CoDa_FPCA: Compositional data analytic approach and functional principal...

In ftsa: Functional Time Series Analysis

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)

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

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

Value

Out-of-sample forecast densities

Author(s)

Han Lin Shang

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

## Not run: 
CoDa_FPCA(data = DJI_return, normalization = "TRUE", band_choice = "DPI", 
	kernel = "epanechnikov", varprop = 0.9, fmethod = "ETS")

## End(Not run)

ftsa documentation built on May 29, 2024, 2:47 a.m.