that the usage of other forecast methods and /or algorithms for correcting predicted values for mentioned types of time series is preferable.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation W. H. Wan Zakiyatussariroh, Z. Mohammad Said, M. R. Norazan; Lee-Carter state space modeling: Application to the Malaysia mortality data. AIP Conference Proceedings 19 June 2014; 1602 (1): 1002–1008. https://doi.org/10.1063/1.4882606 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

A person's life expectancy is one of the statistical measures used to determine how long they will live. However, in Sri Lanka, there is a lack of long-term, data-driven mortality forecasting, which limits the ability to make informed decisions in public health, insurance, and policy planning. This study addresses this gap by applying the Lee-Carter (LC) mortality estimation method to improve life expectancy analysis and mortality forecasting. In general, a life table that details the effects of mortality is used to calculate life expectancy. As a result, mortality predictions and life table analysis are important in the insurance, actuarial science, government, and pension planning sectors. The Registrar General's Office and the Department of Census and Statistics in Sri Lanka provided the mid-year population data and deaths as historical data for this study from 1992 to 2014. The Lee-Carter (LC) mortality estimation method is used to forecast mortality using actual death rates and mid-year populations from 1992 to 2014. ax (the average age-specific log mortality rate over time), bx (the sensitivity of mortality at each age to changes in the mortality index), and kt (the overall mortality index over time) parameters are estimated using the Singular Value Decomposition (SVD) method in the Lee-Carter methodology between 1992 and 2014. kt is forecasted for the years 2015–2035 using the traditional time series approach, and no specific time series model such as ARIMA or Exponential Smoothing was used. In 2035, the probability of dying as a 55-year-old woman and man are 0.023 and 0.051, respectively, according to the research. The following is a statement of the study's results: South Asia's average life expectancy is 69.41 years, while Sri Lanka's is 74.5 years. A country's future can be improved by thoroughly investigating demographics and life expectancy, as these factors directly affect financial stability.

BackgroundPrecise predictions of incidence and mortality rates due to breast cancer (BC) are required for planning of public health programs as well as for clinical services. A number of approaches has been established for prediction of mortality using stochastic models. The performance of these models intensely depends on different patterns shown by mortality data in different countries.MethodsThe BC mortality data is retrieved from the Global burden of disease (GBD) study 2017 database. This study include BC mortality rates from 1990 to 2017, with ages 20 to 80+ years old women, for different Asian countries. Our study extend the current literature on Asian BC mortality data, on both the number of considered stochastic mortality models and their rigorous evaluation using multivariate Diebold-Marino test and by range of graphical analysis for multiple countries.ResultsStudy findings reveal that stochastic smoothed mortality models based on functional data analysis generally outperform on quadratic structure of BC mortality rates than the other lee-carter models, both in term of goodness of fit and on forecast accuracy. Besides, smoothed lee carter (SLC) model outperform the functional demographic model (FDM) in case of symmetric structure of BC mortality rates, and provides almost comparable results to FDM in within and outside data forecast accuracy for heterogeneous set of BC mortality rates.ConclusionConsidering the SLC model in comparison to the other can be obliging to forecast BC mortality and life expectancy at birth, since it provides even better results in some cases. In the current situation, we can assume that there is no single model, which can truly outperform all the others on every population. Therefore, we also suggest generating BC mortality forecasts using multiple models rather than relying upon any single model.

A multi-granularity hierarchical network for long- and short-term forecasting on multivariate time series data

We derive internal consistency restrictions on short-, medium- and long-term oil price forecasts. We then analyse whether oil price forecasts extracted from the Survey of Professional Forecasters (SPF) conducted by the European Central Bank (ECB) satisfy these internal consistency restrictions. We find that neither short-term forecasts are consistent with medium-term forecasts nor that medium-term forecasts are consistent with long-term forecasts. Using a more complex expectation formation structure featuring a distributed lag structure, however, we find stronger evidence of internal consistency of medium-term forecasts with long-term forecasts.

Mortality forecasting plays a central role in both demographic and actuarial studies. Classical approaches, such as the Lee-Carter (LC) model, typically rely on mortality rates as the primary measure. In recent years, compositional data analysis (CoDA), which respects summability and non-negativity constraints, has gained increasing attention for mortality forecasting. While the centred log-ratio (CLR) transformation is commonly used to map compositional data to real space, the α-transformation, a generalisation of log-ratio transformations, offers greater flexibility and adaptability. This study introduces the α-transformation as an alternative to the CLR transformation within a CoDA framework under a discrete-age setting for all-cause mortality forecasting, which has not been previously investigated. To enable a fair comparison of transformation choices, zero values in the data are imputed, although the α-transformation can inherently accommodate them. Using age-specific life table death counts for males and females in 31 selected European countries/regions from 1983 to 2018, the proposed method demonstrates comparable performance to the CLR transformation in most cases, with improved forecast accuracy in some instances. These findings highlight the potential of the α-transformation to enhance mortality forecasting within the CoDA framework.

There has been a significant increase in the life expectancies of the Taiwanese population after the end of Second World War. Like in many developed countries, due to the prolonging life expectancy and lower fertility rates, the aging population has now become a major policy concern in Taiwan. The search for feasible methods for modeling the future mortality changes has become a popular issue in Taiwan. The Lee-Carter (LC) model, the reduction factor (RF) model and the age-period-cohort (APC) model are three frequently used methods for modeling future mortality dynamics. In this paper, we introduce these three models and discuss their respective pros and cons. We carry out an empirical study using these models based on Taiwan mortality experience. In addition, we make a comparison analysis of different models with different mortality experience in Japan, England and Wales, and the US.

Improving Longevity and Mortality Risk Models with Common Stochastic Long-Run Trends