fdm: Functional demographic model

Description

Fits a basis function model to demographic data. The function uses optimal orthonormal basis functions obtained from a principal components decomposition.

Usage

fdm(data, series = names(data$rate)[1], order = 6, ages = data$age, 
    max.age = 100, method = c("classical", "M", "rapca"), lambda = 3, 
    mean = TRUE, level = FALSE, transform = TRUE, ...)

Arguments

data

demogdata object. Output from read.demogdata.

series

name of series within data holding rates (1x1)

order

Number of basis functions to fit.

ages

Ages to include in fit.

max.age

Maximum age to fit.

method

Method to use for principal components decomposition. Possibilities are M, rapca and classical. See ftsm for details.

lambda

Tuning parameter for robustness when method="M".

mean

If TRUE, will estimate mean term in the model before computing basis terms. If FALSE, the mean term is assumed to be zero.

level

If TRUE, will include an additional (intercept) term that depends on the year but not on ages.

transform

If TRUE, the data are transformed with a Box-Cox transformation before the model is fitted.

...

Extra arguments passed to ftsm.

Value

Object of class fdm with the following components:
labelName of country
ageAges from data object.
yearYears from data object.
Matrix of demographic data as contained in data. It takes the name given by the series argument.
fittedMatrix of fitted values.
residualsResiduals (difference between observed and fitted).
basisMatrix of basis functions evaluated at each age level (one column for each basis function). The first column is the fitted mean.
coeffsMatrix of coefficients (one column for each coefficient series). The first column are all ones.
mean.seStandard errors for the estimated mean function.
varpropProportion of variation explained by each basis function.
weightsWeight associated with each time period.
vMeasure of variation for each time period.
typeData type (mortality, fertility, etc.)
yThe data stored as a functional time series object.

References

Hyndman, R.J., and Ullah, S. (2007) Robust forecasting of mortality and fertility rates: a functional data approach. Computational Statistics & Data Analysis, 51, 4942-4956. http://robjhyndman.com/papers/funcfor

Examples

Run this code

france.fit <- fdm(fr.mort)
summary(france.fit)
plot(france.fit)
plot(residuals(france.fit))