ABSTRACT
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.
Subject(s)
Life Expectancy , Models, Statistical , Forecasting , Mortality , ProbabilityABSTRACT
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.
ABSTRACT
The paper reviews the Lee-Carter modelling framework, illustrated with an application, and then extends the framework through the development of a wider class of generalised, parametric, non-linear models. The choice of error distribution is also generalised. These extensions permit the modelling and extrapolation of age-specific cohort effects as well as the more familiar age-specific period effects: the age-period-cohort version of the model is discussed with a worked example. The paper also provides a comparative study of simulation strategies for assessing risk in mortality rate predictions and the associated forecast estimates of life expectancy and annuity values in both period and cohort perspectives.
