demofit (version 0.1.4)

ENI: Mortality ensemble interval

Description

Generates ensemble interval forecast of mortality rates.

Usage

ENI(..., width = 0.95, method = 1, wm, nsim = 10, seed = 123)

Value

An object of class ENI with associated S3 methods forecast and plot.

Arguments

...

fitted model objects returned by LCS(), RHS(), APCS(), CBDS(), CBDCS(), CBDQCS(), and / or STARS().

width

coverage probability of interval (default = 0.95).

method

if 1, simple averaging; if 2, weighted averaging; if 3, envelope; if 4, interior trimming (default = 1).

wm

vector of weights for LC, RH, APC, M5, M6, M7, and / or STAR models if method = 2 (default = equal weights).

nsim

number of simulations (default = 10).

seed

seed for random number generator (default = 123).

Details

Ensemble interval forecast is constructed by combining interval forecasts from individual stochastic mortality models using different methods including simple averaging, weighted averaging, envelope, and interior trimming. See LCS(), RHS(), APCS(), CBDS(), CBDCS(), CBDQCS(), and STARS() for more details of different stochastic mortality models.

References

Li, J., Wang, M., Liu, J., and Tickle, L. (2025). Ensemble interval forecasts of mortality. Scandinavian Actuarial Journal, 2025(6), 598-616.

Examples

x <- 60:69
a <- c(-4.8499,-4.7676,-4.6719,-4.5722,-4.4847,-4.3841,-4.2813,-4.1863,-4.0861,-3.9962)
b <- c(0.0801,0.0909,0.0948,0.0951,0.0965,0.1014,0.1042,0.1141,0.1110,0.1118)
k <- c(12.11,10.69,11.18,9.64,9.35,8.21,6.89,5.74,4.56,3.60,
3.27,2.04,1.11,-0.44,-1.05,-1.03,-1.84,-2.90,-4.03,-4.12,
-5.18,-5.64,-6.00,-6.51,-6.91,-6.90,-8.32,-8.53,-9.69,-9.31)
set.seed(123)
M <- exp(outer(k,b)+matrix(a,nrow=30,ncol=10,byrow=TRUE)+rnorm(300,0,0.035))
fit1 <- LCS(x=x,M=M,curve="makeham",h=30,jumpoff=2)
fit2 <- RHS(x=x,M=M,curve="makeham",h=30,jumpoff=2)
fit3 <- APCS(x=x,M=M,curve="makeham",h=30,jumpoff=2)
fit4 <- CBDS(x=x,M=M,curve="makeham",h=30,jumpoff=2)
fit <- ENI(fit1,fit2,fit3,fit4)
forecast::forecast(fit)
plot(fit)