demofit (version 0.1.4)

LCLS: Lee-Carter model for limited data

Description

Fits and forecasts mortality rates using Lee-Carter model with sparse data in irregular years.

Usage

LCLS(
  x,
  t,
  M,
  curve = c("gompertz", "makeham", "oppermann", "thiele", "wittsteinbumsted", "perks",
    "weibull", "vandermaen", "beard", "heligmanpollard", "rogersplanck", "siler",
    "martinelle", "thatcher", "gompertz2", "makeham2", "oppermann2", "thiele2",
    "wittsteinbumsted2", "perks2", "weibull2", "vandermaen2", "beard2",
    "heligmanpollard2", "rogersplanck2", "siler2", "martinelle2", "thatcher2"),
  h = 10,
  jumpoff = 1
)

Value

An object of class LCLS with associated S3 methods coef, forecast (which = 1 for smoothed (default); which = 2 for raw), plot, residuals, and simulate (nsim for setting number of simulations; seed for initialising random number generator).

Arguments

x

vector of ages.

t

vector of years.

M

matrix of mortality rates (rows as years and columns as ages).

curve

name of mortality curve for smoothing forecasted mortality rates (including gompertz, makeham, oppermann, thiele, wittsteinbumsted, perks, weibull, vandermaen, beard, heligmanpollard, rogersplanck, siler, martinelle, thatcher, gompertz2, makeham2, oppermann2, thiele2, wittsteinbumsted2, perks2, weibull2, vandermaen2, beard2, heligmanpollard2, rogersplanck2, siler2, martinelle2, thatcher2, where first 14 curves' parameters are unconstrained and last 14 curves' parameters are generally restricted to be positive).

h

forecast horizon (default = 10).

jumpoff

if 1, forecasts are based on estimated parameters only; if 2, forecasts are anchored to observed mortality rates in final year (default = 1).

Details

The Lee-Carter (LC) model is specified as

\(ln(m_{x,t}) = \alpha_x + \beta_x \kappa_t + \epsilon_{x,t}\).

The model is estimated by singular value decomposition and is forecasted by random walk with drift applied to \(\kappa_t\). Constraints include sum of \(\beta_x\) is one and sum of \(\kappa_t\) is zero. It can be applied to whole age range.

References

Li, N., Lee, R., and Tuljapurkar, S. (2004). Using the Lee-Carter method to forecast mortality for populations with limited data. International Statistical Review, 72(1), 19-36.

Examples

x <- 60:89
t <- c(1991,1996,2001,2006,2011:2020)
a <- c(-4.8499,-4.7676,-4.6719,-4.5722,-4.4847,-4.3841,-4.2813,-4.1863,-4.0861,-3.9962,
-3.8885,-3.7896,-3.6853,-3.5737,-3.4728,-3.3718,-3.2586,-3.1474,-3.0371,-2.9206,
-2.7998,-2.6845,-2.5653,-2.4581,-2.3367,-2.2159,-2.1017,-1.9941,-1.8821, -1.7697)
b <- c(0.0283,0.0321,0.0335,0.0336,0.0341,0.0358,0.0368,0.0403,0.0392,0.0395,
0.0396,0.0399,0.0397,0.0386,0.039,0.0375,0.0367,0.0368,0.035,0.0354,
0.0336,0.0323,0.0313,0.0295,0.0282,0.0265,0.024,0.0226,0.0219,0.0183)
k <- c(12.11,8.21,
3.27,-1.03,
-5.18,-5.64,-6,-6.51,-6.91,-6.9,-8.32,-8.53,-9.69,-9.31)
set.seed(123)
M <- exp(outer(k,b)+matrix(a,nrow=14,ncol=30,byrow=TRUE)+rnorm(420,0,0.035))
fit <- LCLS(x=x,t=t,M=M,curve="makeham",h=30,jumpoff=2)
coef(fit)
forecast::forecast(fit)
plot(fit)
residuals(fit)