A multivariate time series approach to projected life tables

Lazăr, Dan Tudor; Denuit, Michel

doi:10.1002/asmb.781

Cited by 35 publications

(33 citation statements)

References 31 publications

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“…It is notable that the random walk model with drift provides satisfactory results in many cases (Tuljapurkar, Li, and Boe 2000;Lee and Miller 2001;Lazar and Denuit 2009). From this forecast of the principal component scores, the forecast age-specific log mortality rates are obtained using the estimated age effects a x and b x in (1).…”

Section: Lee-carter (Lc) Methodsmentioning

confidence: 99%

Point and interval forecasts of mortality rates and life expectancy: A comparison of ten principal component methods

Shang

Booth

Hyndman

2011

DemRes

102

111

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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 HyndmanUllah method provides the most accurate point forecasts of mortality rates and the LeeMiller 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 LeeMiller 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. IntroductionIn recent years, the rapid ageing of the population has been a growing concern for governments and societies. In many developed countries, the concerns are concentrated on the sustainability of pensions and health and aged care systems, especially given increased longevity. This has resulted in a surge of interest among government policy makers and planners in accurately modeling and forecasting age-specific mortality rates. Any improvements in the forecast accuracy of mortality rates would be beneficial for policy decisions regarding the allocation of current and future resources. In particular, future mortality rates are of great interest to the insurance and pension industries. Several authors have proposed new approaches for forecasting mortality rates and life expectancy using statistical modeling (see Booth 2006; Booth and Tickle 2008, for reviews). Of these, a significant milestone in demographic forecasting was the work of Lee and Carter (1992). They used a principal component method to extract a single timevarying index of the level of mortality rates, from which the forecasts are obtained using a random walk with drift. Since then, this method has been widely used for forecasting mortality rates in various countries, including Australia The strengths of the Lee-Carter (LC) method are its simplicity and robustness in situations where age-specific log mortality rates have linear trends . A weakness of the LC method is that it attempts to capture the patterns of mortality rates using only one principal component and its scores. To address this, Hyndman and Ullah (2007) propose a model that utilizes second and higher order principal components to capture additional dimensions of change in mortality rates. Although other methods have been developed (e.g., Renshaw and Haberman 2003a,b,c;Currie, Durban, and Eilers 2004;Bongaarts 2005;Girosi and King 2008;Renshaw and Haberman 2006;Haberman and Renshaw 2008;Ediev 2008), the LC method is often considered as the benchmark method. For example, the LC method is compared with other approach...

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Section: Lee-carter (Lc) Methodsmentioning

confidence: 99%

Point and interval forecasts of mortality rates and life expectancy: A comparison of ten principal component methods

Shang

Booth

Hyndman

2011

DemRes

102

111

View full text Add to dashboard Cite

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“…All these indicators can be projected using the projections of q xt , obtained from an adequate methodology, in our study the Lee-Carter model (Lee and 3 Carter, 1992;Brouhns et al, 2002;Debón et al, 2008b). We used the simple Lee-Carter model as, while the other versions improved the adjustment, the goodness of fit had little influence on the mortality indicators (Lazar et al, 2009;Debón et al, 2010) and this paper is focused on the evolution of these indicators. The errors associated with these estimations can be calculated by means of a bootstrap methodology (Renshaw and Haberman, 2007) and a confidence interval can be provided.…”

Section: Introductionmentioning

confidence: 99%

Temporal Evolution of Mortality Indicators

Debón

Martínez-Ruiz

Montes

2012

North American Actuarial Journal

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In Spain, as in other developed countries, there have been significant changes in mortality patterns during the 20th and 21st centuries. One reflection of these changes is life expectancy, which has improved in this period, though the robustness of this indicator prevents these changes from being of the same order as those for the probability of death, q xt . If, moreover, we bear in mind that life expectancy offers no information as to whether this improvement is the same for different age groups, it is important and necessary to turn to other mortality indicators whose past and future evolution in Spain we are going to study.These indicators are applied to Spanish mortality data for the period 1981-2008, for the age range 0 to 99. To study its future evolution, the mortality ratios have to be projected using an adequate methodology, namely the Lee-Carter model (Lee and Carter, 1992;Brouhns et al., 2002;Debón et al., 2008b). With the aim of incorporating the uncertainty measures suggested by Pedroza (2006) into predictions, confidence intervals are obtained for these predictions. These intervals can be calculated using the methodology which Lee and Carter apply in their original article for expected lifetime confidence intervals, but they only take into account the error in the prediction of the mortality index k t obtained from the ARIMA model adjusted to its temporal series, excluding other sources of error such as that introduced by estimations of the other parameters in the model. That is why bootstrap procedures are preferred, as used in Koissi et al. (2006), permitting the combination of all sources of uncertainty.

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“…, T share a common random walk trend as in the Lee-Carter forecast, while the individual series from the different samples deviate from that common trend in a stationary fashion. Such an approach was suggested by Renshaw and Haberman in a discussion paper from 2003 and followed up by Lazar and Denuit (2009). Since the scale and level of the series κ i,t for t = 1, .…”

Section: Multi-sample Problemmentioning

confidence: 99%