leecarter.estimate {MortCast}

Lee-Carter Estimation

Description

Estimate Lee-Carter parameters (Lee and Carter 1992).

Usage

leecarter.estimate(
  mx,
  ax.index = NULL,
  ax.smooth = FALSE,
  ax.smooth.df = NULL,
  bx.postprocess = TRUE,
  nx = 5
)

Arguments

mx

A matrix of age-specific mortality rates where rows correspond to age groups and columns correspond to time periods. Rownames define the starting ages of the age groups.

ax.index

A vector of column indices of mx to be used to estimate the a_x parameter. By default all time periods are used.

ax.smooth

Logical allowing to smooth the a_x over ages.

ax.smooth.df

Degree of freedom for smoothing if ax.smooth is TRUE. Default is half the length of a_x.

bx.postprocess

Logical determining if numerical anomalies in b_x should be dealt with.

nx

Size of age groups. By default ages are determined by rownames of mx. This argument is only used if mx has no rownames. If nx is 5, the age groups are interpreted as 0, 1, 5, 10, .... For nx equals 1, the age groups are interpreted as 0, 1, 2, 3, ....

Details

The function estimates parameters of \log(m_x(t)) = a_x + b_x k(t) + \epsilon_x(t) (Lee and Carter 1992). The argument ax.index determines which time periods to use to estimate the a_x parameter, while ax.smooth controls if the resulting a_x should be smoothened over ages (see Sevcikova et al. 2016 for details).

Value

List with elements ax, bx and kt corresponding to the estimated parameters.

References

Lee, R. D. and Carter, L. (1992). Modeling and forecasting the time series of US mortality. Journal of the American Statistical Association, 87, 659-671.

Sevcikova H., Li N., Kantorova V., Gerland P., Raftery A.E. (2016). Age-Specific Mortality and Fertility Rates for Probabilistic Population Projections. In: Schoen R. (eds) Dynamic Demographic Analysis. The Springer Series on Demographic Methods and Population Analysis, vol 39. Springer, Cham

See Also

mortcast, lileecarter.estimate

Examples

data(mxM, package = "wpp2017")
mx <- subset(mxM, name == "Netherlands")[,4:16]
rownames(mx) <- c(0,1, seq(5, 100, by=5))
lc.ax.avg <- leecarter.estimate(mx)
lc.ax.last <- leecarter.estimate(mx, ax.index=ncol(mx))
plot(lc.ax.avg$ax, type="l")
lines(lc.ax.last$ax, col="blue")