ftsa (version 6.4)

CoDa_FPCA: Compositional data analytic approach and functional principal component analysis for forecasting density

Description

Log-ratio transformation from constrained space to unconstrained space, where a standard functional principal component analysis can be applied.

Usage

CoDa_FPCA(data, normalization, h_scale = 1, m = 5001, 
	band_choice = c("Silverman", "DPI"), 
	kernel = c("gaussian", "epanechnikov"), 
	varprop = 0.99, fmethod)

Value

Out-of-sample forecast densities

Arguments

data

Densities or raw data matrix of dimension n by p, where n denotes sample size and p denotes dimensionality

normalization

If a standardization should be performed?

h_scale

Scaling parameter in the kernel density estimator

m

Grid point within the data range

band_choice

Selection of optimal bandwidth

kernel

Type of kernel functions

varprop

Proportion of variance explained

fmethod

Univariate time series forecasting method

Author

Han Lin Shang

Details

1) Compute the geometric mean function 2) Apply the centered log-ratio transformation 3) Apply FPCA to the transformed data 4) Forecast principal component scores 5) Transform forecasts back to the compositional data 6) Add back the geometric means, to obtain the forecasts of the density function

References

Boucher, M.-P. B., Canudas-Romo, V., Oeppen, J. and Vaupel, J. W. (2017) `Coherent forecasts of mortality with compositional data analysis', Demographic Research, 37, 527-566.

Egozcue, J. J., Diaz-Barrero, J. L. and Pawlowsky-Glahn, V. (2006) `Hilbert space of probability density functions based on Aitchison geometry', Acta Mathematica Sinica, 22, 1175-1182.

See Also

Horta_Ziegelmann_FPCA, LQDT_FPCA, skew_t_fun

Examples

if (FALSE) {
CoDa_FPCA(data = DJI_return, normalization = "TRUE", band_choice = "DPI", 
	kernel = "epanechnikov", varprop = 0.9, fmethod = "ETS")
}